Themordynamics Cengel & Boles 5th edition - Chapter 12 - Solutions

Get 12.0 exercise solution

12–1C Consider the function z(x, y). Plot a differential surface on x-y-z coordinates and indicate dx, dx, dy, dy,( dz)x, (dz)y, and dz. Get 12.1 exercise solution

12–2C What is the difference between partial differentials and ordinary differentials? Get 12.2 exercise solution

12–3C Consider the function z(x, y), its partial derivatives (dz/dx)y and (dz/dy)x, and the total derivative dz/dx. (a) How do the magnitudes (dx)y and dx compare? (b) How do the magnitudes (dz)y and dz compare? (c) Is there any relation among dz,( dz)x, and (dz)y? Get 12.3 exercise solution

12–4C Consider a function z(x, y) and its partial derivative (dz/dy)x. Under what conditions is this partial derivative equal to the total derivative dz/dy? Get 12.4 exercise solution

12–5C Consider a function z(x, y) and its partial derivative (dz/dy)x. If this partial derivative is equal to zero for all values of x, what does it indicate? Get 12.5 exercise solution

12–6C Consider a function z(x, y) and its partial derivative (dz/dy)x. Can this partial derivative still be a function of x? Get 12.6 exercise solution

12–7C Consider a function f(x) and its derivative df/dx. Can this derivative be determined by evaluating dx/df and taking its inverse? Get 12.7 exercise solution

12–8 Consider air at 400 K and 0.90 m3/kg. Using Eq. 12–3, determine the change in pressure corresponding to an increase of (a) 1 percent in temperature at constant specific volume, (b) 1 percent in specific volume at constant temperature, and (c) 1 percent in both the temperature and specific volume. Get 12.8 exercise solution

12–9 Repeat Problem 12–8 for helium. Get 12.9 exercise solution

12–10 Prove for an ideal gas that (a) the P = constant lines on a T-v diagram are straight lines and (b) the high-pressure lines are steeper than the low-pressure lines. Get 12.10 exercise solution

12–11 Derive a relation for the slope of the v = constant lines on a T-P diagram for a gas that obeys the van der Waals equation of state. Get 12.11 exercise solution

12–12 Nitrogen gas at 400 K and 300 kPa behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A–18, and compare them to the values listed in Table A–2b. Get 12.12 exercise solution

12–13E Nitrogen gas at 600 R and 30 psia behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A–18E, and compare them to the values listed in Table A–2Eb. Get 12.13 exercise solution

12–14 Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and 96 kPa. Estimate the change in the specific volume of the gas using (a) Eq. 12–3 and (b) the ideal-gas relation at each state. Get 12.14 exercise solution

12–15 Using the equation of state P(v - a) = RT, verify (a) the cyclic relation and (b) the reciprocity relation at constant v. Get 12.15 exercise solution

12–16 Verify the validity of the last Maxwell relation (Eq. 12–19) for refrigerant-134a at 80°C and 1.2 MPa. Get 12.16 exercise solution

12–17 Reconsider Prob. 12–16. Using EES (or other) software, verify the validity of the last Maxwell relation for refrigerant-134a at the specified state. Get 12.17 exercise solution

12–18E Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at 800°F and 400 psia. Get 12.18 exercise solution

12–19 Using the Maxwell relations, determine a relation for (ds/dP)T for a gas whose equation of state is P(v - b) = RT. Get 12.19 exercise solution

12–20 Using the Maxwell relations, determine a relation for (ds/dv)T for a gas whose equation of state is (P - a/v2) (v - b) = RT. Get 12.20 exercise solution

12–21 Using the Maxwell relations and the ideal-gas equation of state, determine a relation for (ds/dv)T for an ideal gas. Get 12.21 exercise solution

12–22C What is the value of the Clapeyron equation in thermodynamics? Get 12.22 exercise solution

12–23C Does the Clapeyron equation involve any approximations, or is it exact? Get 12.23 exercise solution

12–24C What approximations are involved in the ClapeyronClausius equation? Get 12.24 exercise solution

12–25 Using the Clapeyron equation, estimate the enthalpy of vaporization of refrigerant-134a at 40°C, and compare it to the tabulated value. Get 12.25 exercise solution

12–26 Reconsider Prob. 12–25. Using EES (or other) software, plot the enthalpy of vaporization of refrigerant-134a as a function of temperature over the temperature range -20 to 80°C by using the Clapeyron equation and the refrigerant-134a data in EES. Discuss your results. Get 12.26 exercise solution

12–27 Using the Clapeyron equation, estimate the enthalpy of vaporization of steam at 300 kPa, and compare it to the tabulated value. Get 12.27 exercise solution

12–28 Calculate the hfg and sfg of steam at 120°C from the Clapeyron equation, and compare them to the tabulated values. Get 12.28 exercise solution

12–29E Determine the hfg of refrigerant-134a at 50°F on the basis of (a) the Clapeyron equation and (b) the Clapeyron-Clausius equation. Compare your results to the tabulated hfg value. Get 12.29 exercise solution

12–30 Plot the enthalpy of vaporization of steam as a function of temperature over the temperature range 10 to 200°C by using the Clapeyron equation and steam data in EES. Get 12.30 exercise solution

12–31 Using the Clapeyron-Clausius equation and the triplepoint data of water, estimate the sublimation pressure of water at -30°C and compare to the value in Table A–8. Get 12.31 exercise solution

12–32C Can the variation of specific heat cp with pressure at a given temperature be determined from a knowledge of Pv-T data alone? Get 12.32 exercise solution

12–33 Show that the enthalpy of an ideal gas is a function of temperature only and that for an incompressible substance it also depends on pressure. Get 12.33 exercise solution

12–34 Derive expressions for (a) du,( b) dh, and (c) ds for a gas that obeys the van der Waals equation of state for an isothermal process. Get 12.34 exercise solution

12–35 Derive expressions for (a) du,( b) dh, and (c) ds for a gas whose equation of state is P(v - a) = RT for an isothermal process. Get 12.35 exercise solution

12–36 Derive expressions for (du/dP)T and (dh/dv)T in terms of P, v, and T only. Get 12.36 exercise solution

12–37 Derive an expression for the specific-heat difference cp = cv for (a) an ideal gas, (b) a van der Waals gas, and (c) an incompressible substance. Get 12.37 exercise solution

12–38 Estimate the specific-heat difference cp = cv for liquid water at 15 MPa and 80°C. Get 12.38 exercise solution

12–39E Estimate the specific-heat difference cp = cv for liquid water at 1000 psia and 150°F. Get 12.39 exercise solution

12–40 Derive a relation for the volume expansivity b and the isothermal compressibility a (a) for an ideal gas and (b) for a gas whose equation of state is P(v - a) = RT. Get 12.40 exercise solution

12–41 Estimate the volume expansivity b and the isothermal compressibility a of refrigerant-134a at 200 kPa and 30°C. Get 12.41 exercise solution

12–42C What does the Joule-Thomson coefficient represent? Get 12.42 exercise solution

12–43C Describe the inversion line and the maximum inversion temperature. Get 12.43 exercise solution

12–44C The pressure of a fluid always decreases during an adiabatic throttling process. Is this also the case for the temperature? Get 12.44 exercise solution

12–45C Does the Joule-Thomson coefficient of a substance change with temperature at a fixed pressure? Get 12.45 exercise solution

12–46C Will the temperature of helium change if it is throttled adiabatically from 300 K and 600 kPa to 150 kPa? Get 12.46 exercise solution

12–47 Consider a gas whose equation of state is P(v - a) = RT, where a is a positive constant. Is it possible to cool this gas by throttling? Get 12.47 exercise solution

12–48 Derive a relation for the Joule-Thomson coefficient and the inversion temperature for a gas whose equation of state is (P + a/v2)v = RT. Get 12.48 exercise solution

12–49 Estimate the Joule-Thomson coefficient of steam at (a) 3 MPa and 300°C and (b) 6 MPa and 500°C. Get 12.49 exercise solution

12–50E Estimate the Joule-Thomson coefficient of nitrogen at (a) 200 psia and 500 R and (b) 2000 psia and 400 R. Use nitrogen properties from EES or other source. Get 12.50 exercise solution

12–51E Reconsider Prob. 12–50E. Using EES (or other) software, plot the Joule-Thomson coefficient for nitrogen over the pressure range 100 to 1500 psia at the enthalpy values 100,175,and 225 Btu/lbm. Discuss the results. Get 12.51 exercise solution

12–52 Estimate the Joule-Thomson coefficient of refrigerant-134a at 0.7 MPa and 50°C. Get 12.52 exercise solution

12–53 Steam is throttled slightly from 1 MPa and 300°C. Will the temperature of the steam increase, decrease, or remain the same during this process? Get 12.53 exercise solution

12–54C What is the enthalpy departure? Get 12.54 exercise solution

12–55C On the generalized enthalpy departure chart, the normalized enthalpy departure values seem to approach zero as the reduced pressure PR approaches zero. How do you explain this behavior? Get 12.55 exercise solution

12–56C Why is the generalized enthalpy departure chart prepared by using PR and TR as the parameters instead of P and T? Get 12.56 exercise solution

12–57 Determine the enthalpy of nitrogen, in kJ/kg, at 175 K and 8 MPa using (a) data from the ideal-gas nitrogen table and (b) the generalized enthalpy departure chart. Compare your results to the actual value of 125.5 kJ/kg. Get 12.57 exercise solution

12–58E Determine the enthalpy of nitrogen, in Btu/lbm, at 400 R and 2000 psia using (a) data from the ideal-gas nitrogen table and (b) the generalized enthalpy chart. Compare your results to the actual value of 177.8 Btu/lbm. Get 12.58 exercise solution

12–59 What is the error involved in the (a) enthalpy and (b) internal energy of CO2 at 350 K and 10 MPa if it is assumed to be an ideal gas? Answers: (a) 50%, (b) 49% Get 12.59 exercise solution

12–60 Determine the enthalpy change and the entropy change of nitrogen per unit mole as it undergoes a change of state from 225 K and 6 MPa to 320 K and 12 MPa, (a) by assuming ideal-gas behavior and (b) by accounting for the deviation from ideal-gas behavior through the use of generalized charts. Get 12.60 exercise solution

12–61 Determine the enthalpy change and the entropy change of CO2 per unit mass as it undergoes a change of state from 250 K and 7 MPa to 280 K and 12 MPa, (a) by assuming ideal-gas behavior and (b) by accounting for the deviation from ideal-gas behavior. Get 12.61 exercise solution

12–62 Methane is compressed adiabatically by a steady-flow compressor from 2 MPa and -10°C to 10 MPa and 110°C at a rate of 0.55 kg/s. Using the generalized charts, determine the required power input to the compressor. Get 12.62 exercise solution

12–63 Propane is compressed isothermally by a piston– cylinder device from 100°C and 1 MPa to 4 MPa. Using the generalized charts, determine the work done and the heat transfer per unit mass of propane. Get 12.63 exercise solution

12–64 Reconsider Prob. 12–63. Using EES (or other) software, extend the problem to compare the solutions based on the ideal-gas assumption, generalized chart data, and real fluid data. Also extend the solution to methane. Get 12.64 exercise solution

12–65E Propane is compressed isothermally by a piston– cylinder device from 200°F and 200 psia to 800 psia. Using the generalized charts, determine the work done and the heat transfer per unit mass of the propane. Get 12.65 exercise solution

12–66 Determine the exergy destruction associated with the process described in Prob. 12–63. Assume T0 = 30°C. Get 12.66 exercise solution

12–67 Carbon dioxide enters an adiabatic nozzle at 8 MPa and 450 K with a low velocity and leaves at 2 MPa and 350 K. Using the generalized enthalpy departure chart, determine the exit velocity of the carbon dioxide. Get 12.67 exercise solution

12–68 Reconsider Prob. 12–67. Using EES (or other) software, compare the exit velocity to the nozzle assuming ideal-gas behavior, the generalized chart data, and EES data for carbon dioxide. Get 12.68 exercise solution

12–69 A 0.08-m3 well-insulated rigid tank contains oxygen at 220 K and 10 MPa. A paddle wheel placed in the tank is turned on, and the temperature of the oxygen rises to 250 K. Using the generalized charts, determine (a) the final pressure in the tank and (b) the paddle-wheel work done during this process. Get 12.69 exercise solution

12–70 Carbon dioxide is contained in a constant-volume tank and is heated from 100°C and 1 MPa to 8 MPa. Determine the heat transfer and entropy change per unit mass of the carbon dioxide using (a) the ideal-gas assumption, (b) the generalized charts, and (c) real fluid data from EES or other sources. Get 12.70 exercise solution

12–71 For B>= 0, prove that at every point of a singlephase region of an h-s diagram, the slope of a constantpressure (P = constant) line is greater than the slope of a constant-temperature (T = constant) line, but less than the slope of a constant-volume (v = constant) line. Get 12.71 exercise solution

12–72 Using the cyclic relation and the first Maxwell relation, derive the other three Maxwell relations. Get 12.72 exercise solution

12–73 Starting with the relation dh = T ds + v dP, show that the slope of a constant-pressure line on an h-s diagram (a) is constant in the saturation region and (b) increases with temperature in the superheated region. Get 12.73 exercise solution

12–74 Derive relations for (a) du,( b) dh, and (c) ds of a gas that obeys the equation of state (P + a/v2)v = RT for an isothermal process. Get 12.74 exercise solution

12–75 Show that


  Get 12.75 exercise solution

12–76 Estimate the cp of nitrogen at 300 kPa and 400 K, using (a) the relation in the above problem and (b) its definition. Compare your results to the value listed in Table A–2b. Get 12.76 exercise solution

12–77 Steam is throttled from 4.5 MPa and 300°C to 2.5 MPa. Estimate the temperature change of the steam during this process and the average Joule-Thomson coefficient. Get 12.77 exercise solution

12–78 A rigid tank contains 1.2 m3 of argon at -100°C and 1 MPa. Heat is now transferred to argon until the temperature in the tank rises to 0°C. Using the generalized charts, determine (a) the mass of the argon in the tank, (b) the final pressure, and (c) the heat transfer. Answers: (a) 35.1 kg, (b) 1531 kPa, (c) 1251 kJ Get 12.78 exercise solution

12–79 Argon gas enters a turbine at 7 MPa and 600 K with a velocity of 100 m/s and leaves at 1 MPa and 280 K with a velocity of 150 m/s at a rate of 5 kg/s. Heat is being lost to the surroundings at 25°C at a rate of 60 kW. Using the generalized charts, determine (a) the power output of the turbine and (b) the exergy destruction associated with the process. Get 12.79 exercise solution

12–80 Reconsider Prob. 12–79. Using EES (or other) software, solve the problem assuming steam is the working fluid by using the generalized chart method and EES data for steam. Plot the power output and the exergy destruction rate for these two calculation methods against the turbine exit pressure as it varies over the range 0.1 to 1 MPa when the turbine exit temperature is 455 K. Get 12.80 exercise solution

12–81E Argon gas enters a turbine at 1000 psia and 1000 R with a velocity of 300 ft/s and leaves at 150 psia and 500 R with a velocity of 450 ft/s at a rate of 12 lbm/s. Heat is being lost to the surroundings at 75°F at a rate of 80 Btu/s. Using the generalized charts, determine (a) the power output of the turbine and (b) the exergy destruction associated with the process. Answers: (a) 922 hp, (b) 121.5 Btu/s Get 12.81 exercise solution

12–82 An adiabatic 0.2-m3 storage tank that is initially evacuated is connected to a supply line that carries nitrogen at 225 K and 10 MPa. A valve is opened, and nitrogen flows into the tank from the supply line. The valve is closed when the pressure in the tank reaches 10 MPa. Determine the final temperature in the tank (a) treating nitrogen as an ideal gas and (b) using generalized charts. Compare your results to the actual value of 293 K. Get 12.82 exercise solution

12–83 For a homogeneous (single-phase) simple pure substance, the pressure and temperature are independent properties, and any property can be expressed as a function of these two properties. Taking v = v(P, T), show that the change in specific volume can be expressed in terms of the volume expansivity b and isothermal compressibility a as



Also, assuming constant average values for b and a, obtain a relation for the ratio of the specific volumes v2/v1 as a homogeneous system undergoes a process from state 1 to state 2. Get 12.83 exercise solution

12–84 Repeat Prob. 12–83 for an isobaric process. Get 12.84 exercise solution

12–85 The volume expansivity of water at 20°C is b = 0.207 x 10-6 K-1. Treating this value as a constant, determine the change in volume of 1 m3 of water as it is heated from 10°C to 30°C at constant pressure. Get 12.85 exercise solution

12–86 The volume expansivity b values of copper at 300 K and 500 K are 49.2 x 10-6 K-1 and 54.2 x 10-6 K-1, respectively, and b varies almost linearly in this temperature range. Determine the percent change in the volume of a copper block as it is heated from 300 K to 500 K at atmospheric pressure. Get 12.86 exercise solution

12–87 Starting with mJT = (1/cp) [T(dv/dT)p - v] and noting that Pv = ZRT, where Z = Z(P, T) is the compressibility factor, show that the position of the Joule-Thomson coefficient inversion curve on the T-P plane is given by the equation (dZ/dT)P = 0. Get 12.87 exercise solution

12–88 Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pvk = constant, where k is the isentropic expansion exponent defined as



Also, show that the isentropic expansion exponent k reduces to the specific heat ratio cp/cv for an ideal gas. Get 12.88 exercise solution

12–89 Refrigerant-134a undergoes an isothermal process at 60°C from 3 to 0.1 MPa in a closed system. Determine the work done by the refrigerant-134a by using the tabular (EES) data and the generalized charts, in kJ/kg. Get 12.89 exercise solution

12–90 Methane is contained in a piston–cylinder device and is heated at constant pressure of 4 MPa from 100 to 350°C. Determine the heat transfer, work and entropy change per unit mass of the methane using (a) the ideal-gas assumption, (b) the generalized charts, and (c) real fluid data from EES or other sources. Get 12.90 exercise solution

12–91 A substance whose Joule-Thomson coefficient is negative is throttled to a lower pressure. During this process, (select the correct statement) (a) the temperature of the substance will increase. (b) the temperature of the substance will decrease. (c) the entropy of the substance will remain constant. (d) the entropy of the substance will decrease. (e) the enthalpy of the substance will decrease. Get 12.91 exercise solution

12–92 Consider the liquid–vapor saturation curve of a pure substance on the P-T diagram. The magnitude of the slope of the tangent line to this curve at a temperature T (in Kelvin) is (a) proportional to the enthalpy of vaporization hfg at that temperature. (b) proportional to the temperature T. (c) proportional to the square of the temperature T. (d) proportional to the volume change vfg at that temperature. (e) inversely proportional to the entropy change sfg at that temperature. Get 12.92 exercise solution

12–93 Based on the generalized charts, the error involved in the enthalpy of CO2 at 350 K and 8 MPa if it is assumed to be an ideal gas is (a) 0 (b) 20% (c) 35% (d) 26% (e) 65% Get 12.93 exercise solution

12–94 Based on data from the refrigerant-134a tables, the Joule-Thompson coefficient of refrigerant-134a at 0.8 MPa and 100°C is approximately (a) 0 ( b) -5°C/MPa (c) 11°C/MPa (d)8°C/MPa (e) 26°C/MPa Get 12.94 exercise solution

12–95 For a gas whose equation of state is P(v - b) = RT, the specified heat difference cp -cv is equal to (a) R (b) R - b (c) R + b (d) 0 (e) R(1 + v/b)  Get 12.95 exercise solution

Themordynamics Cengel & Boles 5th edition - Chapter 11 - Solutions

11–1C Why is the reversed Carnot cycle executed within the saturation dome not a realistic model for refrigeration cycles? Get 11.1 exercise solution

11–2 A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the working fluid. The refrigerant changes from saturated vapor to saturated liquid at 30°C in the condenser as it rejects heat. The evaporator pressure is 160 kPa. Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the amount of heat absorbed from the refrigerated space, and (c) the net work input. Answers: (a) 5.64, (b) 147 kJ/kg, (c) 26.1 kJ/kg Get 11.2 exercise solution

11–3E Refrigerant-134a enters the condenser of a steadyflow Carnot refrigerator as a saturated vapor at 90 psia, and it leaves with a quality of 0.05. The heat absorption from the refrigerated space takes place at a pressure of 30 psia. Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the quality at the beginning of the heat-absorption process, and (c) the net work input. Ideal and Actual Vapor-Compression Refrigeration Cycles Get 11.3 exercise solution

11–4C Does the ideal vapor-compression refrigeration cycle involve any internal irreversibilities? Get 11.4 exercise solution

11–5C Why is the throttling valve not replaced by an isentropic turbine in the ideal vapor-compression refrigeration cycle? Get 11.5 exercise solution

11–6C It is proposed to use water instead of refrigerant134a as the working fluid in air-conditioning applications where the minimum temperature never falls below the freezing point. Would you support this proposal? Explain. Get 11.6 exercise solution

11–7C In a refrigeration system, would you recommend condensing the refrigerant-134a at a pressure of 0.7 or 1.0 MPa if heat is to be rejected to a cooling medium at 15°C? Why? Get 11.7 exercise solution

11–8C Does the area enclosed by the cycle on a T-s diagram represent the net work input for the reversed Carnot cycle? How about for the ideal vapor-compression refrigeration cycle? Get 11.8 exercise solution

11–9C Consider two vapor-compression refrigeration cycles. The refrigerant enters the throttling valve as a saturated liquid at 30°C in one cycle and as subcooled liquid at 30°C in the other one. The evaporator pressure for both cycles is the same. Which cycle do you think will have a higher COP? Get 11.9 exercise solution

11–10C The COP of vapor-compression refrigeration cycles improves when the refrigerant is subcooled before it enters the throttling valve. Can the refrigerant be subcooled indefinitely to maximize this effect, or is there a lower limit? Explain. Get 11.10 exercise solution

11–11 A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at -30°C by rejecting its waste heat to cooling water that enters the condenser at 18°C at a rate of 0.25 kg/s and leaves at 26°C. The refrigerant enters the condenser at 1.2 MPa and 65°C and leaves at 42°C. The inlet state of the compressor is 60 kPa and -34°C and the compressor is estimated to gain a net heat of 450 W from the surroundings. Determine (a) the quality of the refrigerant at the evaporator inlet, (b) the refrigeration load, (c) the COP of the refrigerator, and (d) the theoretical maximum refrigeration load for the same power input to the compressor. Get 11.11 exercise solution

11–12 A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.12 and 0.7 MPa. The mass flow rate of the refrigerant is 0.05 kg/s. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the rate of heat rejection to the environment, and (c) the coefficient of performance. Answers: (a) 7.41 kW, 1.83 kW, (b) 9.23 kW, (c) 4.06 Get 11.12 exercise solution

11–13 Repeat Prob. 11–12 for a condenser pressure of 0.9 MPa. Get 11.13 exercise solution

11–14 If the throttling valve in Prob. 11–12 is replaced by an isentropic turbine, determine the percentage increase in the COP and in the rate of heat removal from the refrigerated space. Answers: 4.2 percent, 4.2 percent Get 11.14 exercise solution

11–15 Consider a 300 kJ/min refrigeration system that operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 140 kPa and is compressed to 800 kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality of the refrigerant at the end of the throttling process, (b) the coefficient of performance, and (c) the power input to the compressor. Get 11.15 exercise solution

11–16 Reconsider Prob. 11–15. Using EES (or other) software, investigate the effect of evaporator pressure on the COP and the power input. Let the evaporator pressure vary from 100 to 400 kPa. Plot the COP and the power input as functions of evaporator pressure, and discuss the results. Get 11.16 exercise solution

11–17 Repeat Prob. 11–15 assuming an isentropic efficiency of 85 percent for the compressor. Also, determine the rate of exergy destruction associated with the compression process in this case. Take T0 = 298 K. Get 11.17 exercise solution

11–18 Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 MPa and -10°C at a rate of 0.12 kg/s, and it leaves at 0.7 MPa and 50°C. The refrigerant is cooled in the condenser to 24°C and 0.65 MPa, and it is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the isentropic efficiency of the compressor, and (c) the COP of the refrigerator. Get 11.18 exercise solution

11–19E An ice-making machine operates on the ideal vapor-compression cycle, using refrigerant-134a. The refrigerant enters the compressor as saturated vapor at 20 psia and leaves the condenser as saturated liquid at 80 psia. Water enters the ice machine at 55°F and leaves as ice at 25°F. For an ice production rate of 15 lbm/h, determine the power input to the ice machine (169 Btu of heat needs to be removed from each lbm of water at 55°F to turn it into ice at 25°F). Get 11.19 exercise solution

11–20 Refrigerant-134a enters the compressor of a refrigerator at 140 kPa and -10°C at a rate of 0.3 m3/min and leaves at 1 MPa. The isentropic efficiency of the compressor is 78 percent. The refrigerant enters the throttling valve at 0.95 MPa and 30°C and leaves the evaporator as saturated vapor at -18.5°C. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the power input to the compressor, (b) the rate of heat removal from the refrigerated space, and (c) the pressure drop and rate of heat gain in the line between the evaporator and the compressor. Get 11.20 exercise solution

11–21 Reconsider Prob. 11–20. Using EES (or other) software, investigate the effects of varying the compressor isentropic efficiency over the range 60 to 100 percent and the compressor inlet volume flow rate from 0.1 to 1.0 m3/min on the power input and the rate of refrigeration. Plot the rate of refrigeration and the power input to the compressor as functions of compressor efficiency for compressor inlet volume flow rates of 0.1, 0.5, and 1.0 m3/min, and discuss the results. Get 11.21 exercise solution

11–22 A refrigerator uses refrigerant-134a as the working fluid and operates on the ideal vapor-compression refrigeration cycle. The refrigerant enters the evaporator at 120 kPa with a quality of 30 percent and leaves the compressor at 60°C. If the compressor consumes 450 W of power, determine (a) the mass flow rate of the refrigerant, (b) the condenser pressure, and (c) the COP of the refrigerator. Answers: (a) 0.00727 kg/s, (b) 672 kPa, (c) 2.43 Selecting the Right Refrigerant Get 11.22 exercise solution

11–23C When selecting a refrigerant for a certain application, what qualities would you look for in the refrigerant? Get 11.23 exercise solution

11–24C Consider a refrigeration system using refrigerant134a as the working fluid. If this refrigerator is to operate in an environment at 30°C, what is the minimum pressure to which the refrigerant should be compressed? Why? Get 11.24 exercise solution

11–25C A refrigerant-134a refrigerator is to maintain the refrigerated space at -10°C. Would you recommend an evaporator pressure of 0.12 or 0.14 MPa for this system? Why? Get 11.25 exercise solution

11–26 A refrigerator that operates on the ideal vaporcompression cycle with refrigerant-134a is to maintain the refrigerated space at -10°C while rejecting heat to the environment at 25°C. Select reasonable pressures for the evaporator and the condenser, and explain why you chose those values. Get 11.26 exercise solution

11–27 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house and maintain it at 22°C by using underground water at 10°C as the heat source. Select reasonable pressures for the evaporator and the condenser, and explain why you chose those values. Get 11.27 exercise solution

11–28C Do you think a heat pump system will be more cost-effective in New York or in Miami? Why? Get 11.28 exercise solution

11–29C What is a water-source heat pump? How does the COP of a water-source heat pump system compare to that of an air-source system? Get 11.29 exercise solution

11–30E A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house and maintain it at 75°F by using underground water at 50°F as the heat source. The house is losing heat at a rate of 60,000 Btu/h. The evaporator and condenser pressures are 50 and 120 psia, respectively. Determine the power input to the heat pump and the electric power saved by using a heat pump instead of a resistance heater. Answers: 2.46 hp, 21.1 hp Get 11.30 exercise solution

11–31 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat water from 15 to 45°C at a rate of 0.12 kg/s. The condenser and evaporator pressures are 1.4 and 0.32 MPa, respectively. Determine the power input to the heat pump. Get 11.31 exercise solution

11–32 A heat pump using refrigerant-134a heats a house by using underground water at 8°C as the heat source. The house is losing heat at a rate of 60,000 kJ/h. The refrigerant enters the compressor at 280 kPa and 0°C, and it leaves at 1 MPa and 60°C. The refrigerant exits the condenser at 30°C. Determine (a) the power input to the heat pump, (b) the rate of heat absorption from the water, and (c) the increase in electric power input if an electric resistance heater is used instead of a heat pump. Get 11.32 exercise solution

11–33 Reconsider Prob. 11–32. Using EES (or other) software, investigate the effect of varying the compressor isentropic efficiency over the range 60 to 100 percent. Plot the power input to the compressor and the electric power saved by using a heat pump rather than electric resistance heating as functions of compressor efficiency, and discuss the results. Get 11.33 exercise solution

11–34 Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 55°C at a rate of 0.018 kg/s and leaves at 750 kPa subcooled by 3°C. The refrigerant enters the compressor at 200 kPa superheated by 4°C. Determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the COP of the heat pump. Also, determine (d) the COP and the rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kPa. Get 11.34 exercise solution

11–35 A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25°C by absorbing heat from geothermal water that enters the evaporator at 50°C at a rate of 0.065 kg/s and leaves at 40°C. The refrigerant enters the evaporator at 20°C with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. The refrigerant loses 300 W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor at 1.4 MPa at the same entropy as the inlet. Determine (a) the degrees of subcooling of the refrigerant in the condenser, (b) the mass flow rate of the refrigerant, (c) the heating load and the COP of the heat pump, and (d) the theoretical minimum power input to the compressor for the same heating load. Answers: (a) 3.8°C, (b) 0.0194 kg/s, (c) 3.07 kW, 4.68, (d) 0.238 kW Innovative Refrigeration Systems Get 11.35 exercise solution

11–36C What is cascade refrigeration? What are the advantages and disadvantages of cascade refrigeration? Get 11.36 exercise solution

11–37C How does the COP of a cascade refrigeration system compare to the COP of a simple vapor-compression cycle operating between the same pressure limits? Get 11.37 exercise solution

11–38C A certain application requires maintaining the refrigerated space at -32°C. Would you recommend a simple refrigeration cycle with refrigerant-134a or a two-stage cascade refrigeration cycle with a different refrigerant at the bottoming cycle? Why? Get 11.38 exercise solution

11–39C Consider a two-stage cascade refrigeration cycle and a two-stage compression refrigeration cycle with a flash chamber. Both cycles operate between the same pressure limits and use the same refrigerant. Which system would you favor? Why? Get 11.39 exercise solution

11–40C Can a vapor-compression refrigeration system with a single compressor handle several evaporators operating at different pressures? How? Get 11.40 exercise solution

11–41C In the liquefaction process, why are gases compressed to very high pressures? Get 11.41 exercise solution

11–42 Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. Each stage operates on the ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about 0.4 MPa. If the mass flow rate of the refrigerant through the upper cycle is 0.24 kg/s, determine (a) the mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat removal from the refrigerated space and the power input to the compressor, and (c) the coefficient of performance of this cascade refrigerator. Get 11.42 exercise solution

11–43 Repeat Prob. 11–42 for a heat exchanger pressure of 0.55 MPa. Get 11.43 exercise solution

11–44 A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1 and 0.14 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.5 MPa. The refrigerant leaving the low-pressure compressor at 0.5 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 0.25 kg/s through the condenser, and (c) the coefficient of performance. Get 11.44 exercise solution

11–45 Reconsider Prob. 11–44. Using EES (or other) software, investigate the effect of the various refrigerants for compressor efficiencies of 80, 90, and 100 percent. Compare the performance of the refrigeration system with different refrigerants. Get 11.45 exercise solution

11–46 Repeat Prob. 11–44 for a flash chamber pressure of 0.32 MPa. Get 11.46 exercise solution

11–47 Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where the pressure in the upper and lower cycles are 0.4 and 0.5 MPa, respectively. In both cycles, the refrigerant is a saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the isentropic efficiency of the compressor is 80 percent. If the mass flow rate of the refrigerant through the lower cycle is 0.15 kg/s, determine (a) the mass flow rate of the refrigerant through the upper cycle, (b) the rate of heat removal from the refrigerated space, and (c) the COP of this refrigerator. Get 11.47 exercise solution

11–48 Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the working fluid. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.45 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure and cools the refrigerated space as it vaporizes in the evaporator. The mass flow rate of the refrigerant through the low-pressure compressor is 0.15 kg/s. Assuming the refrigerant leaves the evaporator as a saturated vapor and the isentropic efficiency is 80 percent for both compressors, determine (a) the mass flow rate of the refrigerant through the high-pressure compressor, (b) the rate of heat removal from the refrigerated space, and (c) the COP of this refrigerator. Also, determine (d) the rate of heat removal and the COP if this refrigerator operated on a single-stage cycle between the same pressure limits with the same compressor efficiency and the same flow rate as in part (a). Get 11.48 exercise solution

11–49C How does the ideal-gas refrigeration cycle differ from the Brayton cycle? Get 11.49 exercise solution

11–50C Devise a refrigeration cycle that works on the reversed Stirling cycle. Also, determine the COP for this cycle. Get 11.50 exercise solution

11–51C How does the ideal-gas refrigeration cycle differ from the Carnot refrigeration cycle? Get 11.51 exercise solution

11–52C How is the ideal-gas refrigeration cycle modified for aircraft cooling? Get 11.52 exercise solution

11–53C In gas refrigeration cycles, can we replace the turbine by an expansion valve as we did in vapor-compression refrigeration cycles? Why? Get 11.53 exercise solution

11–54C How do we achieve very low temperatures with gas refrigeration cycles? Get 11.54 exercise solution

11–55 An ideal gas refrigeration cycle using air as the working fluid is to maintain a refrigerated space at -23°C while rejecting heat to the surrounding medium at 27°C. If the pressure ratio of the compressor is 3, determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of performance, and (c) the rate of refrigeration for a mass flow rate of 0.08 kg/s. Get 11.55 exercise solution

11–56 Air enters the compressor of an ideal gas refrigeration cycle at 12°C and 50 kPa and the turbine at 47°C and 250 kPa. The mass flow rate of air through the cycle is 0.08 kg/s. Assuming variable specific heats for air, determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Get 11.56 exercise solution

11–57 Reconsider Prob. 11–56. Using EES (or other) software, study the effects of compressor and turbine isentropic efficiencies as they are varied from 70 to 100 percent on the rate of refrigeration, the net power input, and the COP. Plot the T-s diagram of the cycle for the isentropic case. Get 11.57 exercise solution

11–58E Air enters the compressor of an ideal gas refrigeration cycle at 40°F and 10 psia and the turbine at 120°F and 30 psia. The mass flow rate of air through the cycle is 0.5 lbm/s. Determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Get 11.58 exercise solution

11–59 Repeat Prob. 11–56 for a compressor isentropic efficiency of 80 percent and a turbine isentropic efficiency of 85 percent. Get 11.59 exercise solution

11–60 A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is -10°C at the compressor inlet and 50°C at the turbine inlet. Assuming adiabatic efficiencies of 80 percent for both the turbine and the compressor, determine (a) the minimum temperature in the cycle, (b) the coefficient of performance, and (c) the mass flow rate of the helium for a refrigeration rate of 18 kW. Get 11.60 exercise solution

11–61 A gas refrigeration system using air as the working fluid has a pressure ratio of 4. Air enters the compressor at -7°C. The high-pressure air is cooled to 27°C by rejecting heat to the surroundings. It is further cooled to -15°C by regenerative cooling before it enters the turbine. Assuming both the turbine and the compressor to be isentropic and using constant specific heats at room temperature, determine (a) the lowest temperature that can be obtained by this cycle, (b) the coefficient of performance of the cycle, and (c) the mass flow rate of air for a refrigeration rate of 12 kW. Answers: (a) -99.4°C, (b) 1.12, (c) 0.237 kg/s Get 11.61 exercise solution

11–62 Repeat Prob. 11–61 assuming isentropic efficiencies of 75 percent for the compressor and 80 percent for the turbine. Get 11.62 exercise solution

11–63 A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure air is cooled to 35°C by rejecting heat to the surroundings. The refrigerant leaves the turbine at -80°C and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using constant specific heats at room temperature, determine (a) the effectiveness of the regenerator, (b) the rate of heat removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies. Answers: (a) 0.434, (b) 21.4 kW, (c) 0.478, (d) 24.7 kW, 0.599 Absorption Refrigeration Systems Get 11.63 exercise solution

11–64C What is absorption refrigeration? How does an absorption refrigeration system differ from a vapor-compression refrigeration system? Get 11.64 exercise solution

11–65C What are the advantages and disadvantages of absorption refrigeration? Get 11.65 exercise solution

11–66C Can water be used as a refrigerant in air-conditioning applications? Explain. Get 11.66 exercise solution

11–67C In absorption refrigeration cycles, why is the fluid in the absorber cooled and the fluid in the generator heated? Get 11.67 exercise solution

11–68C How is the coefficient of performance of an absorption refrigeration system defined? Get 11.68 exercise solution

11–69C What are the functions of the rectifier and the regenerator in an absorption refrigeration system? Get 11.69 exercise solution

11–70 An absorption refrigeration system that receives heat from a source at 130°C and maintains the refrigerated space at -5°C is claimed to have a COP of 2. If the environment temperature is 27°C, can this claim be valid? Justify your answer. Get 11.70 exercise solution

11–71 An absorption refrigeration system receives heat from a source at 120°C and maintains the refrigerated space at 0°C. If the temperature of the environment is 25°C, what is the maximum COP this absorption refrigeration system can have? Get 11.71 exercise solution

11–72 Heat is supplied to an absorption refrigeration system from a geothermal well at 130°C at a rate of 5 x 105 kJ/h. The environment is at 25°C, and the refrigerated space is maintained at -30°C. Determine the maximum rate at which this system can remove heat from the refrigerated space. Get 11.72 exercise solution

11–73E Heat is supplied to an absorption refrigeration system from a geothermal well at 250°F at a rate of 105 Btu/h. The environment is at 80°F, and the refrigerated space is maintained at 0°F. If the COP of the system is 0.55, determine the rate at which this system can remove heat from the refrigerated space. Get 11.73 exercise solution

11–74 A reversible absorption refrigerator consists of a reversible heat engine and a reversible refrigerator. The system removes heat from a cooled space at -10°C at a rate of 22 kW. The refrigerator operates in an environment at 25°C. If the heat is supplied to the cycle by condensing saturated steam at 200°C, determine (a) the rate at which the steam condenses and (b) the power input to the reversible refrigerator. (c) If the COP of an actual absorption chiller at the same temperature limits has a COP of 0.7, determine the second law efficiency of this chiller. Get 11.74 exercise solution

11–75C What is a thermoelectric circuit? Get 11.75 exercise solution

11–76C Describe the Seebeck and the Peltier effects. Get 11.76 exercise solution

11–77C Consider a circular copper wire formed by connecting the two ends of a copper wire. The connection point is now heated by a burning candle. Do you expect any current to flow through the wire? Get 11.77 exercise solution

11–78C An iron and a constantan wire are formed into a closed circuit by connecting the ends. Now both junctions are heated and are maintained at the same temperature. Do you expect any electric current to flow through this circuit? Get 11.78 exercise solution

11–79C A copper and a constantan wire are formed into a closed circuit by connecting the ends. Now one junction is heated by a burning candle while the other is maintained at room temperature. Do you expect any electric current to flow through this circuit? Get 11.79 exercise solution

11–80C How does a thermocouple work as a temperature measurement device? Get 11.80 exercise solution

11–81C Why are semiconductor materials preferable to metals in thermoelectric refrigerators? Get 11.81 exercise solution

11–82C Is the efficiency of a thermoelectric generator limited by the Carnot efficiency? Why? Get 11.82 exercise solution

11–83E A thermoelectric generator receives heat from a source at 340°F and rejects the waste heat to the environment at 90°F. What is the maximum thermal efficiency this thermoelectric generator can have? Get 11.83 exercise solution

11–84 A thermoelectric refrigerator removes heat from a refrigerated space at -5°C at a rate of 130 W and rejects it to an environment at 20°C. Determine the maximum coefficient of performance this thermoelectric refrigerator can have and the minimum required power input. Get 11.84 exercise solution

11–85 A thermoelectric cooler has a COP of 0.15 and removes heat from a refrigerated space at a rate of 180 W. Determine the required power input to the thermoelectric cooler, in W. Get 11.85 exercise solution

11–86E A thermoelectric cooler has a COP of 0.15 and removes heat from a refrigerated space at a rate of 20 Btu/min. Determine the required power input to the thermoelectric cooler, in hp. Get 11.86 exercise solution

11–87 A thermoelectric refrigerator is powered by a 12-V car battery that draws 3 A of current when running. The refrigerator resembles a small ice chest and is claimed to cool nine canned drinks, 0.350-L each, from 25 to 3°C in 12 h. Determine the average COP of this refrigerator. Get 11.87 exercise solution

11–88E Thermoelectric coolers that plug into the cigarette lighter of a car are commonly available. One such cooler is claimed to cool a 12-oz (0.771-lbm) drink from 78 to 38°F or to heat a cup of coffee from 75 to 130°F in about 15 min in a well-insulated cup holder. Assuming an average COP of 0.2 in the cooling mode, determine (a) the average rate of heat removal from the drink, (b) the average rate of heat supply to the coffee, and (c) the electric power drawn from the battery of the car, all in W. Get 11.88 exercise solution

11–89 It is proposed to run a thermoelectric generator in conjunction with a solar pond that can supply heat at a rate of 106 kJ/h at 80°C. The waste heat is to be rejected to the environment at 30°C. What is the maximum power this thermoelectric generator can produce? Get 11.89 exercise solution

11–90 Consider a steady-flow Carnot refrigeration cycle that uses refrigerant-134a as the working fluid. The maximum and minimum temperatures in the cycle are 30 and -20°C, respectively. The quality of the refrigerant is 0.15 at the beginning of the heat absorption process and 0.80 at the end. Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the condenser and evaporator pressures, and (c) the net work input. Get 11.90 exercise solution

11–91 A large refrigeration plant is to be maintained at -15°C, and it requires refrigeration at a rate of 100 kW. The condenser of the plant is to be cooled by liquid water, which experiences a temperature rise of 8°C as it flows over the coils of the condenser. Assuming the plant operates on the ideal vapor-compression cycle using refrigerant-134a between the pressure limits of 120 and 700 kPa, determine (a) the mass flow rate of the refrigerant, (b) the power input to the compressor, and (c) the mass flow rate of the cooling water. Get 11.91 exercise solution

11–92 Reconsider Prob. 11–91. Using EES (or other) software, investigate the effect of evaporator pressure on the COP and the power input. Let the evaporator pressure vary from 120 to 380 kPa. Plot the COP and the power input as functions of evaporator pressure, and discuss the results. Get 11.92 exercise solution

11–93 Repeat Prob. 11–91 assuming the compressor has an isentropic efficiency of 75 percent. Also, determine the rate of exergy destruction associated with the compression process in this case. Take T0 = 25°C. Get 11.93 exercise solution

11–94 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house. The mass flow rate of the refrigerant is 0.32 kg/s. The condenser and evaporator pressures are 900 and 200 kPa, respectively. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the rate of heat supply to the house, (b) the volume flow rate of the refrigerant at the compressor inlet, and (c) the COP of this heat pump. Get 11.94 exercise solution

11–95 Derive a relation for the COP of the two-stage refrigeration system with a flash chamber as shown in Fig. 11–12 in terms of the enthalpies and the quality at state 6. Consider a unit mass in the condenser. Get 11.95 exercise solution

11–96 Consider a two-stage compression refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. The working fluid is refrigerant-134a. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure, and it cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the amount of heat removed from the refrigerated space and the compressor work per unit mass of refrigerant flowing through the condenser, and (c) the coefficient of performance. Answers: (a) 0.165, (b) 146.4 kJ/kg, 32.6 kJ/kg, (c) 4.49 Get 11.96 exercise solution

11–97 An aircraft on the ground is to be cooled by a gas refrigeration cycle operating with air on an open cycle. Air enters the compressor at 30°C and 100 kPa and is compressed to 250 kPa. Air is cooled to 70°C before it enters the turbine. Assuming both the turbine and the compressor to be isentropic, determine the temperature of the air leaving the turbine and entering the cabin. Get 11.97 exercise solution

11–98 Consider a regenerative gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and -10°C and is compressed to 300 kPa. Helium is then cooled to 20°C by water. It then enters the regenerator where it is cooled further before it enters the turbine. Helium leaves the refrigerated space at -25°C and enters the regenerator. Assuming both the turbine and the compressor to be isentropic, determine (a) the temperature of the helium at the turbine inlet, (b) the coefficient of performance of the cycle, and (c) the net power input required for a mass flow rate of 0.45 kg/s. Get 11.98 exercise solution

11–99 An absorption refrigeration system is to remove heat from the refrigerated space at -10°C at a rate of 12 kW while operating in an environment at 25°C. Heat is to be supplied from a solar pond at 85°C. What is the minimum rate of heat supply required? Get 11.99 exercise solution

11–100 Reconsider Prob. 11–99. Using EES (or other) software, investigate the effect of the source temperature on the minimum rate of heat supply. Let the source temperature vary from 50 to 250°C. Plot the minimum rate of heat supply as a function of source temperature, and discuss the results. Get 11.100 exercise solution

11–101 A typical 200-m2 house can be cooled adequately by a 3.5-ton air conditioner whose COP is 4.0. Determine the rate of heat gain of the house when the air conditioner is running continuously to maintain a constant temperature in the house. Get 11.101 exercise solution

11–102 Rooms with floor areas of up to 15-m2 are cooled adequately by window air conditioners whose cooling capacity is 5000 Btu/h. Assuming the COP of the air conditioner to be 3.5, determine the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room temperature. Get 11.102 exercise solution

11–103 A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure air is cooled to 35°C by rejecting heat to the surroundings. The refrigerant leaves the turbine at -80°C and enters the refrigerated space where it absorbs heat before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using variable specific heats, determine (a) the effectiveness of the regenerator, (b) the rate of heat removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies. Get 11.103 exercise solution

11–104 An air conditioner with refrigerant-134a as the working fluid is used to keep a room at 26°C by rejecting the waste heat to the outside air at 34°C. The room is gaining heat through the walls and the windows at a rate of 250 kJ/min while the heat generated by the computer, TV, and lights amounts to 900 W. An unknown amount of heat is also generated by the people in the room. The condenser and evaporator pressures are 1200 and 500 kPa, respectively. The refrigerant is saturated liquid at the condenser exit and saturated vapor at the compressor inlet. If the refrigerant enters the compressor at a rate of 100 L/min and the isentropic efficiency of the compressor is 75 percent, determine (a) the temperature of the refrigerant at the compressor exit, (b) the rate of heat generation by the people in the room, (c) the COP of the air conditioner, and (d) the minimum volume flow rate of the refrigerant at the compressor inlet for the same compressor inlet and exit conditions. Get 11.104 exercise solution

11–105 A heat pump water heater (HPWH) heats water by absorbing heat from the ambient air and transferring it to water. The heat pump has a COP of 2.2 and consumes 2 kW of electricity when running. Determine if this heat pump can be used to meet the cooling needs of a room most of the time for “free” by absorbing heat from the air in the room. The rate of heat gain of a room is usually less than 5000 kJ/h. Get 11.105 exercise solution

11–106 The vortex tube (also known as a Ranque or Hirsch tube) is a device that produces a refrigeration effect by expanding pressurized gas such as air in a tube (instead of a turbine as in the reversed Brayton cycle). It was invented and patented by Ranque in 1931 and improved by Hirsch in 1945, and is commercially available in various sizes. The vortex tube is simply a straight circular tube equipped with a nozzle, as shown in the figure. The compressed gas at temperature T1 and pressure P1 is accelerated in the nozzle by expanding it to nearly atmospheric pressure and is introduced into the tube tangentially at a very high (typically supersonic) velocity to produce a swirling motion (vortex) within the tube. The rotating gas is allowed to exit through the full-size tube that extends to the right, and the mass flow rate is controlled by a valve located about 30 diameters downstream. A smaller amount of air at the core region is allowed to escape to the left through a small aperture at the center. It is observed that the gas that is in the core region and escapes through the central aperture is cold while the gas that is in the peripheral region and escapes through the full-size tube is hot. If the temperature and the mass flow rate of the cold stream are Tc and m . c, respectively, the rate of refrigeration in the vortex tube can be expressed as

 

where cp is the specific heat of the gas and T1 Tc is the temperature drop of the gas in the vortex tube (the cooling effect). Temperature drops as high as 60°C (or 108°F) are obtained at high pressure ratios of about 10. The coefficient of performance of a vortex tube can be defined as the ratio of the refrigeration rate as given above to the power used to compress the gas. It ranges from about 0.1 to 0.15, which is well below the COPs of ordinary vapor compression refrigerators. This interesting phenomenon can be explained as follows: the centrifugal force creates a radial pressure gradient in the vortex, and thus the gas at the periphery is pressurized and heated by the gas at the core region, which is cooled as a result. Also, energy is transferred from the inner layers toward the outer layers as the outer layers slow down the inner layers because of fluid viscosity that tends to produce a solid vortex. Both of these effects cause the energy and thus the temperature of the gas in the core region to decline. The conservation of energy requires the energy of the fluid at the outer layers to increase by an equivalent amount. The vortex tube has no moving parts, and thus it is inherently reliable and durable. The ready availability of the compressed air at pressures up to 10 atm in most industrial facilities makes the vortex tube particularly attractive in such settings. Despite its low efficiency, the vortex tube has found application in small-scale industrial spot-cooling operations such as cooling of soldered parts or critical electronic components, cooling drinking water, and cooling the suits of workers in hot environments. Consider a vortex tube that receives compressed air at 500 kPa and 300 K and supplies 25 percent of it as cold air at 100 kPa and 278 K. The ambient air is at 300 K and 100 kPa, and the compressor has an isentropic efficiency of 80 percent. The air suffers a pressure drop of 35 kPa in the aftercooler and the compressed air lines between the compressor and the vortex tube. (a) Without performing any calculations, explain how the COP of the vortex tube would compare to the COP of an actual air refrigeration system based on the reversed Brayton cycle for the same pressure ratio. Also, compare the minimum temperatures that can be obtained by the two systems for the same inlet temperature and pressure. (b) Assuming the vortex tube to be adiabatic and using specific heats at room temperature, determine the exit temperature of the hot fluid stream. (c) Show, with calculations, that this process does not violate the second law of thermodynamics. (d) Determine the coefficient of performance of this refrigeration system, and compare it to the COP of a Carnot refrigerator. Get 11.106 exercise solution

11–107 Repeat Prob. 11–106 for a pressure of 600 kPa at the vortex tube intake. Get 11.107 exercise solution

11–108 Using EES (or other) software, investigate the effect of the evaporator pressure on the COP of an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Assume the condenser pressure is kept constant at 1 MPa while the evaporator pressure is varied from 100 kPa to 500 kPa. Plot the COP of the refrigeration cycle against the evaporator pressure, and discuss the results. Get 11.108 exercise solution

11–109 Using EES (or other) software, investigate the effect of the condenser pressure on the COP of an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Assume the evaporator pressure is kept constant at 120 kPa while the condenser pressure is varied from 400 to 1400 kPa. Plot the COP of the refrigeration cycle against the condenser pressure, and discuss the results. Get 11.109 exercise solution

11–110 Consider a heat pump that operates on the reversed Carnot cycle with R-134a as the working fluid executed under the saturation dome between the pressure limits of 140 and 800 kPa. R-134a changes from saturated vapor to saturated liquid during the heat rejection process. The net work input for this cycle is (a) 28 kJ/kg (b) 34 kJ/kg (c) 49 kJ/kg (d)144 kJ/kg (e) 275 kJ/kg Get 11.110 exercise solution

11–111 A refrigerator removes heat from a refrigerated space at -5°C at a rate of 0.35 kJ/s and rejects it to an environment at 20°C. The minimum required power input is (a) 30 W (b) 33 W (c) 56 W (d)124 W (e) 350 W Get 11.111 exercise solution

11–112 A refrigerator operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 120 and 800 kPa. If the rate of heat removal from the refrigerated space is 32 kJ/s, the mass flow rate of the refrigerant is (a) 0.19 kg/s (b) 0.15 kg/s (c) 0.23 kg/s (d)0.28 kg/s (e) 0.81 kg/s Get 11.112 exercise solution

11–113 A heat pump operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 0.32 and 1.2 MPa. If the mass flow rate of the refrigerant is 0.193 kg/s, the rate of heat supply by the heat pump to the heated space is (a) 3.3 kW (b) 23 kW (c) 26 kW (d)31 kW (e) 45 kW Get 11.113 exercise solution

11–114 An ideal vapor compression refrigeration cycle with R-134a as the working fluid operates between the pressure limits of 120 kPa and 1000 kPa. The mass fraction of the refrigerant that is in the liquid phase at the inlet of the evaporator is (a) 0.65 (b) 0.60 (c) 0.40 (d)0.55 (e) 0.35 Get 11.114 exercise solution

11–115 Consider a heat pump that operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 0.32 and 1.2 MPa. The coefficient of performance of this heat pump is (a) 0.17 (b) 1.2 (c) 3.1 (d)4.9 (e) 5.9 Get 11.115 exercise solution

11–116 An ideal gas refrigeration cycle using air as the working fluid operates between the pressure limits of 80 and 280 kPa. Air is cooled to 35°C before entering the turbine. The lowest temperature of this cycle is (a) -58°C (b) -26°C (c) 5°C (d)11°C (e) 24°C Get 11.116 exercise solution

11–117 Consider an ideal gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and -10°C and compressed to 250 kPa. Helium is then cooled to 20°C before it enters the turbine. For a mass flow rate of 0.2 kg/s, the net power input required is (a) 9.3 kW (b) 27.6 kW (c) 48.8 kW (d)93.5 kW (e) 119 kW Get 11.117 exercise solution

11–118 An absorption air-conditioning system is to remove heat from the conditioned space at 20°C at a rate of 150 kJ/s while operating in an environment at 35°C. Heat is to be supplied from a geothermal source at 140°C. The minimum rate of heat supply is (a) 86 kJ/s (b) 21 kJ/s (c) 30 kJ/s (d)61 kJ/s (e) 150 kJ/s Get 11.118 exercise solution

11–119 Consider a refrigerator that operates on the vapor compression refrigeration cycle with R-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 160 kPa, and exits at 800 kPa and 50°C, and leaves the condenser as saturated liquid at 800 kPa. The coefficient of performance of this refrigerator is (a) 2.6 (b) 1.0 (c) 4.2 (d)3.2 (e) 4.4 Get 11.119 exercise solution

Themordynamics Cengel & Boles 5th edition - Chapter 10 - Solutions

10–1C Why is excessive moisture in steam undesirable in steam turbines? What is the highest moisture content allowed? Get 10.1 exercise solution

10–2C Why is the Carnot cycle not a realistic model for steam power plants? Get 10.2 exercise solution

10–3E Water enters the boiler of a steady-flow Carnot engine as a saturated liquid at 180 psia and leaves with a quality of 0.90. Steam leaves the turbine at a pressure of 14.7 psia. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the quality at the end of the isothermal heat-rejection process, and (c) the net work output. Answers: (a) 19.3 percent, (b) 0.153, (c) 148 Btu/lbm Get 10.3 exercise solution

10–4 A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250°C. Heat rejection takes place at a pressure of 20 kPa. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the amount of heat rejected, in kJ/kg, and (c) the net work output. Get 10.4 exercise solution

10–5 Repeat Prob. 10–4 for a heat rejection pressure of 10 kPa. Get 10.5 exercise solution

10–6 Consider a steady-flow Carnot cycle with water as the working fluid. The maximum and minimum temperatures in the cycle are 350 and 60°C. The quality of water is 0.891 at the beginning of the heat-rejection process and 0.1 at the end. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the pressure at the turbine inlet, and (c) the net work output. Answers: (a) 0.465, (b) 1.40 MPa, (c) 1623 kJ/kg The Simple Rankine Cycle Get 10.6 exercise solution

10–7C What four processes make up the simple ideal Rankine cycle? Get 10.7 exercise solution

10–8C Consider a simple ideal Rankine cycle with fixed turbine inlet conditions. What is the effect of lowering the condenser pressure on Pump work input: (a) increases, (b) decreases, (c) remains the same Turbine work (a) increases, (b) decreases, output: (c) remains the same Heat supplied: (a) increases, (b) decreases, (c) remains the same Heat rejected: (a) increases, (b) decreases, (c) remains the same Cycle efficiency: (a) increases, (b) decreases, (c) remains the same Moisture content (a) increases, (b) decreases, at turbine exit: (c) remains the same Get 10.8 exercise solution

10–9C Consider a simple ideal Rankine cycle with fixed turbine inlet temperature and condenser pressure. What is the effect of increasing the boiler pressure on Pump work input: (a) increases, (b) decreases, (c) remains the same Turbine work (a) increases, (b) decreases, output: (c) remains the same Heat supplied: (a) increases, (b) decreases, (c) remains the same Heat rejected: (a) increases, (b) decreases, (c) remains the same Cycle efficiency: (a) increases, (b) decreases, (c) remains the same Moisture content (a) increases, (b) decreases, at turbine exit: (c) remains the same Get 10.9 exercise solution

10–10C Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. What is the effect of superheating the steam to a higher temperature on Pump work input: (a) increases, (b) decreases, (c) remains the same Turbine work (a) increases, (b) decreases, output: (c) remains the same Heat supplied: (a) increases, (b) decreases, (c) remains the same Heat rejected: (a) increases, (b) decreases, (c) remains the same Cycle efficiency: (a) increases, (b) decreases, (c) remains the same Moisture content (a) increases, (b) decreases, at turbine exit: (c) remains the same Get 10.10 exercise solution

10–11C How do actual vapor power cycles differ from idealized ones? Get 10.11 exercise solution

10–12C Compare the pressures at the inlet and the exit of the boiler for (a) actual and (b) ideal cycles. Get 10.12 exercise solution

10–13C The entropy of steam increases in actual steam turbines as a result of irreversibilities. In an effort to control entropy increase, it is proposed to cool the steam in the turbine by running cooling water around the turbine casing. It is argued that this will reduce the entropy and the enthalpy of the steam at the turbine exit and thus increase the work output. How would you evaluate this proposal? Get 10.13 exercise solution

10–14C Is it possible to maintain a pressure of 10 kPa in a condenser that is being cooled by river water entering at 20°C? Get 10.14 exercise solution

10–15 A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 3 MPa and 50 kPa. The temperature of the steam at the turbine inlet is 300°C, and the mass flow rate of steam through the cycle is 35 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the net power output of the power plant. Get 10.15 exercise solution

10–16 Consider a 210-MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam. Get 10.16 exercise solution

10–17 Repeat Prob. 10–16 assuming an isentropic efficiency of 85 percent for both the turbine and the pump. Answers: (a) 0.874, (b) 34.1 percent, (c) 194 kg/s Get 10.17 exercise solution

10–18E A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 1250 and 2 psia. The mass flow rate of steam through the cycle is 75 lbm/s. The moisture content of the steam at the turbine exit is not to exceed 10 percent. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the minimum turbine inlet temperature, (b) the rate of heat input in the boiler, and (c) the thermal efficiency of the cycle. Get 10.18 exercise solution

10–19E Repeat Prob. 10–18E assuming an isentropic efficiency of 85 percent for both the turbine and the pump. Get 10.19 exercise solution

10–20 Consider a coal-fired steam power plant that produces 300 MW of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of 5 MPa and 450°C and a condenser pressure of 25 kPa. The coal has a heating value (energy released when the fuel is burned) of 29,300 kJ/kg. Assuming that 75 percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of 96 percent, determine (a) the overall plant efficiency (the ratio of net electric power output to the energy input as fuel) and (b) the required rate of coal supply. Get 10.20 exercise solution

10–21 Consider a solar-pond power plant that operates on a simple ideal Rankine cycle with refrigerant-134a as the working fluid. The refrigerant enters the turbine as a saturated vapor at 1.4 MPa and leaves at 0.7 MPa. The mass flow rate of the refrigerant is 3 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the power output of this plant. Get 10.21 exercise solution

10–22 Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the steam, and (c) the temperature rise of the cooling water. Answers: (a) 38.9 percent, (b) 36 kg/s, (c) 8.4°C Get 10.22 exercise solution

10–23 Repeat Prob. 10–22 assuming an isentropic efficiency of 87 percent for both the turbine and the pump. Answers: (a) 33.8 percent, (b) 41.4 kg/s, (c) 10.5°C Get 10.23 exercise solution

10–24 The net work output and the thermal efficiency for the Carnot and the simple ideal Rankine cycles with steam as the working fluid are to be calculated and compared. Steam enters the turbine in both cases at 10 MPa as a saturated vapor, and the condenser pressure is 20 kPa. In the Rankine cycle, the condenser exit state is saturated liquid and in the Carnot cycle, the boiler inlet state is saturated liquid. Draw the T-s diagrams for both cycles. Get 10.24 exercise solution

10–25 A binary geothermal power plant uses geothermal water at 160°C as the heat source. The cycle operates on the simple Rankine cycle with isobutane as the working fluid. Heat is transferred to the cycle by a heat exchanger in which geothermal liquid water enters at 160°C at a rate of 555.9 kg/s and leaves at 90°C. Isobutane enters the turbine at 3.25 MPa and 147°C at a rate of 305.6 kg/s, and leaves at 79.5°C and 410 kPa. Isobutane is condensed in an air-cooled condenser and pumped to the heat exchanger pressure. Assuming the pump to have an isentropic efficiency of 90 percent, determine (a) the isentropic efficiency of the turbine, (b) the net power output of the plant, and (c) the thermal efficiency of the cycle. Get 10.25 exercise solution

10–26 The schematic of a single-flash geothermal power plant with state numbers is given in Fig. P10–26. Geothermal resource exists as saturated liquid at 230°C. The geothermal liquid is withdrawn from the production well at a rate of 230 kg/s, and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and directed to the turbine. The steam leaves the turbine at 10 kPa with a moisture content of 10 percent and enters the condenser where it is condensed and routed to a reinjection well along with the liquid coming off the separator. Determine (a) the mass flow rate of steam through the turbine, (b) the isentropic efficiency of the turbine, (c) the power output of the turbine, and (d) the thermal efficiency of the plant (the ratio of the turbine work output to the energy of the geothermal fluid relative to standard ambient conditions). Get 10.26 exercise solution

10–27 Reconsider Prob. 10–26. Now, it is proposed that the liquid water coming out of the separator be routed through another flash chamber maintained at 150 kPa, and the steam produced be directed to a lower stage of the same turbine. Both streams of steam leave the turbine at the same state of 10 kPa and 90 percent quality. Determine (a) the temperature of steam at the outlet of the second flash chamber, (b) the power produced by the lower stage of the turbine, and (c) the thermal efficiency of the plant. Get 10.27 exercise solution

10–28 Reconsider Prob. 10–26. Now, it is proposed that the liquid water coming out of the separator be used as the heat source in a binary cycle with isobutane as the working fluid. Geothermal liquid water leaves the heat exchanger at 90°C while isobutane enters the turbine at 3.25 MPa and 145°C and leaves at 80°C and 400 kPa. Isobutane is condensed in an air-cooled condenser and then pumped to the heat exchanger pressure. Assuming an isentropic efficiency of 90 percent for the pump, determine (a) the mass flow rate of isobutane in the binary cycle, (b) the net power outputs of both the flashing and the binary sections of the plant, and (c) the thermal efficiencies of the binary cycle and the combined plant Get 10.28 exercise solution

10–29C How do the following quantities change when a simple ideal Rankine cycle is modified with reheating? Assume the mass flow rate is maintained the same. Pump work input: (a) increases, (b) decreases, (c) remains the same Turbine work (a) increases, (b) decreases, output: (c) remains the same Heat supplied: (a) increases, (b) decreases, (c) remains the same Heat rejected: (a) increases, (b) decreases, (c) remains the same Moisture content (a) increases, (b) decreases, at turbine exit: (c) remains the same Get 10.29 exercise solution

10–30C Show the ideal Rankine cycle with three stages of reheating on a T-s diagram. Assume the turbine inlet temperature is the same for all stages. How does the cycle efficiency vary with the number of reheat stages? Get 10.30 exercise solution

10–31C Consider a simple Rankine cycle and an ideal Rankine cycle with three reheat stages. Both cycles operate between the same pressure limits. The maximum temperature is 700°C in the simple cycle and 450°C in the reheat cycle. Which cycle do you think will have a higher thermal efficiency? Get 10.31 exercise solution

10–32 A steam power plant operates on the ideal reheat Rankine cycle. Steam enters the highpressure turbine at 8 MPa and 500°C and leaves at 3 MPa. Steam is then reheated at constant pressure to 500°C before it expands to 20 kPa in the low-pressure turbine. Determine the turbine work output, in kJ/kg, and the thermal efficiency of the cycle. Also, show the cycle on a T-s diagram with respect to saturation lines. Get 10.32 exercise solution

10–33 Reconsider Prob. 10–32. Using EES (or other) software, solve this problem by the diagram window data entry feature of EES. Include the effects of the turbine and pump efficiencies and also show the effects of reheat on the steam quality at the low-pressure turbine exit. Plot the cycle on a T-s diagram with respect to the saturation lines. Discuss the results of your parametric studies. Get 10.33 exercise solution

10–34 Consider a steam power plant that operates on a reheat Rankine cycle and has a net power output of 80 MW. Steam enters the high-pressure turbine at 10 MPa and 500°C and the low-pressure turbine at 1 MPa and 500°C. Steam leaves the condenser as a saturated liquid at a pressure of 10 kPa. The isentropic efficiency of the turbine is 80 percent, and that of the pump is 95 percent. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality (or temperature, if superheated) of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam. Get 10.34 exercise solution

10–35 Repeat Prob. 10–34 assuming both the pump and the turbine are isentropic. Answers: (a) 0.949, (b) 41.3 percent, (c) 50.0 kg/s Get 10.35 exercise solution

10–36E Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 800 psia and 900°F and leaves as saturated vapor. Steam is then reheated to 800°F before it expands to a pressure of 1 psia. Heat is transferred to the steam in the boiler at a rate of 6 x 104 Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 45°F. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the pressure at which reheating takes place, (b) the net power output and thermal efficiency, and (c) the minimum mass flow rate of the cooling water required. Get 10.36 exercise solution

10–37 A steam power plant operates on an ideal reheat Rankine cycle between the pressure limits of 15 MPa and 10 kPa. The mass flow rate of steam through the cycle is 12 kg/s. Steam enters both stages of the turbine at 500°C. If the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10 percent, determine (a) the pressure at which reheating takes place, (b) the total rate of heat input in the boiler, and (c) the thermal efficiency of the cycle. Also, show the cycle on a T-s diagram with respect to saturation lines. Get 10.37 exercise solution

10–38 A steam power plant operates on the reheat Rankine cycle. Steam enters the high-pressure turbine at 12.5 MPa and 550°C at a rate of 7.7 kg/s and leaves at 2 MPa. Steam is then reheated at constant pressure to 450°C before it expands in the low-pressure turbine. The isentropic efficiencies of the turbine and the pump are 85 percent and 90 percent, respectively. Steam leaves the condenser as a saturated liquid. If the moisture content of the steam at the exit of the turbine is not to exceed 5 percent, determine (a) the condenser pressure, (b) the net power output, and (c) the thermal efficiency Get 10.38 exercise solution

10–39C How do the following quantities change when the simple ideal Rankine cycle is modified with regeneration? Assume the mass flow rate through the boiler is the same. Turbine work (a) increases, (b) decreases, output: (c) remains the same Heat supplied: (a) increases, (b) decreases, (c) remains the same Heat rejected: (a) increases, (b) decreases, (c) remains the same Moisture content (a) increases, (b) decreases, at turbine exit: (c) remains the same Get 10.39 exercise solution

10–40C During a regeneration process, some steam is extracted from the turbine and is used to heat the liquid water leaving the pump. This does not seem like a smart thing to do since the extracted steam could produce some more work in the turbine. How do you justify this action? Get 10.40 exercise solution

10–41C How do open feedwater heaters differ from closed feedwater heaters? Get 10.41 exercise solution

10–42C Consider a simple ideal Rankine cycle and an ideal regenerative Rankine cycle with one open feedwater heater. The two cycles are very much alike, except the feedwater in the regenerative cycle is heated by extracting some steam just before it enters the turbine. How would you compare the efficiencies of these two cycles? Get 10.42 exercise solution

10–43C Devise an ideal regenerative Rankine cycle that has the same thermal efficiency as the Carnot cycle. Show the cycle on a T-s diagram. Get 10.43 exercise solution

10–44 A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa and 450°C and is condensed in the condenser at 20 kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine (a) the net work output per kilogram of steam flowing through the boiler and (b) the thermal efficiency of the cycle. Answers: (a) 1017 kJ/kg, (b) 37.8 percent Get 10.44 exercise solution

10–45 Repeat Prob. 10–44 by replacing the open feedwater heater with a closed feedwater heater. Assume that the feedwater leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater. Get 10.45 exercise solution

10–46 A steam power plant operates on an ideal regenerative Rankine cycle with two open feedwater heaters. Steam enters the turbine at 10 MPa and 600°C and exhausts to the condenser at 5 kPa. Steam is extracted from the turbine at 0.6 and 0.2 MPa. Water leaves both feedwater heaters as a saturated liquid. The mass flow rate of steam through the boiler is 22 kg/s. Show the cycle on a T-s diagram, and determine (a) the net power output of the power plant and (b) the thermal efficiency of the cycle. Get 10.46 exercise solution

10–47 Consider an ideal steam regenerative Rankine cycle with two feedwater heaters, one closed and one open. Steam enters the turbine at 12.5 MPa and 550°C and exhausts to the condenser at 10 kPa. Steam is extracted from the turbine at 0.8 MPa for the closed feedwater heater and at 0.3 MPa for the open one. The feedwater is heated to the condensation temperature of the extracted steam in the closed feedwater heater. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the mass flow rate of steam through the boiler for a net power output of 250 MW and (b) the thermal efficiency of the cycle. Get 10.47 exercise solution

10–48 Reconsider Prob. 10–47. Using EES (or other) software, investigate the effects of turbine and pump efficiencies as they are varied from 70 percent to 100 percent on the mass flow rate and thermal efficiency. Plot the mass flow rate and the thermal efficiency as a function of turbine efficiency for pump efficiencies of 70, 85, and 100 percent, and discuss the results. Also plot the T-s diagram for turbine and pump efficiencies of 85 percent. Get 10.48 exercise solution

10–49 A steam power plant operates on an ideal reheat– regenerative Rankine cycle and has a net power output of 80 MW. Steam enters the high-pressure turbine at 10 MPa and 550°C and leaves at 0.8 MPa. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500°C and is expanded in the low-pressure turbine to the condenser pressure of 10 kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the mass flow rate of steam through the boiler and (b) the thermal efficiency of the cycle. Answers: (a) 54.5 kg/s, (b) 44.4 percent Get 10.49 exercise solution

10–50 Repeat Prob. 10–49, but replace the open feedwater heater with a closed feedwater heater. Assume that the feed water leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater. Get 10.50 exercise solution

10–51E A steam power plant operates on an ideal reheat–regenerative Rankine cycle with one reheater and two open feedwater heaters. Steam enters the high-pressure turbine at 1500 psia and 1100°F and leaves the low-pressure turbine at 1 psia. Steam is extracted from the turbine at 250 and 40 psia, and it is reheated to 1000°F at a pressure of 140 psia. Water leaves both feedwater heaters as a saturated liquid. Heat is transferred to the steam in the boiler at a rate of 4 105 Btu/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the mass flow rate of steam through the boiler, (b) the net power output of the plant, and (c) the thermal efficiency of the cycle. Get 10.51 exercise solution

10–52 A steam power plant operates on the reheatregenerative Rankine cycle with a closed feedwater heater. Steam enters the turbine at 12.5 MPa and 550°C at a rate of 24 kg/s and is condensed in the condenser at a pressure of 20 kPa. Steam is reheated at 5 MPa to 550°C. Some steam is extracted from the low-pressure turbine at 1.0 MPa, is completely condensed in the closed feedwater heater, and pumped to 12.5 MPa before it mixes with the feedwater at the same pressure. Assuming an isentropic efficiency of 88 percent for both the turbine and the pump, determine (a) the temperature of the steam at the inlet of the closed feedwater heater, (b) the mass flow rate of the steam extracted from the turbine for the closed feedwater heater, (c) the net power output, and (d) the thermal efficiency. Get 10.52 exercise solution

10–53C How can the second-law efficiency of a simple ideal Rankine cycle be improved? Get 10.53 exercise solution

10–54 Determine the exergy destruction associated with each of the processes of the Rankine cycle described in Prob. 10–15, assuming a source temperature of 1500 K and a sink temperature of 290 K. Get 10.54 exercise solution

10–55 Determine the exergy destruction associated with each of the processes of the Rankine cycle described in Prob. 10–16, assuming a source temperature of 1500 K and a sink temperature of 290 K. Get 10.55 exercise solution

10–56 Determine the exergy destruction associated with the heat rejection process in Prob. 10–22. Assume a source temperature of 1500 K and a sink temperature of 290 K. Also, determine the exergy of the steam at the boiler exit. Take P0 = 100 kPa. Get 10.56 exercise solution

10–57 Determine the exergy destruction associated with each of the processes of the reheat Rankine cycle described in Prob. 10–32. Assume a source temperature of 1800 K and a sink temperature of 300 K. Get 10.57 exercise solution

10–58 Reconsider Prob. 10–57. Using EES (or other) software, solve this problem by the diagram window data entry feature of EES. Include the effects of the turbine and pump efficiencies to evaluate the irreversibilities associated with each of the processes. Plot the cycle on a T-s diagram with respect to the saturation lines. Discuss the results of your parametric studies. Get 10.58 exercise solution

10–59 Determine the exergy destruction associated with the heat addition process and the expansion process in Prob. 10–34. Assume a source temperature of 1600 K and a sink temperature of 285 K. Also, determine the exergy of the steam at the boiler exit. Take P0 = 100 kPa. Answers: 1289 kJ/kg, 247.9 kJ/kg, 1495 kJ/kg Get 10.59 exercise solution

10–60 Determine the exergy destruction associated with the regenerative cycle described in Prob. 10–44. Assume a source temperature of 1500 K and a sink temperature of 290 K. Get 10.60 exercise solution

10–61 Determine the exergy destruction associated with the reheating and regeneration processes described in Prob. 10–49. Assume a source temperature of 1800 K and a sink temperature of 290 K. Get 10.61 exercise solution

10–62 The schematic of a single-flash geothermal power plant with state numbers is given in Fig. P10–62. Geothermal resource exists as saturated liquid at 230°C. The geothermal liquid is withdrawn from the production well at a rate of 230 kg/s and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and is directed to the turbine. The steam leaves the turbine at 10 kPa with a moisture content of 5 percent and enters the condenser where it is condensed; it is routed to a reinjection well along with the liquid coming off the separator. Determine (a) the power output of the turbine and the thermal efficiency of the plant, (b) the exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destructions and the second-law (exergetic) efficiencies for (c) the flash chamber, (d) the turbine, and (e) the entire plant. Get 10.62 exercise solution

10–63C How is the utilization factor Pu for cogeneration plants defined? Could Pu be unity for a cogeneration plant that does not produce any power? Get 10.63 exercise solution

10–64C Consider a cogeneration plant for which the utilization factor is 1. Is the irreversibility associated with this cycle necessarily zero? Explain. Get 10.64 exercise solution

10–65C Consider a cogeneration plant for which the utilization factor is 0.5. Can the exergy destruction associated with this plant be zero? If yes, under what conditions? Get 10.65 exercise solution

10–66C What is the difference between cogeneration and regeneration? Get 10.66 exercise solution

10–67 Steam enters the turbine of a cogeneration plant at 7 MPa and 500°C. One-fourth of the steam is extracted from the turbine at 600-kPa pressure for process heating. The remaining steam continues to expand to 10 kPa. The extracted steam is then condensed and mixed with feedwater at constant pressure and the mixture is pumped to the boiler pressure of 7 MPa. The mass flow rate of steam through the boiler is 30 kg/s. Disregarding any pressure drops and heat losses in the piping, and assuming the turbine and the pump to be isentropic, determine the net power produced and the utilization factor of the plant. Get 10.67 exercise solution

10–68E A large food-processing plant requires 2 lbm/s of saturated or slightly superheated steam at 80 psia, which is extracted from the turbine of a cogeneration plant. The boiler generates steam at 1000 psia and 1000°F at a rate of 5 lbm/s,and the condenser pressure is 2 psia. Steam leaves the process heater as a saturated liquid. It is then mixed with the feedwater at the same pressure and this mixture is pumped to the boiler pressure. Assuming both the pumps and the turbine have isentropic efficiencies of 86 percent, determine (a) the rate of heat transfer to the boiler and (b) the power output of the cogeneration plant. Get 10.68 exercise solution

10–69 Steam is generated in the boiler of a cogeneration plant at 10 MPa and 450°C at a steady rate of 5 kg/s. In normal operation, steam expands in a turbine to a pressure of 0.5 MPa and is then routed to the process heater, where it supplies the process heat. Steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. In this mode, no steam passes through the condenser, which operates at 20 kPa. (a) Determine the power produced and the rate at which process heat is supplied in this mode. (b) Determine the power produced and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. Get 10.69 exercise solution

10–70 Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 6 MPa and 450°C and expands to a pressure of 0.4 MPa. At this pressure, 60 percent of the steam is extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is used to heat the feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as a saturated liquid at 0.4 MPa. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines and the pumps to be isentropic, show the cycle on a T-s diagram with respect to saturation lines, and determine the mass flow rate of steam through the boiler for a net power output of 15 MW. Get 10.70 exercise solution

10–71 Reconsider Prob. 10–70. Using EES (or other) software, investigate the effect of the extraction pressure for removing steam from the turbine to be used for the process heater and open feedwater heater on the required mass flow rate. Plot the mass flow rate through the boiler as a function of the extraction pressure, and discuss the results. Get 10.71 exercise solution

10–72E Steam is generated in the boiler of a cogeneration plant at 600 psia and 800°F at a rate of 18 lbm/s. The plant is to produce power while meeting the process steam requirements for a certain industrial application. One-third of the steam leaving the boiler is throttled to a pressure of 120 psia and is routed to the process heater. The rest of the steam is expanded in an isentropic turbine to a pressure of 120 psia and is also routed to the process heater. Steam leaves the process heater at 240°F. Neglecting the pump work, determine (a) the net power produced, (b) the rate of process heat supply, and (c) the utilization factor of this plant. Get 10.72 exercise solution

10–73 A cogeneration plant is to generate power and 8600 kJ/s of process heat. Consider an ideal cogeneration steam plant. Steam enters the turbine from the boiler at 7 MPa and 500°C. One-fourth of the steam is extracted from the turbine at 600-kPa pressure for process heating. The remainder of the steam continues to expand and exhausts to the condenser at 10 kPa. The steam extracted for the process heater is condensed in the heater and mixed with the feedwater at 600 kPa. The mixture is pumped to the boiler pressure of 7 MPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the mass flow rate of steam that must be supplied by the boiler, (b) the net power produced by the plant, and (c) the utilization factor. Get 10.73 exercise solution

10–74C In combined gas–steam cycles, what is the energy source for the steam? Get 10.74 exercise solution

10–75C Why is the combined gas–steam cycle more efficient than either of the cycles operated alone? Get 10.75 exercise solution

10–76 The gas-turbine portion of a combined gas–steam power plant has a pressure ratio of 16. Air enters the compressor at 300 K at a rate of 14 kg/s and is heated to 1500 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400°C at 10 MPa in a heat exchanger. The combustion gases leave the heat exchanger at 420 K. The steam leaving the turbine is condensed at 15 kPa. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate of the steam, (b) the net power output, and (c) the thermal efficiency of the combined cycle. For air, assume constant specific heats at room temperature. Get 10.76 exercise solution

10–77 Consider a combined gas–steam power plant that has a net power output of 450 MW. The pressure ratio of the gas-turbine cycle is 14. Air enters the compressor at 300 K and the turbine at 1400 K. The combustion gases leaving the gas turbine are used to heat the steam at 8 MPa to 400°C in a heat exchanger. The combustion gases leave the heat exchanger at 460 K. An open feedwater heater incorporated with the steam cycle operates at a pressure of 0.6 MPa. The condenser pressure is 20 kPa. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate ratio of air to steam, (b) the required rate of heat input in the combustion chamber, and (c) the thermal efficiency of the combined cycle. Get 10.77 exercise solution

10–78 Reconsider Prob. 10–77. Using EES (or other) software, study the effects of the gas cycle pressure ratio as it is varied from 10 to 20 on the ratio of gas flow rate to steam flow rate and cycle thermal efficiency. Plot your results as functions of gas cycle pressure ratio, and discuss the results. Get 10.78 exercise solution

10–79 Repeat Prob. 10–77 assuming isentropic efficiencies of 100 percent for the pump, 82 percent for the compressor, and 86 percent for the gas and steam turbines. Get 10.79 exercise solution

10–80 Reconsider Prob. 10–79. Using EES (or other) software, study the effects of the gas cycle pressure ratio as it is varied from 10 to 20 on the ratio of gas flow rate to steam flow rate and cycle thermal efficiency. Plot your results as functions of gas cycle pressure ratio, and discuss the results. Get 10.80 exercise solution

10–81 Consider a combined gas–steam power cycle. The topping cycle is a simple Brayton cycle that has a pressure ratio of 7. Air enters the compressor at 15°C at a rate of 10 kg/s and the gas turbine at 950°C. The bottoming cycle is a reheat Rankine cycle between the pressure limits of 6 MPa and 10 kPa. Steam is heated in a heat exchanger at a rate of 1.15 kg/s by the exhaust gases leaving the gas turbine and the exhaust gases leave the heat exchanger at 200°C. Steam leaves the high-pressure turbine at 1.0 MPa and is reheated to 400°C in the heat exchanger before it expands in the lowpressure turbine. Assuming 80 percent isentropic efficiency for all pumps and turbine, determine (a) the moisture content at the exit of the low-pressure turbine, (b) the steam temperature at the inlet of the high-pressure turbine, (c) the net power output and the thermal efficiency of the combined plant. Get 10.81 exercise solution

10–82C What is a binary power cycle? What is its purpose? Get 10.82 exercise solution

10–83C By writing an energy balance on the heat exchanger of a binary vapor power cycle, obtain a relation for the ratio of mass flow rates of two fluids in terms of their enthalpies. Get 10.83 exercise solution

10–84C Why is steam not an ideal working fluid for vapor power cycles? Get 10.84 exercise solution

10–85C Why is mercury a suitable working fluid for the topping portion of a binary vapor cycle but not for the bottoming cycle? Get 10.85 exercise solution

10–86C What is the difference between the binary vapor power cycle and the combined gas–steam power cycle? Get 10.86 exercise solution

10–87 Show that the thermal efficiency of a combined gas–steam power plant hcc can be expressed as hcc = hg + hs - hghs where hg = Wg/Qin and hs = Ws/Qg,out are the thermal efficiencies of the gas and steam cycles, respectively. Using this relation, determine the thermal efficiency of a combined power cycle that consists of a topping gas-turbine cycle with an efficiency of 40 percent and a bottoming steam-turbine cycle with an efficiency of 30 percent. Get 10.87 exercise solution

10–88 It can be shown that the thermal efficiency of a combined gas–steam power plant hcc can be expressed in terms of the thermal efficiencies of the gas- and the steam-turbine cycles as hcc = hg + hs - hghs Prove that the value of hcc is greater than either of hg or hs. That is, the combined cycle is more efficient than either of the gas-turbine or steam-turbine cycles alone. Get 10.88 exercise solution

10–89 Consider a steam power plant operating on the ideal Rankine cycle with reheat between the pressure limits of 25 MPa and 10 kPa with a maximum cycle temperature of 600°C and a moisture content of 8 percent at the turbine exit. For a reheat temperature of 600°C, determine the reheat pressures of the cycle for the cases of (a) single and (b) double reheat. Get 10.89 exercise solution

10–90E The Stillwater geothermal power plant in Nevada, which started full commercial operation in 1986, is designed to operate with seven identical units. Each of these seven units consists of a pair of power cycles, labeled Level I and Level II, operating on the simple Rankine cycle using an organic fluid as the working fluid. The heat source for the plant is geothermal water (brine) entering the vaporizer (boiler) of Level I of each unit at 325°F at a rate of 384,286 lbm/h and delivering 22.79 MBtu/h (“M” stands for “million”). The organic fluid that enters the vaporizer at 202.2°F at a rate of 157,895 lbm/h leaves it at 282.4°F and 225.8 psia as saturated vapor. This saturated vapor expands in the turbine to 95.8°F and 19.0 psia and produces 1271 kW of electric power. About 200 kW of this power is used by the pumps, the auxiliaries, and the six fans of the condenser. Subsequently, the organic working fluid is condensed in an air-cooled condenser by air that enters the condenser at 55°F at a rate of 4,195,100 lbm/h and leaves at 84.5°F. The working fluid is pumped and then preheated in a preheater to 202.2°F by absorbing 11.14 MBtu/h of heat from the geothermal water (coming from the vaporizer of Level II) entering the preheater at 211.8°F and leaving at 154.0°F. Taking the average specific heat of the geothermal water to be 1.03 Btu/lbm · °F, determine (a) the exit temperature of the geothermal water from the vaporizer, (b) the rate of heat rejection from the working fluid to the air in the condenser, (c) the mass flow rate of the geothermal water at the preheater, and (d) the thermal efficiency of the Level I cycle of this geothermal power plant. Get 10.90 exercise solution

10–91 Steam enters the turbine of a steam power plant that operates on a simple ideal Rankine cycle at a pressure of 6 MPa, and it leaves as a saturated vapor at 7.5 kPa. Heat is transferred to the steam in the boiler at a rate of 40,000 kJ/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 15°C. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the turbine inlet temperature, (b) the net power output and thermal efficiency, and (c) the minimum mass flow rate of the cooling water required. Get 10.91 exercise solution

10–92 A steam power plant operates on an ideal Rankine cycle with two stages of reheat and has a net power output of 120 MW. Steam enters all three stages of the turbine at 500°C. The maximum pressure in the cycle is 15 MPa, and the minimum pressure is 5 kPa. Steam is reheated at 5 MPa the first time and at 1 MPa the second time. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of the steam. Answers: (a) 45.5 percent, (b) 64.4 kg/s Get 10.92 exercise solution

10–93 Consider a steam power plant that operates on a regenerative Rankine cycle and has a net power output of 150 MW. Steam enters the turbine at 10 MPa and 500°C and the condenser at 10 kPa. The isentropic efficiency of the turbine is 80 percent, and that of the pumps is 95 percent. Steam is extracted from the turbine at 0.5 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine (a) the mass flow rate of steam through the boiler and (b) the thermal efficiency of the cycle. Also, determine the exergy destruction associated with the regeneration process. Assume a source temperature of 1300 K and a sink temperature of 303 K. Get 10.93 exercise solution

10–94 Repeat Prob. 10–93 assuming both the pump and the turbine are isentropic. Get 10.94 exercise solution

10–95 Consider an ideal reheat–regenerative Rankine cycle with one open feedwater heater. The boiler pressure is 10 MPa, the condenser pressure is 15 kPa, the reheater pressure is 1 MPa, and the feedwater pressure is 0.6 MPa. Steam enters both the high- and low-pressure turbines at 500°C. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the fraction of steam extracted for regeneration and (b) the thermal efficiency of the cycle Get 10.95 exercise solution

10–96 Repeat Prob. 10–95 assuming an isentropic efficiency of 84 percent for the turbines and 100 percent for the pumps. Get 10.96 exercise solution

10–97 A steam power plant operates on an ideal reheat– regenerative Rankine cycle with one reheater and two feedwater heaters, one open and one closed. Steam enters the high-pressure turbine at 15 MPa and 600°C and the lowpressure turbine at 1 MPa and 500°C. The condenser pressure is 5 kPa. Steam is extracted from the turbine at 0.6 MPa for the closed feedwater heater and at 0.2 MPa for the open feedwater heater. In the closed feedwater heater, the feedwater is heated to the condensation temperature of the extracted steam. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the fraction of steam extracted from the turbine for the open feedwater heater, (b) the thermal efficiency of the cycle, and (c) the net power output for a mass flow rate of 42 kg/s through the boiler. Get 10.97 exercise solution

10–98 Consider a cogeneration power plant that is modified with reheat and that produces 3 MW of power and supplies 7 MW of process heat. Steam enters the high-pressure turbine at 8 MPa and 500°C and expands to a pressure of 1 MPa. At this pressure, part of the steam is extracted from the turbine and routed to the process heater, while the remainder is reheated to 500°C and expanded in the low-pressure turbine to the condenser pressure of 15 kPa. The condensate from the condenser is pumped to 1 MPa and is mixed with the extracted steam, which leaves the process heater as a compressed liquid at 120°C. The mixture is then pumped to the boiler pressure. Assuming the turbine to be isentropic, show the cycle on a T-s diagram with respect to saturation lines, and disregarding pump work, determine (a) the rate of heat input in the boiler and (b) the fraction of steam extracted for process heating. Get 10.98 exercise solution

10–99 The gas-turbine cycle of a combined gas–steam power plant has a pressure ratio of 8. Air enters the compressor at 290 K and the turbine at 1400 K. The combustion gases leaving the gas turbine are used to heat the steam at 15 MPa to 450°C in a heat exchanger. The combustion gases leave the heat exchanger at 247°C. Steam expands in a highpressure turbine to a pressure of 3 MPa and is reheated in the combustion chamber to 500°C before it expands in a lowpressure turbine to 10 kPa. The mass flow rate of steam is 30 kg/s. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate of air in the gas-turbine cycle, (b) the rate of total heat input, and (c) the thermal efficiency of the combined cycle. Get 10.99 exercise solution

10–100 Repeat Prob. 10–99 assuming isentropic efficiencies of 100 percent for the pump, 80 percent for the compressor, and 85 percent for the gas and steam turbines. Get 10.100 exercise solution

10–101 Starting with Eq. 10–20, show that the exergy destruction associated with a simple ideal Rankine cycle can be expressed as i = qin(hth,Carnot - hth), where hth is efficiency of the Rankine cycle and hth,Carnot is the efficiency of the Carnot cycle operating between the same temperature limits. Get 10.101 exercise solution

10–102 Steam is to be supplied from a boiler to a highpressure turbine whose isentropic efficiency is 75 percent at conditions to be determined. The steam is to leave the high-pressure turbine as a saturated vapor at 1.4 MPa, and the turbine is to produce 1 MW of power. Steam at the turbine exit is extracted at a rate of 1000 kg/min and routed to a process heater while the rest of the steam is supplied to a low-pressure turbine whose isentropic efficiency is 60 percent. The low-pressure turbine allows the steam to expand to 10 kPa pressure and produces 0.8 MW of power. Determine the temperature, pressure, and the flow rate of steam at the inlet of the high-pressure turbine. Get 10.102 exercise solution

10–103 A textile plant requires 4 kg/s of saturated steam at 2 MPa, which is extracted from the turbine of a cogeneration plant. Steam enters the turbine at 8 MPa and 500°C at a rate of 11 kg/s and leaves at 20 kPa. The extracted steam leaves the process heater as a saturated liquid and mixes with the feedwater at constant pressure. The mixture is pumped to the boiler pressure. Assuming an isentropic efficiency of 88 percent for both the turbine and the pumps, determine (a) the rate of process heat supply, (b) the net power output, and (c) the utilization factor of the plant. Get 10.103 exercise solution

10–104 Using EES (or other) software, investigate the effect of the condenser pressure on the performance of a simple ideal Rankine cycle. Turbine inlet conditions of steam are maintained constant at 5 MPa and 500°C while the condenser pressure is varied from 5 to 100 kPa. Determine the thermal efficiency of the cycle and plot it against the condenser pressure, and discuss the results. Get 10.104 exercise solution

10–105 Using EES (or other) software, investigate the effect of the boiler pressure on the performance of a simple ideal Rankine cycle. Steam enters the turbine at 500°C and exits at 10 kPa. The boiler pressure is varied from 0.5 to 20 MPa. Determine the thermal efficiency of the cycle and plot it against the boiler pressure, and discuss the results. Get 10.105 exercise solution

10–106 Using EES (or other) software, investigate the effect of superheating the steam on the performance of a simple ideal Rankine cycle. Steam enters the turbine at 3 MPa and exits at 10 kPa. The turbine inlet temperature is varied from 250 to 1100°C. Determine the thermal efficiency of the cycle and plot it against the turbine inlet temperature, and discuss the results. Get 10.106 exercise solution

10–107 Using EES (or other) software, investigate the effect of reheat pressure on the performance of an ideal Rankine cycle. The maximum and minimum pressures in the cycle are 15 MPa and 10 kPa, respectively, and steam enters both stages of the turbine at 500°C. The reheat pressure is varied from 12.5 to 0.5 MPa. Determine the thermal efficiency of the cycle and plot it against the reheat pressure, and discuss the results. Get 10.107 exercise solution

10–108 Using EES (or other) software, investigate the effect of number of reheat stages on the performance of an ideal Rankine cycle. The maximum and minimum pressures in the cycle are 15 MPa and 10 kPa, respectively, and steam enters all stages of the turbine at 500°C. For each case, maintain roughly the same pressure ratio across each turbine stage. Determine the thermal efficiency of the cycle and plot it against the number of reheat stages 1, 2, 4, and 8, and discuss the results. Get 10.108 exercise solution

10–109 Using EES (or other) software, investigate the effect of extraction pressure on the performance of an ideal regenerative Rankine cycle with one open feedwater heater. Steam enters the turbine at 15 MPa and 600°C and the condenser at 10 kPa. Determine the thermal efficiency of the cycle, and plot it against extraction pressures of 12.5, 10, 7, 5, 2, 1, 0.5, 0.1, and 0.05 MPa, and discuss the results. Get 10.109 exercise solution

10–110 Using EES (or other) software, investigate the effect of the number of regeneration stages on the performance of an ideal regenerative Rankine cycle. Steam enters the turbine at 15 MPa and 600°C and the condenser at 5 kPa. For each case, maintain about the same temperature difference between any two regeneration stages. Determine the thermal efficiency of the cycle, and plot it against the number of regeneration stages for 1, 2, 3, 4, 5, 6, 8, and 10 regeneration stages. Fundamentals of Engineering (FE) Exam Problems Get 10.110 exercise solution

10–111 Consider a steady-flow Carnot cycle with water as the working fluid executed under the saturation dome between the pressure limits of 8 MPa and 20 kPa. Water changes from saturated liquid to saturated vapor during the heat addition process. The net work output of this cycle is (a) 494 kJ/kg (b) 975 kJ/kg (c) 596 kJ/kg (d) 845 kJ/kg (e) 1148 kJ/kg Get 10.111 exercise solution

10–112 A simple ideal Rankine cycle operates between the pressure limits of 10 kPa and 3 MPa, with a turbine inlet temperature of 600°C. Disregarding the pump work, the cycle efficiency is (a) 24 percent (b) 37 percent (c) 52 percent (d) 63 percent (e) 71 percent Get 10.112 exercise solution

10–113 A simple ideal Rankine cycle operates between the pressure limits of 10 kPa and 5 MPa, with a turbine inlet temperature of 600°C. The mass fraction of steam that condenses at the turbine exit is (a) 6 percent (b) 9 percent (c) 12 percent (d) 15 percent (e) 18 percent Get 10.113 exercise solution

10–114 A steam power plant operates on the simple ideal Rankine cycle between the pressure limits of 10 kPa and 10 MPa, with a turbine inlet temperature of 600°C. The rate of heat transfer in the boiler is 800 kJ/s. Disregarding the pump work, the power output of this plant is (a) 243 kW (b) 284 kW (c) 508 kW (d) 335 kW (e) 800 kW Get 10.114 exercise solution

10–115 Consider a combined gas-steam power plant. Water for the steam cycle is heated in a well-insulated heat exchanger by the exhaust gases that enter at 800 K at a rate of 60 kg/s and leave at 400 K. Water enters the heat exchanger at 200°C and 8 MPa and leaves at 350°C and 8 MPa. If the exhaust gases are treated as air with constant specific heats at room temperature, the mass flow rate of water through the heat exchanger becomes (a) 11 kg/s (b) 24 kg/s (c) 46 kg/s (d) 53 kg/s (e) 60 kg/s Get 10.115 exercise solution

10–116 An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with reheat occurring at 4 MPa. The temperature of steam at the inlets of both turbines is 500°C, and the enthalpy of steam is 3185 kJ/kg at the exit of the high-pressure turbine, and 2247 kJ/kg at the exit of the low-pressure turbine. Disregarding the pump work, the cycle efficiency is (a) 29 percent (b) 32 percent (c) 36 percent (d) 41 percent (e) 49 percent Get 10.116 exercise solution

10–117 Pressurized feedwater in a steam power plant is to be heated in an ideal open feedwater heater that operates at a pressure of 0.5 MPa with steam extracted from the turbine. If the enthalpy of feedwater is 252 kJ/kg and the enthalpy of extracted steam is 2665 kJ/kg, the mass fraction of steam extracted from the turbine is (a) 4 percent (b) 10 percent (c) 16 percent (d) 27 percent (e) 12 percent Get 10.117 exercise solution

10–118 Consider a steam power plant that operates on the regenerative Rankine cycle with one open feedwater heater. The enthalpy of the steam is 3374 kJ/kg at the turbine inlet, 2797 kJ/kg at the location of bleeding, and 2346 kJ/kg at the turbine exit. The net power output of the plant is 120 MW, and the fraction of steam bled off the turbine for regeneration is 0.172. If the pump work is negligible, the mass flow rate of steam at the turbine inlet is (a) 117 kg/s (b) 126 kg/s (c) 219 kg/s (d) 268 kg/s (e) 679 kg/s Get 10.118 exercise solution

10–119 Consider a simple ideal Rankine cycle. If the condenser pressure is lowered while keeping turbine inlet state the same, (a) the turbine work output will decrease. (b) the amount of heat rejected will decrease. (c) the cycle efficiency will decrease. (d) the moisture content at turbine exit will decrease. (e) the pump work input will decrease. Get 10.119 exercise solution

10–120 Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the steam is superheated to a higher temperature, (a) the turbine work output will decrease. (b) the amount of heat rejected will decrease. (c) the cycle efficiency will decrease. (d) the moisture content at turbine exit will decrease. (e) the amount of heat input will decrease. Get 10.120 exercise solution

10–121 Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with reheating, (a) the turbine work output will decrease. (b) the amount of heat rejected will decrease. (c) the pump work input will decrease. (d) the moisture content at turbine exit will decrease. (e) the amount of heat input will decrease. Get 10.121 exercise solution

10–122 Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with regeneration that involves one open feedwater heater (select the correct statement per unit mass of steam flowing through the boiler), (a) the turbine work output will decrease. (b) the amount of heat rejected will increase. (c) the cycle thermal efficiency will decrease. (d) the quality of steam at turbine exit will decrease. (e) the amount of heat input will increase. Get 10.122 exercise solution

10–123 Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 6 MPa and 450°C at a rate of 20 kg/s and expands to a pressure of 0.4 MPa. At this pressure, 60 percent of the steam is extracted from the turbine, and the remainder expands to a pressure of 10 kPa. Part of the extracted steam is used to heat feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as a saturated liquid at 0.4 MPa. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. The steam in the condenser is cooled and condensed by the cooling water from a nearby river, which enters the adiabatic condenser at a rate of 463 kg/s. 1. The total power output of the turbine is (a) 17.0 MW (b) 8.4 MW (c) 12.2 MW (d) 20.0 MW (e) 3.4 MW 2. The temperature rise of the cooling water from the river in the condenser is (a) 8.0°C (b) 5.2°C (c) 9.6°C (d) 12.9°C (e) 16.2°C 3. The mass flow rate of steam through the process heater is (a) 1.6 kg/s (b) 3.8 kg/s (c) 5.2 kg/s (d) 7.6 kg/s (e) 10.4 kg/s 4. The rate of heat supply from the process heater per unit mass of steam passing through it is (a) 246 kJ/kg (b) 893 kJ/kg (c) 1344 kJ/kg (d) 1891 kJ/kg (e) 2060 kJ/kg 5. The rate of heat transfer to the steam in the boiler is (a) 26.0 MJ/s (b) 53.8 MJ/s (c) 39.5 MJ/s (d) 62.8 MJ/s (e) 125.4 MJ/s Get 10.123 exercise solution