5–1C Name four physical quantities that are conserved and two quantities that are not conserved during a process.
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5–2C Define mass and volume flow rates. How are they related to each other?
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5–3C
Does the amount of mass entering a control volume have to be equal to
the amount of mass leaving during an unsteady-flow process?
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5–4C When is the flow through a control volume steady?
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5–5C
Consider a device with one inlet and one outlet. If the volume flow
rates at the inlet and at the outlet are the same, is the flow through
this device necessarily steady? Why?
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5–6E
A garden hose attached with a nozzle is used to fill a 20-gal bucket.
The inner diameter of the hose is 1 in and it reduces to 0.5 in at the
nozzle exit. If the average velocity in the hose is 8 ft/s, determine
(a) the volume and mass flow rates of water through the hose, (b) how
long it will take to fill the bucket with water, and (c) the average
velocity of water at the nozzle exit.
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5–7
Air enters a nozzle steadily at 2.21 kg/m3 and 40 m/s and leaves at
0.762 kg/m3 and 180 m/s. If the inlet area of the nozzle is 90 cm2,
determine (a) the mass flow rate through the nozzle, and (b) the exit
area of the nozzle. Answers: (a) 0.796 kg/s, (b) 58 cm2
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5–8
A hair dryer is basically a duct of constant diameter in which a few
layers of electric resistors are placed. A small fan pulls the air in
and forces it through the resistors where it is heated. If the density
of air is 1.20 kg/m3 at the inlet and 1.05 kg/m3 at the exit, determine
the percent increase in the velocity of air as it flows through the
dryer.
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5–9E
Air whose density is 0.078 lbm/ft3 enters the duct of an
air-conditioning system at a volume flow rate of 450 ft3/min. If the
diameter of the duct is 10 in, determine the velocity of the air at the
duct inlet and the mass flow rate of air.
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5–10
A 1-m3 rigid tank initially contains air whose density is 1.18 kg/m3.
The tank is connected to a high-pressure supply line through a valve.
The valve is opened, and air is allowed to enter the tank until the
density in the tank rises to 7.20 kg/m3. Determine the mass of air that
has entered the tank. Answer: 6.02 kg
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5–11
The ventilating fan of the bathroom of a building has a volume flow
rate of 30 L/s and runs continuously. If the density of air inside is
1.20 kg/m3, determine the mass of air vented out in one day.
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5–12
A desktop computer is to be cooled by a fan whose flow rate is 0.34
m3/min. Determine the mass flow rate of air through the fan at an
elevation of 3400 m where the air density is 0.7 kg/m3. Also, if the
average velocity of air is not to exceed 110 m/min, determine the
diameter of the casing of the fan.
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5–13
A smoking lounge is to accommodate 15 heavy smokers. The minimum fresh
air requirement for smoking lounges is specified to be 30 L/s per person
(ASHRAE, Standard 62, 1989). Determine the minimum required flow rate
of fresh air that needs to be supplied to the lounge, and the diameter
of the duct if the air velocity is not to exceed 8 m/s.
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5–14
The minimum fresh air requirement of a residential building is
specified to be 0.35 air change per hour (ASHRAE, Standard 62, 1989).
That is, 35 percent of the entire air contained in a residence should be
replaced by fresh outdoor air every hour. If the ventilation
requirement of a 2.7-m-high, 200-m2 residence is to be met entirely by a
fan, determine the flow capacity in L/min of the fan that needs to be
installed. Also determine the diameter of the duct if the air velocity
is not to exceed 6 m/s.
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5–15
Air enters a 28-cm diameter pipe steadily at 200 kPa and 20°C with a
velocity of 5 m/s. Air is heated as it flows, and leaves the pipe at 180
kPa and 40°C. Determine (a) the volume flow rate of air at the inlet,
(b) the mass flow rate of air, and (c) the velocity and volume flow rate
at the exit.
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5–16
Refrigerant-134a enters a 28-cm diameter pipe steadily at 200 kPa and
20°C with a velocity of 5 m/s. The refrigerant gains heat as it flows
and leaves the pipe at 180 kPa and 40°C. Determine (a) the volume flow
rate of the refrigerant at the inlet, (b) the mass flow rate of the
refrigerant, and (c) the velocity and volume flow rate at the exit.
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5–17
Consider a 300-L storage tank of a solar water heating system initially
filled with warm water at 45°C. Warm water is withdrawn from the tank
through a 2-cm diameter hose at an average velocity of 0.5 m/s while
cold water enters the tank at 20°C at a rate of 5 L/min. Determine the
amount of water in the tank after a 20-minute period. Assume the
pressure in the tank remains constant at 1 atm.
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5–18C What are the different mechanisms for transferring energy to or from a control volume?
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5–19C What is flow energy? Do fluids at rest possess any flow energy?
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5–20C
How do the energies of a flowing fluid and a fluid at rest compare?
Name the specific forms of energy associated with each case.
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5–21E
Steam is leaving a pressure cooker whose operating pressure is 30 psia.
It is observed that the amount of liquid in the cooker has decreased by
0.4 gal in 45 minutes after the steady operating conditions are
established, and the crosssectional area of the exit opening is 0.15
in2. Determine (a) the mass flow rate of the steam and the exit velocity
(b) the total and flow energies of the steam per unit mass, and (c) the
rate at which energy is leaving the cooker by steam.
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5–22
Refrigerant-134a enters the compressor of a refrigeration system as
saturated vapor at 0.14 MPa, and leaves as superheated vapor at 0.8 MPa
and 60°C at a rate of 0.06 kg/s. Determine the rates of energy transfers
by mass into and out of the compressor. Assume the kinetic and
potential energies to be negligible.
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5–23
A house is maintained at 1 atm and 24°C, and warm air inside a house is
forced to leave the house at a rate of 150 m3/h as a result of outdoor
air at 5°C infiltrating into the house through the cracks. Determine the
rate of net energy loss of the house due to mass transfer. Answer:
0.945 kW
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5–24
Air flows steadily in a pipe at 300 kPa, 77°C, and 25 m/s at a rate of
18 kg/min. Determine (a) the diameter of the pipe, (b) the rate of flow
energy, (c) the rate of energy transport by mass, and (d) also determine
the error involved in part (c) if the kinetic energy is neglected.
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5–25C How is a steady-flow system characterized?
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5–26C Can a steady-flow system involve boundary work?
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5–27C
A diffuser is an adiabatic device that decreases the kinetic energy of
the fluid by slowing it down. What happens to this lost kinetic energy?
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5–28C The kinetic energy of a fluid increases as it is accelerated in an adiabatic nozzle. Where does this energy come from?
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5–29C
Is heat transfer to or from the fluid desirable as it flows through a
nozzle? How will heat transfer affect the fluid velocity at the nozzle
exit?
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5–30
Air enters an adiabatic nozzle steadily at 300 kPa, 200°C, and 30 m/s
and leaves at 100 kPa and 180 m/s. The inlet area of the nozzle is 80
cm2. Determine (a) the mass flow rate through the nozzle, (b) the exit
temperature of the air, and (c) the exit area of the nozzle.
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5–31
Reconsider Prob. 5–30. Using EES (or other) software, investigate the
effect of the inlet area on the mass flow rate, exit temperature, and
the exit area. Let the inlet area vary from 50 cm2 to 150 cm2. Plot the
final results against the inlet area, and discuss the results.
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5–32
Steam at 5 MPa and 400°C enters a nozzle steadily with a velocity of 80
m/s, and it leaves at 2 MPa and 300°C. The inlet area of the nozzle is
50 cm2, and heat is being lost at a rate of 120 kJ/s. Determine (a) the
mass flow rate of the steam, (b) the exit velocity of the steam, and (c)
the exit area of the nozzle.
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5–33E
Air enters a nozzle steadily at 50 psia, 140°F, and 150 ft/s and leaves
at 14.7 psia and 900 ft/s. The heat loss from the nozzle is estimated
to be 6.5 Btu/lbm of air flowing. The inlet area of the nozzle is 0.1
ft2. Determine (a) the exit temperature of air and (b) the exit area of
the nozzle.
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5–34
Steam at 3 MPa and 400°C enters an adiabatic nozzle steadily with a
velocity of 40 m/s and leaves at 2.5 MPa and 300 m/s. Determine (a) the
exit temperature and (b) the ratio of the inlet to exit area A1/A2.
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5–35
Air at 600 kPa and 500 K enters an adiabatic nozzle that has an
inlet-to-exit area ratio of 2:1 with a velocity of leaves at 100 kPa and
450 m/s. The inlet area of the nozzle is 40 cm2. Determine (a) the
inlet velocity and (b) the exit temperature.
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5–36
Air at 80 kPa and 127°C enters an adiabatic diffuser steadily at a rate
of 6000 kg/h and leaves at 100 kPa. The velocity of the airstream is
decreased from 230 to 30 m/s as it passes through the diffuser. Find (a)
the exit temperature of the air and (b) the exit area of the diffuser.
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5–37E
Air at 13 psia and 20°F enters an adiabatic diffuser steadily with a
velocity of 600 ft/s and leaves with a low velocity at a pressure of
14.5 psia. The exit area of the diffuser is 5 times the inlet area.
Determine (a) the exit temperature and (b) the exit velocity of the air.
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5–38
Carbon dioxide enters an adiabatic nozzle steadily at 1 MPa and 500°C
with a mass flow rate of 6000 kg/h and leaves at 100 kPa and 450 m/s.
The inlet area of the nozzle is 40 cm2. Determine (a) the inlet velocity
and (b) the exit temperature.
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5–39
Refrigerant-134a at 700 kPa and 120°C enters an adiabatic nozzle
steadily with a velocity of 20 m/s and leaves at 400 kPa and 30°C.
Determine (a) the exit velocity and (b) the ratio of the inlet to exit
area A1/A2.
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5–40
Air at 80 kPa, 27°C, and 220 m/s enters a diffuser at a rate of 2.5
kg/s and leaves at 42°C. The exit area of the diffuser is 400 cm2. The
air is estimated to lose heat at a rate of 18 kJ/s during this process.
Determine (a) the exit velocity and (b) the exit pressure of the air.
Answers: (a) 62.0 m/s, (b) 91.1 kPa
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5–41
Nitrogen gas at 60 kPa and 7°C enters an adiabatic diffuser steadily
with a velocity of 200 m/s and leaves at 85 kPa and 22°C. Determine (a)
the exit velocity of the nitrogen and (b) the ratio of the inlet to exit
area A1/A2.
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5–42
Reconsider Prob. 5–41. Using EES (or other) software, investigate the
effect of the inlet velocity on the exit velocity and the ratio of the
inlet-to-exit area. Let the inlet velocity vary from 180 to 260 m/s.
Plot the final results against the inlet velocity, and discuss the
results.
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5–43
Refrigerant-134a enters a diffuser steadily as saturated vapor at 800
kPa with a velocity of 120 m/s, and it leaves at 900 kPa and 40°C. The
refrigerant is gaining heat at a rate of 2 kJ/s as it passes through the
diffuser. If the exit area is 80 percent greater than the inlet area,
determine (a) the exit velocity and (b) the mass flow rate of the
refrigerant.
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5–44
Steam enters a nozzle at 400°C and 800 kPa with a velocity of 10 m/s,
and leaves at 300°C and 200 kPa while losing heat at a rate of 25 kW.
For an inlet area of 800 cm2, determine the velocity and the volume flow
rate of the steam at the nozzle exit.
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5–45C
Consider an adiabatic turbine operating steadily. Does the work output
of the turbine have to be equal to the decrease in the energy of the
steam flowing through it?
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5–46C
Consider an air compressor operating steadily. How would you compare
the volume flow rates of the air at the compressor inlet and exit?
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5–47C Will the temperature of air rise as it is compressed by an adiabatic compressor? Why?
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5–48C
Somebody proposes the following system to cool a house in the summer:
Compress the regular outdoor air, let it cool back to the outdoor
temperature, pass it through a turbine, and discharge the cold air
leaving the turbine into the house. From a thermodynamic point of view,
is the proposed system sound?
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5–49
Steam flows steadily through an adiabatic turbine. The inlet conditions
of the steam are 10 MPa, 450°C, and 80 m/s, and the exit conditions are
10 kPa, 92 percent quality, and 50 m/s. The mass flow rate of the steam
is 12 kg/s. Determine (a) the change in kinetic energy, (b) the power
output, and (c) the turbine inlet area. Answers: (a) -1.95 kJ/kg, (b)
10.2 MW, (c) 0.00447 m2
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5–50
Reconsider Prob. 5–49. Using EES (or other) software, investigate the
effect of the turbine exit pressure on the power output of the turbine.
Let the exit pressure vary from 10 to 200 kPa. Plot the power output
against the exit pressure, and discuss the results.
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5–51
Steam enters an adiabatic turbine at 10 MPa and 500°C and leaves at 10
kPa with a quality of 90 percent. Neglecting the changes in kinetic and
potential energies, determine the mass flow rate required for a power
output of 5 MW.
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5–52E
Steam flows steadily through a turbine at a rate of 45,000 lbm/h,
entering at 1000 psia and 900°F and leaving at 5 psia as saturated
vapor. If the power generated by the turbine is 4 MW, determine the rate
of heat loss from the steam.
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5–53
Steam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 3
kg/s and leaves at 20 kPa. If the power output of the turbine is 2.5 MW,
determine the temperature of the steam at the turbine exit. Neglect
kinetic energy changes. Answer: 60.1°C
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5–54
Argon gas enters an adiabatic turbine steadily at 900 kPa and 450°C
with a velocity of 80 m/s and leaves at 150 kPa with a velocity of 150
m/s. The inlet area of the turbine is 60 cm2. If the power output of the
turbine is 250 kW, determine the exit temperature of the argon.
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5–55E
Air flows steadily through an adiabatic turbine, entering at 150 psia,
900°F, and 350 ft/s and leaving at 20 psia 300°F, and 700 ft/s. The
inlet area of the turbine is 0.1 ft2. Determine (a) the mass flow rate
of the air and (b) the power output of the turbine.
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5–56
Refrigerant-134a enters an adiabatic compressor as saturated vapor at
-24°C and leaves at 0.8 MPa and 60°C. The mass flow rate of the
refrigerant is 1.2 kg/s. Determine (a) the power input to the compressor
and (b) the volume flow rate of the refrigerant at the compressor
inlet.
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5–57
Air enters the compressor of a gas-turbine plant at ambient conditions
of 100 kPa and 25°C with a low velocity and exits at 1 MPa and 347°C
with a velocity of 90 m/s. The compressor is cooled at a rate of 1500
kJ/min, and the power input to the compressor is 250 kW. Determine the
mass flow rate of air through the compressor.
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5–58E
Air is compressed from 14.7 psia and 60°F to a pressure of 150 psia
while being cooled at a rate of 10 Btu/lbm by circulating water through
the compressor casing. The volume flow rate of the air at the inlet
conditions is 5000 ft3/min, and the power input to the compressor is 700
hp. Determine (a) the mass flow rate of the air and (b) the temperature
at the compressor exit.
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5–59E
Reconsider Prob. 5–58E. Using EES (or other) software, investigate the
effect of the rate of cooling of the compressor on the exit temperature
of air. Let the cooling rate vary from 0 to 100 Btu/lbm. Plot the air
exit temperature against the rate of cooling, and discuss the results.
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5–60
Helium is to be compressed from 120 kPa and 310 K to 700 kPa and 430 K.
A heat loss of 20 kJ/kg occurs during the compression process.
Neglecting kinetic energy changes, determine the power input required
for a mass flow rate of 90 kg/min.
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5–61
Carbon dioxide enters an adiabatic compressor at 100 kPa and 300 K at a
rate of 0.5 kg/s and leaves at 600 kPa and 450 K. Neglecting kinetic
energy changes, determine (a) the volume flow rate of the carbon dioxide
at the compressor inlet and (b) the power input to the compressor.
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5–62C Why are throttling devices commonly used in refrigeration and air-conditioning applications?
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5–63C During a throttling process, the temperature of a fluid drops from 30 to -20°C. Can this process occur adiabatically?
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5–64C Would you expect the temperature of air to drop as it undergoes a steady-flow throttling process? Explain.
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5–65C Would you expect the temperature of a liquid to change as it is throttled? Explain.
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5–66
Refrigerant-134a is throttled from the saturated liquid state at 700
kPa to a pressure of 160 kPa. Determine the temperature drop during this
process and the final specific volume of the refrigerant.
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5–67
Refrigerant-134a at 800 kPa and 25°C is throttled to a temperature of
-20°C. Determine the pressure and the internal energy of the refrigerant
at the final state.
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5–68
A well-insulated valve is used to throttle steam from 8 MPa and 500°C
to 6 MPa. Determine the final temperature of the steam.
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5–69
Reconsider Prob. 5–68. Using EES (or other) software, investigate the
effect of the exit pressure of steam on the exit temperature after
throttling. Let the exit pressure vary from 6 to 1 MPa. Plot the exit
temperature of steam against the exit pressure, and discuss the results.
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5–70E
Air at 200 psia and 90°F is throttled to the atmospheric pressure of
14.7 psia. Determine the final temperature of the air.
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5–71
Carbon dioxide gas enters a throttling valve at 5 MPa and 100°C and
leaves at 100 kPa. Determine the temperature change during this process
if CO2 is assumed to be (a) an ideal gas and (b) a real gas.
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5–72C
When two fluid streams are mixed in a mixing chamber, can the mixture
temperature be lower than the temperature of both streams? Explain.
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5–73C
Consider a steady-flow mixing process. Under what conditions will the
energy transported into the control volume by the incoming streams be
equal to the energy transported out of it by the outgoing stream?
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5–74C
Consider a steady-flow heat exchanger involving two different fluid
streams. Under what conditions will the amount of heat lost by one fluid
be equal to the amount of heat gained by the other?
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5–75
A hot-water stream at 80°C enters a mixing chamber with a mass flow
rate of 0.5 kg/s where it is mixed with a stream of cold water at 20°C.
If it is desired that the mixture leave the chamber at 42°C, determine
the mass flow rate of the cold-water stream. Assume all the streams are
at a pressure of 250 kPa.
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5–76
Liquid water at 300 kPa and 20°C is heated in a chamber by mixing it
with superheated steam at 300 kPa and 300°C. Cold water enters the
chamber at a rate of 1.8 kg/s. If the mixture leaves the mixing chamber
at 60°C, determine the mass flow rate of the superheated steam required.
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5–77
In steam power plants, open feedwater heaters are frequently utilized
to heat the feedwater by mixing it with steam bled off the turbine at
some intermediate stage. Consider an open feedwater heater that operates
at a pressure of 1000 kPa. Feedwater at 50°C and 1000 kPa is to be
heated with superheated steam at 200°C and 1000 kPa. In an ideal
feedwater heater, the mixture leaves the heater as saturated liquid at
the feedwater pressure. Determine the ratio of the mass flow rates of
the feedwater and the superheated vapor for this case.
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5–78E
Water at 50°F and 50 psia is heated in a chamber by mixing it with
saturated water vapor at 50 psia. If both streams enter the mixing
chamber at the same mass flow rate, determine the temperature and the
quality of the exiting stream.
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5–79
A stream of refrigerant-134a at 1 MPa and 12°C is mixed with another
stream at 1 MPa and 60°C. If the mass flow rate of the cold stream is
twice that of the hot one, determine the temperature and the quality of
the exit stream.
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5–80
Reconsider Prob. 5–79. Using EES (or other) software, investigate the
effect of the mass flow rate of the cold stream of R-134a on the
temperature and the quality of the exit stream. Let the ratio of the
mass flow rate of the cold stream to that of the hot stream vary from 1
to 4. Plot the mixture temperature and quality against the cold-tohot
mass flow rate ratio, and discuss the results.
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5–81
Refrigerant-134a at 1 MPa and 90°C is to be cooled to 1 MPa and 30°C in
a condenser by air. The air enters at 100 kPa and 27°C with a volume
flow rate of 600 m3/min and leaves at 95 kPa and 60°C. Determine the
mass flow rate of the refrigerant.
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5–82E
Air enters the evaporator section of a window air conditioner at 14.7
psia and 90°F with a volume flow rate of 200 ft3/min. Refrigerant-134a
at 20 psia with a quality of 30 percent enters the evaporator at a rate
of 4 lbm/min and leaves as saturated vapor at the same pressure.
Determine (a) the exit temperature of the air and (b) the rate of heat
transfer from the air.
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5–83
Refrigerant-134a at 700 kPa, 70°C, and 8 kg/min is cooled by water in a
condenser until it exists as a saturated liquid at the same pressure.
The cooling water enters the condenser at 300 kPa and 15°C and leaves at
25°C at the same pressure. Determine the mass flow rate of the cooling
water required to cool the refrigerant.
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5–84E
In a steam heating system, air is heated by being passed over some
tubes through which steam flows steadily. Steam enters the heat
exchanger at 30 psia and 400°F at a rate of 15 lbm/min and leaves at 25
psia and 212°F. Air enters at 14.7 psia and 80°F and leaves at 130°F.
Determine the volume flow rate of air at the inlet.
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5–85
Steam enters the condenser of a steam power plant at 20 kPa and a
quality of 95 percent with a mass flow rate of 20,000 kg/h. It is to be
cooled by water from a nearby river by circulating the water through the
tubes within the condenser. To prevent thermal pollution, the river
water is not allowed to experience a temperature rise above 10°C. If the
steam is to leave the condenser as saturated liquid at 20 kPa,
determine the mass flow rate of the cooling water required
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5–86
Steam is to be condensed in the condenser of a steam power plant at a
temperature of 50°C with cooling water from a nearby lake, which enters
the tubes of the condenser at 18°C at a rate of 101 kg/s and leaves at
27°C. Determine the rate of condensation of the steam in the condenser.
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5–87
Reconsider Prob. 5–86. Using EES (or other) software, investigate the
effect of the inlet temperature of cooling water on the rate of
condensation of steam. Let the inlet temperature vary from 10 to 20°C,
and assume the exit temperature to remain constant. Plot the rate of
condensation of steam against the inlet temperature of the cooling
water, and discuss the results.
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5–88
A heat exchanger is to heat water (cp = 4.18 kJ/kg · °C) from 25 to
60°C at a rate of 0.2 kg/s. The heating is to be accomplished by
geothermal water (cp = 4.31 kJ/kg · °C) available at 140°C at a mass
flow rate of 0.3 kg/s. Determine the rate of heat transfer in the heat
exchanger and the exit temperature of geothermal water.
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5–89
A heat exchanger is to cool ethylene glycol (cp = 2.56 kJ/kg · °C)
flowing at a rate of 2 kg/s from 80°C to 40°C by water (cp = 4.18 kJ/kg ·
°C) that enters at 20°C and leaves at 55°C. Determine (a) the rate of
heat transfer and (b) the mass flow rate of water.
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5–90
Reconsider Prob. 5–89. Using EES (or other) software, investigate the
effect of the inlet temperature of cooling water on the mass flow rate
of water. Let the inlet temperature vary from 10 to 40°C, and assume the
exit temperature to remain constant. Plot the mass flow rate of water
against the inlet temperature, and discuss the results.
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5–91
A thin-walled double-pipe counter-flow heat exchanger is used to cool
oil (cp = 2.20 kJ/kg · °C) from 150 to 40°C at a rate of 2 kg/s by water
(cp = 4.18 kJ/kg · °C) that enters at 22°C at a rate of 1.5 kg/s.
Determine the rate of heat transfer in the heat exchanger and the exit
temperature of water.
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5–92
Cold water (cp = 4.18 kJ/kg · °C) leading to a shower enters a
thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of
0.60 kg/s and is heated to 45°C by hot water (cp = 4.19 kJ/kg · °C)
that enters at 100°C at a rate of 3 kg/s. Determine the rate of heat
transfer in the heat exchanger and the exit temperature of the hot
water.
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5–93
Air (cp = 1.005 kJ/kg · °C) is to be preheated by hot exhaust gases in a
cross-flow heat exchanger before it enters the furnace. Air enters the
heat exchanger at 95 kPa and 20°C at a rate of 0.8 m3/s. The combustion
gases (cp = 1.10 kJ/kg · °C) enter at 180°C at a rate of 1.1 kg/s and
leave at 95°C. Determine the rate of heat transfer to the air and its
outlet temperature.
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5–94
A well-insulated shell-and-tube heat exchanger is used to heat water
(cp = 4.18 kJ/kg · °C) in the tubes from 20 to 70°C at a rate of 4.5
kg/s. Heat is supplied by hot oil (cp = 2.30 kJ/kg · °C) that enters the
shell side at 170°C at a rate of 10 kg/s. Determine the rate of heat
transfer in the heat exchanger and the exit temperature of oil.
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5–95E
Steam is to be condensed on the shell side of a heat exchanger at 85°F.
Cooling water enters the tubes at 60°F at a rate of 138 lbm/s and
leaves at 73°F. Assuming the heat exchanger to be well-insulated,
determine the rate of heat transfer in the heat exchanger and the rate
of condensation of the steam.
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5–96
An air-conditioning system involves the mixing of cold air and warm
outdoor air before the mixture is routed to the conditioned room in
steady operation. Cold air enters the mixing chamber at 5°C and 105 kPa
at a rate of 1.25 m3/s while warm air enters at 34°C and 105 kPa. The
air leaves the room at 24°C. The ratio of the mass flow rates of the hot
to cold air streams is 1.6. Using variable specific heats, determine
(a) the mixture temperature at the inlet of the room and (b) the rate of
heat gain of the room.
Get 5.96 exercise solution
5–97
Hot exhaust gases of an internal combustion engine are to be used to
produce saturated water vapor at 2 MPa pressure. The exhaust gases enter
the heat exchanger at 400°C at a rate of 32 kg/min while water enters
at 15°C. The heat exchanger is not well insulated, and it is estimated
that 10 percent of heat given up by the exhaust gases is lost to the
surroundings. If the mass flow rate of the exhaust gases is 15 times
that of the water, determine (a) the temperature of the exhaust gases at
the heat exchanger exit and (b) the rate of heat transfer to the water.
Use the constant specific heat properties of air for the exhaust gases.
Get 5.97 exercise solution
5–98
A desktop computer is to be cooled by a fan. The electronic components
of the computer consume 60 W of power under full-load conditions. The
computer is to operate in environments at temperatures up to 45°C and at
elevations up to 3400 m where the average atmospheric pressure is 66.63
kPa. The exit temperature of air is not to exceed 60°C to meet the
reliability requirements. Also, the average velocity of air is not to
exceed 110 m/min at the exit of the computer case where the fan is
installed to keep the noise level down. Determine the flow rate of the
fan that needs to be installed and the diameter of the casing of the
fan.
Get 5.98 exercise solution
5–99 Repeat Prob. 5–98 for a computer that consumes 100 W of power.
Get 5.99 exercise solution
5–100E
Water enters the tubes of a cold plate at 95°F with an average velocity
of 60 ft/min and leaves at 105°F. The diameter of the tubes is 0.25 in.
Assuming 15 percent of the heat generated is dissipated from the
components to the surroundings by convection and radiation, and the
remaining 85 percent is removed by the cooling water, determine the
amount of heat generated by the electronic devices mounted on the cold
plate.
Get 5.100 exercise solution
5–101
A sealed electronic box is to be cooled by tap water flowing through
the channels on two of its sides. It is specified that the temperature
rise of the water not exceed 4°C. The power dissipation of the box is 2
kW, which is removed entirely by water. If the box operates 24 hours a
day, 365 days a year, determine the mass flow rate of water flowing
through the box and the amount of cooling water used per year.
Get 5.101 exercise solution
5–102 Repeat Prob. 5–101 for a power dissipation of 4 kW.
Get 5.102 exercise solution
5–103
A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate (r =
7854 kg/m3 and cp = 0.434 kJ/kg · °C) coming off a furnace at 820°C is
to be quenched in an oil bath at 45°C to a temperature of 51.1°C. If the
metal sheet is moving at a steady velocity of 10 m/min, determine the
required rate of heat removal from the oil to keep its temperature
constant at 45°C.
Get 5.103 exercise solution
5–104
Reconsider Prob. 5–103. Using EES (or other) software, investigate the
effect of the moving velocity of the steel plate on the rate of heat
transfer from the oil bath. Let the velocity vary from 5 to 50 m/min.
Plot the rate of heat transfer against the plate velocity, and discuss
the results.
Get 5.104 exercise solution
5–105
The components of an electronic system dissipating 180 W are located in
a 1.4-m-long horizontal duct whose cross section is 20 cm x 20 cm. The
components in the duct are cooled by forced air that enters the duct at
30°C and 1 atm at a rate of 0.6 m3/min and leaves at 40°C. Determine the
rate of heat transfer from the outer surfaces of the duct to the
ambient.
Get 5.105 exercise solution
5–106 Repeat Prob. 5–105 for a circular horizontal duct of diameter 10 cm.
Get 5.106 exercise solution
5–107E
The hot-water needs of a household are to be met by heating water at
55°F to 180°F by a parabolic solar collector at a rate of 4 lbm/s. Water
flows through a 1.25-in-diameter thin aluminum tube whose outer surface
is black-anodized in order to maximize its solar absorption ability.
The centerline of the tube coincides with the focal line of the
collector, and a glass sleeve is placed outside the tube to minimize the
heat losses. If solar energy is transferred to water at a net rate of
400 Btu/h per ft length of the tube, determine the required length of
the parabolic collector to meet the hot-water requirements of this
house.
Get 5.107 exercise solution
5–108
Consider a hollow-core printed circuit board 12 cm high and 18 cm long,
dissipating a total of 20 W. The width of the air gap in the middle of
the PCB is 0.25 cm. If the cooling air enters the 12-cm-wide core at
32°C and 1 atm at a rate of 0.8 L/s, determine the average temperature
at which the air leaves the hollow core.
Get 5.108 exercise solution
5–109
A computer cooled by a fan contains eight PCBs, each dissipating 10 W
power. The height of the PCBs is 12 cm and the length is 18 cm. The
cooling air is supplied by a 25-W fan mounted at the inlet. If the
temperature rise of air as it flows through the case of the computer is
not to exceed 10°C, determine (a) the flow rate of the air that the fan
needs to deliver and (b) the fraction of the temperature rise of air
that is due to the heat generated by the fan and its motor
Get 5.109 exercise solution
5–110
Hot water at 90°C enters a 15-m section of a cast iron pipe whose inner
diameter is 4 cm at an average velocity of 0.8 m/s. The outer surface
of the pipe is exposed to the cold air at 10°C in a basement. If water
leaves the basement at 88°C, determine the rate of heat loss from the
water.
Get 5.110 exercise solution
5–111
Reconsider Prob. 5–110. Using EES (or other) software, investigate the
effect of the inner pipe diameter on the rate of heat loss. Let the pipe
diameter vary from 1.5 to 7.5 cm. Plot the rate of heat loss against
the diameter, and discuss the results.
Get 5.111 exercise solution
5–112
A 5-m x 6-m x 8-m room is to be heated by an electric resistance heater
placed in a short duct in the room. Initially, the room is at 15°C, and
the local atmospheric pressure is 98 kPa. The room is losing heat
steadily to the outside at a rate of 200 kJ/min. A 200-W fan circulates
the air steadily through the duct and the electric heater at an average
mass flow rate of 50 kg/min. The duct can be assumed to be adiabatic,
and there is no air leaking in or out of the room. If it takes 15 min
for the room air to reach an average temperature of 25°C, find (a) the
power rating of the electric heater and (b) the temperature rise that
the air experiences each time it passes through the heater.
Get 5.112 exercise solution
5–113
A house has an electric heating system that consists of a 300-W fan and
an electric resistance heating element placed in a duct. Air flows
steadily through the duct at a rate of 0.6 kg/s and experiences a
temperature rise of 7°C. The rate of heat loss from the air in the duct
is estimated to be 300 W. Determine the power rating of the electric
resistance heating element.
Get 5.113 exercise solution
5–114
A hair dryer is basically a duct in which a few layers of electric
resistors are placed. A small fan pulls the air in and forces it through
the resistors where it is heated. Air enters a 1200-W hair dryer at 100
kPa and 22°C and leaves at 47°C. The cross-sectional area of the hair
dryer at the exit is 60 cm2. Neglecting the power consumed by the fan
and the heat losses through the walls of the hair dryer, determine (a)
the volume flow rate of air at the inlet and (b) the velocity of the air
at the exit.
Get 5.114 exercise solution
5–115
Reconsider Prob. 5–114. Using EES (or other) software, investigate the
effect of the exit cross-sectional area of the hair dryer on the exit
velocity. Let the exit area vary from 25 to 75 cm2. Plot the exit
velocity against the exit cross-sectional area, and discuss the results.
Include the effect of the flow kinetic energy in the analysis.
Get 5.115 exercise solution
5–116
The ducts of an air heating system pass through an unheated area. As a
result of heat losses, the temperature of the air in the duct drops by
4°C. If the mass flow rate of air is 120 kg/min, determine the rate of
heat loss from the air to the cold environment.
Get 5.116 exercise solution
5–117E
Air enters the duct of an air-conditioning system at 15 psia and 50°F
at a volume flow rate of 450 ft3/min. The diameter of the duct is 10 in,
and heat is transferred to the air in the duct from the surroundings at
a rate of 2 Btu/s. Determine (a) the velocity of the air at the duct
inlet and (b) the temperature of the air at the exit.
Get 5.117 exercise solution
5–118
Water is heated in an insulated, constant-diameter tube by a 7-kW
electric resistance heater. If the water enters the heater steadily at
20°C and leaves at 75°C, determine the mass flow rate of water.
Get 5.118 exercise solution
5–119
Steam enters a long, horizontal pipe with an inlet diameter of D1 = 12
cm at 1 MPa and 300°C with a velocity of 2 m/s. Farther downstream, the
conditions are 800 kPa and 250°C, and the diameter is D2 = 10 cm.
Determine (a) the mass flow rate of the steam and (b) the rate of heat
transfer.
Get 5.119 exercise solution
5–120
Steam enters an insulated pipe at 200 kPa and 200°C and leaves at 150
kPa and 150°C. The inlet-to-outlet diameter ratio for the pipe is
D1/D2=1.80. Determine the inlet and exit velocities of the steam.
Get 5.120 exercise solution
5–121
A balloon that initially contains 50 m3 of steam at 100 kPa and 150°C
is connected by a valve to a large reservoir that supplies steam at 150
kPa and 200°C. Now the valve is opened, and steam is allowed to enter
the balloon until the pressure equilibrium with the steam at the supply
line is reached. The material of the balloon is such that its volume
increases linearly with pressure. Heat transfer also takes place between
the balloon and the surroundings, and the mass of the steam in the
balloon doubles at the end of the process. Determine the final
temperature and the boundary work during this process.
Get 5.121 exercise solution
5–122
A rigid, insulated tank that is initially evacuated is connected
through a valve to a supply line that carries steam at 4 MPa. Now the
valve is opened, and steam is allowed to flow into the tank until the
pressure reaches 4 MPa, at which point the valve is closed. If the final
temperature of the steam in the tank is 550°C, determine the
temperature of the steam in the supply line and the flow work per unit
mass of the steam.
Get 5.122 exercise solution
5–123
A vertical piston–cylinder device initially contains 0.25 m3 of air at
600 kPa and 300°C. A valve connected to the cylinder is now opened, and
air is allowed to escape until three-quarters of the mass leave the
cylinder at which point the volume is 0.05 m3. Determine the final
temperature in the cylinder and the boundary work during this process.
Get 5.123 exercise solution
5–124
A rigid, insulated tank that is initially evacuated is connected
through a valve to a supply line that carries helium at 200 kPa and
120°C. Now the valve is opened, and helium is allowed to flow into the
tank until the pressure reaches 200 kPa, at which point the valve is
closed. Determine the flow work of the helium in the supply line and the
final temperature of the helium in the tank.
Get 5.124 exercise solution
5–125
Consider an 8-L evacuated rigid bottle that is surrounded by the
atmosphere at 100 kPa and 17°C. A valve at the neck of the bottle is now
opened and the atmospheric air is allowed to flow into the bottle. The
air trapped in the bottle eventually reaches thermal equilibrium with
the atmosphere as a result of heat transfer through the wall of the
bottle. The valve remains open during the process so that the trapped
air also reaches mechanical equilibrium with the atmosphere. Determine
the net heat transfer through the wall of the bottle during this filling
process.
Get 5.125 exercise solution
5–126
An insulated rigid tank is initially evacuated. A valve is opened, and
atmospheric air at 95 kPa and 17°C enters the tank until the pressure in
the tank reaches 95 kPa, at which point the valve is closed. Determine
the final temperature of the air in the tank. Assume constant specific
heats.
Get 5.126 exercise solution
5–127
A 2-m3 rigid tank initially contains air at 100 kPa and 22°C. The tank
is connected to a supply line through a valve. Air is flowing in the
supply line at 600 kPa and 22°C. The valve is opened, and air is allowed
to enter the tank until the pressure in the tank reaches the line
pressure, at which point the valve is closed. A thermometer placed in
the tank indicates that the air temperature at the final state is 77°C.
Determine (a) the mass of air that has entered the tank and (b) the
amount of heat transfer.
Get 5.127 exercise solution
5–128
A 0.2-m3 rigid tank initially contains refrigerant-134a at 8°C. At this
state, 70 percent of the mass is in the vapor phase, and the rest is in
the liquid phase. The tank is connected by a valve to a supply line
where refrigerant at 1 MPa and 100°C flows steadily. Now the valve is
opened slightly, and the refrigerant is allowed to enter the tank. When
the pressure in the tank reaches 800 kPa, the entire refrigerant in the
tank exists in the vapor phase only. At this point the valve is closed.
Determine (a) the final temperature in the tank, (b) the mass of
refrigerant that has entered the tank, and (c) the heat transfer between
the system and the surroundings.
Get 5.128 exercise solution
5–129E
A 3-ft3 rigid tank initially contains saturated water vapor at 300°F.
The tank is connected by a valve to a supply line that carries steam at
200 psia and 400°F. Now the valve is opened, and steam is allowed to
enter the tank. Heat transfer takes place with the surroundings such
that the temperature in the tank remains constant at 300°F at all times.
The valve is closed when it is observed that one-half of the volume of
the tank is occupied by liquid water. Find (a) the final pressure in the
tank, (b) the amount of steam that has entered the tank, and (c) the
amount of heat transfer.
Get 5.129 exercise solution
5–130
A vertical piston–cylinder device initially contains 0.01 m3 of steam
at 200°C. The mass of the frictionless piston is such that it maintains a
constant pressure of 500 kPa inside. Now steam at 1 MPa and 350°C is
allowed to enter the cylinder from a supply line until the volume inside
doubles. Neglecting any heat transfer that may have taken place during
the process, determine (a) the final temperature of the steam in the
cylinder and (b) the amount of mass that has entered.
Get 5.130 exercise solution
5–131
An insulated, vertical piston–cylinder device initially contains 10 kg
of water, 6 kg of which is in the vapor phase. The mass of the piston is
such that it maintains a constant pressure of 200 kPa inside the
cylinder. Now steam at 0.5 MPa and 350°C is allowed to enter the
cylinder from a supply line until all the liquid in the cylinder has
vaporized. Determine (a) the final temperature in the cylinder and (b)
the mass of the steam that has entered.
Get 5.131 exercise solution
5–132
A 0.12-m3 rigid tank initially contains refrigerant134a at 1 MPa and
100 percent quality. The tank is connected by a valve to a supply line
that carries refrigerant-134a at 1.2 MPa and 36°C. Now the valve is
opened, and the refrigerant is allowed to enter the tank. The valve is
closed when it is observed that the tank contains saturated liquid at
1.2 MPa. Determine (a) the mass of the refrigerant that has entered the
tank and (b) the amount of heat transfer. Get 5.132 exercise solution
5–133
A 0.3-m3 rigid tank is filled with saturated liquid water at 200°C. A
valve at the bottom of the tank is opened, and liquid is withdrawn from
the tank. Heat is transferred to the water such that the temperature in
the tank remains constant. Determine the amount of heat that must be
transferred by the time one-half of the total mass has been withdrawn
Get 5.133 exercise solution
5–134
A 0.12-m3 rigid tank contains saturated refrigerant134a at 800 kPa.
Initially, 25 percent of the volume is occupied by liquid and the rest
by vapor. A valve at the bottom of the tank is now opened, and liquid is
withdrawn from the tank. Heat is transferred to the refrigerant such
that the pressure inside the tank remains constant. The valve is closed
when no liquid is left in the tank and vapor starts to come out.
Determine the total heat transfer for this process.
Get 5.134 exercise solution
5–135E
A 4-ft3 rigid tank contains saturated refrigerant134a at 100 psia.
Initially, 20 percent of the volume is occupied by liquid and the rest
by vapor. A valve at the top of the tank is now opened, and vapor is
allowed to escape slowly from the tank. Heat is transferred to the
refrigerant such that the pressure inside the tank remains constant. The
valve is closed when the last drop of liquid in the tank is vaporized.
Determine the total heat transfer for this process.
Get 5.135 exercise solution
5–136
A 0.2-m3 rigid tank equipped with a pressure regulator contains steam
at 2 MPa and 300°C. The steam in the tank is now heated. The regulator
keeps the steam pressure constant by letting out some steam, but the
temperature inside rises. Determine the amount of heat transferred when
the steam temperature reaches 500°C.
Get 5.136 exercise solution
5–137
A 4-L pressure cooker has an operating pressure of 175 kPa. Initially,
one-half of the volume is filled with liquid and the other half with
vapor. If it is desired that the pressure cooker not run out of liquid
water for 1 h, determine the highest rate of heat transfer allowed.
Get 5.137 exercise solution
5–138
An insulated 0.08-m3 tank contains helium at 2 MPa and 80°C. A valve is
now opened, allowing some helium to escape. The valve is closed when
one-half of the initial mass has escaped. Determine the final
temperature and pressure in the tank.
Get 5.138 exercise solution
5–139E
An insulated 60-ft3 rigid tank contains air at 75 psia and 120°F. A
valve connected to the tank is now opened, and air is allowed to escape
until the pressure inside drops to 30 psia. The air temperature during
this process is maintained constant by an electric resistance heater
placed in the tank. Determine the electrical work done during this
process.
Get 5.139 exercise solution
5–140
A vertical piston–cylinder device initially contains 0.2 m3 of air at
20°C. The mass of the piston is such that it maintains a constant
pressure of 300 kPa inside. Now a valve connected to the cylinder is
opened, and air is allowed to escape until the volume inside the
cylinder is decreased by one-half. Heat transfer takes place during the
process so that the temperature of the air in the cylinder remains
constant. Determine (a) the amount of air that has left the cylinder and
(b) the amount of heat transfer.
Get 5.140 exercise solution
5–141
A balloon initially contains 65 m3 of helium gas at atmospheric
conditions of 100 kPa and 22°C. The balloon is connected by a valve to a
large reservoir that supplies helium gas at 150 kPa and 25°C. Now the
valve is opened, and helium is allowed to enter the balloon until
pressure equilibrium with the helium at the supply line is reached. The
material of the balloon is such that its volume increases linearly with
pressure. If no heat transfer takes place during this process, determine
the final temperature in the balloon.
Get 5.141 exercise solution
5–142
An insulated vertical piston–cylinder device initially contains 0.8 m3
of refrigerant-134a at 1.2 MPa and 120°C. A linear spring at this point
applies full force to the piston. A valve connected to the cylinder is
now opened, and refrigerant is allowed to escape. The spring unwinds as
the piston moves down, and the pressure and volume drop to 0.6 MPa and
0.5 m3 at the end of the process. Determine (a) the amount of
refrigerant that has escaped and (b) the final temperature of the
refrigerant.
Get 5.142 exercise solution
5–143
A 2-m3 rigid insulated tank initially containing saturated water vapor
at 1 MPa is connected through a valve to a supply line that carries
steam at 400°C. Now the valve is opened, and steam is allowed to flow
slowly into the tank until the pressure in the tank rises to 2 MPa. At
this instant the tank temperature is measured to be 300°C. Determine the
mass of the steam that has entered and the pressure of the steam in the
supply line.
Get 5.143 exercise solution
5–144
A piston–cylinder device initially contains 0.6 kg of steam with a
volume of 0.1 m3. The mass of the piston is such that it maintains a
constant pressure of 800 kPa. The cylinder is connected through a valve
to a supply line that carries steam at 5 MPa and 500°C. Now the valve is
opened and steam is allowed to flow slowly into the cylinder until the
volume of the cylinder doubles and the temperature in the cylinder
reaches 250°C, at which point the valve is closed. Determine (a) the
mass of steam that has entered and (b) the amount of heat transfer.
Get 5.144 exercise solution
5–145
A D0 = 10-m-diameter tank is initially filled with water 2 m above the
center of a D = 10-cm-diameter valve near the bottom. The tank surface
is open to the atmosphere, and the tank drains through a L = 100-m-long
pipe connected to the valve. The friction factor of the pipe is given
to be f = 0.015, and the discharge velocity is expressed as
where z is the water height above the center of the valve. Determine (a)
the initial discharge velocity from the tank and (b) the time required
to empty the tank. The tank can be considered to be empty when the water
level drops to the center of the valve.
Get 5.145 exercise solution
5–146
Underground water is being pumped into a pool whose cross section is 3 m
x 4 m while water is discharged through a 5-cm-diameter orifice at a
constant average velocity of 5 m/s. If the water level in the pool rises
at a rate of 1.5 cm/min, determine the rate at which water is supplied
to the pool, in m3/s.
Get 5.146 exercise solution
5–147
The velocity of a liquid flowing in a circular pipe of radius R varies
from zero at the wall to a maximum at the pipe center. The velocity
distribution in the pipe can be represented as V(r), where r is the
radial distance from the pipe center. Based on the definition of mass
flow rate m ., obtain a relation for the average velocity in terms of
V(r), R, and r.
Get 5.147 exercise solution
5–148
Air at 4.18 kg/m3 enters a nozzle that has an inlet-toexit area ratio
of 2:1 with a velocity of 120 m/s and leaves with a velocity of 380 m/s.
Determine the density of air at the exit.
Get 5.148 exercise solution
5–149
The air in a 6-m x 5-m x 4-m hospital room is to be completely replaced
by conditioned air every 15 min. If the average air velocity in the
circular air duct leading to the room is not to exceed 5 m/s, determine
the minimum diameter of the duct.
Get 5.149 exercise solution
5–150
A long roll of 1-m-wide and 0.5-cm-thick 1-Mn manganese steel plate (p =
7854 kg/m3) coming off a furnace is to be quenched in an oil bath to a
specified temperature. If the metal sheet is moving at a steady velocity
of 10 m/min, determine the mass flow rate of the steel plate through
the oil bath
Get 5.150 exercise solution
5–151E
It is well established that indoor air quality (IAQ) has a significant
effect on general health and productivity of employees at a workplace. A
recent study showed that enhancing IAQ by increasing the building
ventilation from 5 cfm (cubic feet per minute) to 20 cfm increased the
productivity by 0.25 percent, valued at $90 per person per year, and
decreased the respiratory illnesses by 10 percent for an average annual
savings of $39 per person while increasing the annual energy consumption
by $6 and the equipment cost by about $4 per person per year (ASHRAE
Journal, December 1998). For a workplace with 120 employees, determine
the net monetary benefit of installing an enhanced IAQ system to the
employer per year.
Get 5.151 exercise solution
5–152
Air enters a pipe at 50°C and 200 kPa and leaves at 40°C and 150 kPa.
It is estimated that heat is lost from the pipe in the amount of 3.3 kJ
per kg of air flowing in the pipe. The diameter ratio for the pipe is
D1/D2 = 1.8. Using constant specific heats for air, determine the inlet
and exit velocities of the air. Answers: 28.6 m/s, 120 m/s
Get 5.152 exercise solution
5–153
In a single-flash geothermal power plant, geothermal water enters the
flash chamber (a throttling valve) at 230°C as a saturated liquid at a
rate of 50 kg/s. The steam resulting from the flashing process enters a
turbine and leaves at 20 kPa with a moisture content of 5 percent.
Determine the temperature of the steam after the flashing process and
the power output from the turbine if the pressure of the steam at the
exit of the flash chamber is (a) 1 MPa, (b) 500 kPa, (c) 100 kPa, (d) 50
kPa.
Get 5.153 exercise solution
5–154
The hot-water needs of a household are met by a 60L electric water
heater whose heaters are rated at 1.6 kW. The hot-water tank is
initially full with hot water at 80°C. Somebody takes a shower by mixing
a constant flow of hot water from the tank with cold water at 20°C at a
rate of 0.06 kg/s. After a shower period of 8 min, the water
temperature in the tank is measured to drop to 60°C. The heater remained
on during the shower and hot water withdrawn from the tank is replaced
by cold water at the same flow rate. Determine the mass flow rate of hot
water withdrawn from the tank during the shower and the average
temperature of mixed water used for the shower.
Get 5.154 exercise solution
5–155
In a gas-fired boiler, water is boiled at 150°C by hot gases flowing
through a stainless steel pipe submerged in water. If the rate of heat
transfer from the hot gases to water is 74 kJ/s, determine the rate of
evaporation of water.
Get 5.155 exercise solution
5–156
Cold water enters a steam generator at 20°C and leaves as saturated
vapor at 150°C. Determine the fraction of heat used in the steam
generator to preheat the liquid water from 20°C to the saturation
temperature of 150°C.
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5–157
Cold water enters a steam generator at 20°C and leaves as saturated
vapor at the boiler pressure. At what pressure will the amount of heat
needed to preheat the water to saturation temperature be equal to the
heat needed to vaporize the liquid at the boiler pressure?
Get 5.157 exercise solution
5–158
Saturated steam at 1 atm condenses on a vertical plate that is
maintained at 90°C by circulating cooling water through the other side.
If the rate of heat transfer by condensation to the plate is 180 kJ/s,
determine the rate at which the condensate drips off the plate at the
bottom.
Get 5.158 exercise solution
5–159 Water is boiled at 100°C electrically by a 3-kW resistance wire. Determine the rate of evaporation of water
Get 5.159 exercise solution
5–160
Two streams of the same ideal gas having different mass flow rates and
temperatures are mixed in a steady-flow, adiabatic mixing device.
Assuming constant specific heats find the simplest expression for the
mixture temperature written in the form
Get 5.160 exercise solution
5–161
An ideal gas expands in an adiabatic turbine from 1200 K, 600 kPa to
700 K. Determine the turbine inlet volume flow rate of the gas, in m3/s,
required to produce turbine work output at the rate of 200 kW. The
average values of the specific heats for this gas over the temperature
range are cp = 1.13 kJ/kg · K and cv = 0.83 kJ/kg · K. R = 0.30 kJ/kg ·
K.
Get 5.161 exercise solution
5–162
Consider two identical buildings: one in Los Angeles, California, where
the atmospheric pressure is 101 kPa and the other in Denver, Colorado,
where the atmospheric pressure is 83 kPa. Both buildings are maintained
at 21°C, and the infiltration rate for both buildings is 1.2 air changes
per hour (ACH). That is, the entire air in the building is replaced
completely by the outdoor air 1.2 times per hour on a day when the
outdoor temperature at both locations is 10°C. Disregarding latent heat,
determine the ratio of the heat losses by infiltration at the two
cities.
Get 5.162 exercise solution
5–163
The ventilating fan of the bathroom of a building has a volume flow
rate of 30 L/s and runs continuously. The building is located in San
Francisco, California, where the average winter temperature is 12.2°C,
and is maintained at 22°C at all times. The building is heated by
electricity whose unit cost is $0.09/kWh. Determine the amount and cost
of the heat “vented out” per month in winter.
Get 5.163 exercise solution
5–164
Consider a large classroom on a hot summer day with 150 students, each
dissipating 60 W of sensible heat. All the lights, with 6.0 kW of rated
power, are kept on. The room has no external walls, and thus heat gain
through the walls and the roof is negligible. Chilled air is available
at 15°C, and the temperature of the return air is not to exceed 25°C.
Determine the required flow rate of air, in kg/s, that needs to be
supplied to the room to keep the average temperature of the room
constant.
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5–165
Chickens with an average mass of 2.2 kg and average specific heat of
3.54 kJ/kg · °C are to be cooled by chilled water that enters a
continuous-flow-type immersion chiller at 0.5°C. Chickens are dropped
into the chiller at a uniform temperature of 15°C at a rate of 500
chickens per hour and are cooled to an average temperature of 3°C before
they are taken out. The chiller gains heat from the surroundings at a
rate of 200 kJ/h. Determine (a) the rate of heat removal from the
chickens, in kW, and (b) the mass flow rate of water, in kg/s, if the
temperature rise of water is not to exceed 2°C.
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5–166 Repeat Prob. 5–165 assuming heat gain of the chiller is negligible.
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5–167
In a dairy plant, milk at 4°C is pasteurized continuously at 72°C at a
rate of 12 L/s for 24 h a day and 365 days a year. The milk is heated to
the pasteurizing temperature by hot water heated in a natural-gas-fired
boiler that has an efficiency of 82 percent. The pasteurized milk is
then cooled by cold water at 18°C before it is finally refrigerated back
to 4°C. To save energy and money, the plant installs a regenerator that
has an effectiveness of 82 percent. If the cost of natural gas is
$1.10/therm (1 therm = 105,500 kJ), determine how much energy and money
the regenerator will save this company per year.
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5–168E
A refrigeration system is being designed to cool eggs (r = 67.4 lbm/ft3
and cp = 0.80 Btu/lbm · °F) with an average mass of 0.14 lbm from an
initial temperature of 90°F to a final average temperature of 50°F by
air at 34°F at a rate of 10,000 eggs per hour. Determine (a) the rate of
heat removal from the eggs, in Btu/h and (b) the required volume flow
rate of air, in ft3/h, if the temperature rise of air is not to exceed
10°F.
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5–169
The heat of hydration of dough, which is 15 kJ/kg, will raise its
temperature to undesirable levels unless some cooling mechanism is
utilized. A practical way of absorbing the heat of hydration is to use
refrigerated water when kneading the dough. If a recipe calls for mixing
2 kg of flour with 1 kg of water, and the temperature of the city water
is 15°C, determine the temperature to which the city water must be
cooled before mixing in order for the water to absorb the entire heat of
hydration when the water temperature rises to 15°C. Take the specific
heats of the flour and the water to be 1.76 and 4.18 kJ/kg · °C,
respectively.
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5–170
A glass bottle washing facility uses a well-agitated hot-water bath at
55°C that is placed on the ground. The bottles enter at a rate of 800
per minute at an ambient temperature of 20°C and leave at the water
temperature. Each bottle has a mass of 150 g and removes 0.2 g of water
as it leaves the bath wet. Make-up water is supplied at 15°C.
Disregarding any heat losses from the outer surfaces of the bath,
determine the rate at which (a) water and (b) heat must be supplied to
maintain steady operation.
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5–171 Repeat Prob. 5–170 for a water bath temperature of 50°C.
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5–172
Long aluminum wires of diameter 3 mm (r = 2702 kg/m3 and cp = 0.896
kJ/kg · °C) are extruded at a temperature of 350°C and are cooled to
50°C in atmospheric air at 30°C. If the wire is extruded at a velocity
of 10 m/min, determine the rate of heat transfer from the wire to the
extrusion room.
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5–173 Repeat Prob. 5–172 for a copper wire (r = 8950 kg/m3 and cp = 0.383 kJ/kg · °C).
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5–174
Steam at 40°C condenses on the outside of a 5-mlong, 3-cm-diameter thin
horizontal copper tube by cooling water that enters the tube at 25°C at
an average velocity of 2 m/s and leaves at 35°C. Determine the rate of
condensation of steam.
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5–175E
The condenser of a steam power plant operates at a pressure of 0.95
psia. The condenser consists of 144 horizontal tubes arranged in a 12 x
12 square array. Steam condenses on the outer surfaces of the tubes
whose inner and outer diameters are 1 in and 1.2 in, respectively. If
steam is to be condensed at a rate of 6800 lbm/h and the temperature
rise of the cooling water is limited to 8°F, determine (a) the rate of
heat transfer from the steam to the cooling water and (b) the average
velocity of the cooling water through the tubes.
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5–176
Saturated refrigerant-134a vapor at 34°C is to be condensed as it flows
in a 1-cm-diameter tube at a rate of 0.1 kg/min. Determine the rate of
heat transfer from the refrigerant. What would your answer be if the
condensed refrigerant is cooled to 20°C?
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5–177E
The average atmospheric pressure in Spokane, Washington (elevation =
2350 ft), is 13.5 psia, and the average winter temperature is 36.5°F.
The pressurization test of a 9-ft-high, 3000-ft2 older home revealed
that the seasonal average infiltration rate of the house is 2.2 air
changes per hour (ACH). That is, the entire air in the house is replaced
completely 2.2 times per hour by the outdoor air. It is suggested that
the infiltration rate of the house can be reduced by half to 1.1 ACH by
winterizing the doors and the windows. If the house is heated by natural
gas whose unit cost is $1.24/therm and the heating season can be taken
to be six months, determine how much the home owner will save from the
heating costs per year by this winterization project. Assume the house
is maintained at 72°F at all times and the efficiency of the furnace is
0.65. Also assume the latent heat load during the heating season to be
negligible.
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5–178
Determine the rate of sensible heat loss from a building due to
infiltration if the outdoor air at -5°C and 90 kPa enters the building
at a rate of 35 L/s when the indoors is maintained at 20°C.
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5–179
The maximum flow rate of standard shower heads is about 3.5 gpm (13.3
L/min) and can be reduced to 2.75 gpm (10.5 L/min) by switching to
low-flow shower heads that are equipped with flow controllers. Consider a
family of four, with each person taking a 5 min shower every morning.
City water at 15°C is heated to 55°C in an electric water heater and
tempered to 42°C by cold water at the T-elbow of the shower before being
routed to the shower heads. Assuming a constant specific heat of 4.18
kJ/kg · °C for water, determine (a) the ratio of the flow rates of the
hot and cold water as they enter the T-elbow and (b) the amount of
electricity that will be saved per year, in kWh, by replacing the
standard shower heads by the low-flow ones.
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5–180
Reconsider Prob. 5–179. Using EES (or other) software, investigate the
effect of the inlet temperature of cold water on the energy saved by
using the lowflow shower head. Let the inlet temperature vary from 10°C
to 20°C. Plot the electric energy savings against the water inlet
temperature, and discuss the results.
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5–181
A fan is powered by a 0.5-hp motor and delivers air at a rate of 85
m3/min. Determine the highest value for the average velocity of air
mobilized by the fan. Take the density of air to be 1.18 kg/m3.
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5–182
An air-conditioning system requires airflow at the main supply duct at a
rate of 180 m3/min. The average velocity of air in the circular duct is
not to exceed 10 m/s to avoid excessive vibration and pressure drops.
Assuming the fan converts 70 percent of the electrical energy it
consumes into kinetic energy of air, determine the size of the electric
motor needed to drive the fan and the diameter of the main duct. Take
the density of air to be 1.20 kg/m3.
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5–183
Consider an evacuated rigid bottle of volume V that is surrounded by
the atmosphere at pressure P0 and temperature T0. A valve at the neck of
the bottle is now opened and the atmospheric air is allowed to flow
into the bottle. The air trapped in the bottle eventually reaches
thermal equilibrium with the atmosphere as a result of heat transfer
through the wall of the bottle. The valve remains open during the
process so that the trapped air also reaches mechanical equilibrium with
the atmosphere. Determine the net heat transfer through the wall of the
bottle during this filling process in terms of the properties of the
system and the surrounding atmosphere.
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5–184
An adiabatic air compressor is to be powered by a direct-coupled
adiabatic steam turbine that is also driving a generator. Steam enters
the turbine at 12.5 MPa and 500°C at a rate of 25 kg/s and exits at 10
kPa and a quality of 0.92. Air enters the compressor at 98 kPa and 295 K
at a rate of 10 kg/s and exits at 1 MPa and 620 K. Determine the net
power delivered to the generator by the turbine.
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5–185
Water flows through a shower head steadily at a rate of 10 L/min. An
electric resistance heater placed in the water pipe heats the water from
16 to 43°C. Taking the density of water to be 1 kg/L, determine the
electric power input to the heater, in kW. In an effort to conserve
energy, it is proposed to pass the drained warm water at a temperature
of 39°C through a heat exchanger to preheat the incoming cold water. If
the heat exchanger has an effectiveness of 0.50 (that is, it recovers
only half of the energy that can possibly be transferred from the
drained water to incoming cold water), determine the electric power
input required in this case. If the price of the electric energy is 8.5
¢/kWh, determine how much money is saved during a 10-min shower as a
result of installing this heat exchanger.
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5–186
Reconsider Prob. 5–185. Using EES (or other) software, investigate the
effect of the heat exchanger effectiveness on the money saved. Let
effectiveness range from 20 to 90 percent. Plot the money saved against
the effectiveness, and discuss the results.
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5–187
Steam enters a turbine steadily at 10 MPa and 550°C with a velocity of
60 m/s and leaves at 25 kPa with a quality of 95 percent. A heat loss of
30 kJ/kg occurs during the process. The inlet area of the turbine is
150 cm2, and the exit area is 1400 cm2. Determine (a) the mass flow rate
of the steam, (b) the exit velocity, and (c) the power output.
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5–188
Reconsider Prob. 5–187. Using EES (or other) software, investigate the
effects of turbine exit area and turbine exit pressure on the exit
velocity and power output of the turbine. Let the exit pressure vary
from 10 to 50 kPa (with the same quality), and the exit area to vary
from 1000 to 3000 cm2. Plot the exit velocity and the power outlet
against the exit pressure for the exit areas of 1000, 2000, and 3000
cm2, and discuss the results.
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5–189E
Refrigerant-134a enters an adiabatic compressor at 15 psia and 20°F
with a volume flow rate of 10 ft3/s and leaves at a pressure of 100
psia. The power input to the compressor is 45 hp. Find (a) the mass flow
rate of the refrigerant and (b) the exit temperature.
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5–190
In large gas-turbine power plants, air is preheated by the exhaust
gases in a heat exchanger called the regenerator before it enters the
combustion chamber. Air enters the regenerator at 1 MPa and 550 K at a
mass flow rate of 800 kg/min. Heat is transferred to the air at a rate
of 3200 kJ/s. Exhaust gases enter the regenerator at 140 kPa and 800 K
and leave at 130 kPa and 600 K. Treating the exhaust gases as air,
determine (a) the exit temperature of the air and (b) the mass flow rate
of exhaust gases.
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5–191
It is proposed to have a water heater that consists of an insulated
pipe of 5-cm diameter and an electric resistor inside. Cold water at
20°C enters the heating section steadily at a rate of 30 L/min. If water
is to be heated to 55°C, determine (a) the power rating of the
resistance heater and (b) the average velocity of the water in the pipe.
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5–192
In large steam power plants, the feedwater is frequently heated in a
closed feedwater heater by using steam extracted from the turbine at
some stage. Steam enters the feedwater heater at 1 MPa and 200°C and
leaves as saturated liquid at the same pressure. Feedwater enters the
heater at 2.5 MPa and 50°C and leaves at 10°C below the exit temperature
of the steam. Determine the ratio of the mass flow rates of the
extracted steam and the feedwater.
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5–193
A building with an internal volume of 400 m3 is to be heated by a 30-kW
electric resistance heater placed in the duct inside the building.
Initially, the air in the building is at 14°C, and the local atmospheric
pressure is 95 kPa. The building is losing heat to the surroundings at a
steady rate of 450 kJ/min. Air is forced to flow through the duct and
the heater steadily by a 250-W fan, and it experiences a temperature
rise of 5°C each time it passes through the duct, which may be assumed
to be adiabatic. (a) How long will it take for the air inside the
building to reach an average temperature of 24°C? (b) Determine the
average mass flow rate of air through the duct.
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5–194
An insulated vertical piston–cylinder device initially contains 0.2 m3
of air at 200 kPa and 22°C. At this state, a linear spring touches the
piston but exerts no force on it. The cylinder is connected by a valve
to a line that supplies air at 800 kPa and 22°C. The valve is opened,
and air from the high-pressure line is allowed to enter the cylinder.
The valve is turned off when the pressure inside the cylinder reaches
600 kPa. If the enclosed volume inside the cylinder doubles during this
process, determine (a) the mass of air that entered the cylinder, and
(b) the final temperature of the air inside the cylinder.
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5–195
A piston–cylinder device initially contains 2 kg of refrigerant-134a at
800 kPa and 80°C. At this state, the piston is touching on a pair of
stops at the top. The mass of the piston is such that a 500-kPa pressure
is required to move it. A valve at the bottom of the tank is opened,
and R-134a is withdrawn from the cylinder. After a while, the piston is
observed to move and the valve is closed when half of the refrigerant is
withdrawn from the tank and the temperature in the tank drops to 20°C.
Determine (a) the work done and (b) the heat transfer.
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5–196
A piston–cylinder device initially contains 1.2 kg of air at 700 kPa
and 200°C. At this state, the piston is touching on a pair of stops. The
mass of the piston is such that 600kPa pressure is required to move it.
A valve at the bottom of the tank is opened, and air is withdrawn from
the cylinder. The valve is closed when the volume of the cylinder
decreases to 80 percent of the initial volume. If it is estimated that
40 kJ of heat is lost from the cylinder, determine (a) the final
temperature of the air in the cylinder, (b) the amount of mass that has
escaped from the cylinder, and (c) the work done. Use constant specific
heats at the average temperature.
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5–197
The pump of a water distribution system is powered by a 15-kW electric
motor whose efficiency is 90 percent. The water flow rate through the
pump is 50 L/s. The diameters of the inlet and outlet pipes are the
same, and the elevation difference across the pump is negligible. If the
pressures at the inlet and outlet of the pump are measured to be 100
kPa and 300 kPa (absolute), respectively, determine (a) the mechanical
efficiency of the pump and (b) the temperature rise of water as it flows
through the pump due to the mechanical inefficiency.
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5–198
Steam enters a nozzle with a low velocity at 150°C and 200 kPa, and
leaves as a saturated vapor at 75 kPa. There is a heat transfer from the
nozzle to the surroundings in the amount of 26 kJ for every kilogram of
steam flowing through the nozzle. Determine (a) the exit velocity of
the steam and (b) the mass flow rate of the steam at the nozzle entrance
if the nozzle exit area is 0.001 m2.
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5–199
The turbocharger of an internal combustion engine consists of a turbine
and a compressor. Hot exhaust gases flow through the turbine to produce
work and the work output from the turbine is used as the work input to
the compressor. The pressure of ambient air is increased as it flows
through the compressor before it enters the engine cylinders. Thus, the
purpose of a turbocharger is to increase the pressure of air so that
more air gets into the cylinder. Consequently, more fuel can be burned
and more power can be produced by the engine. In a turbocharger, exhaust
gases enter the turbine at 400°C and 120 kPa at a rate of 0.02 kg/s and
leave at 350°C. Air enters the compressor at 50°C and 100 kPa and
leaves at 130 kPa at a rate of 0.018 kg/s. The compressor increases the
air pressure with a side effect: It also increases the air temperature,
which increases the possibility of a gasoline engine to experience an
engine knock. To avoid this, an aftercooler is placed after the
compressor to cool the warm air by cold ambient air before it enters the
engine cylinders. It is estimated that the aftercooler must decrease
the air temperature below 80°C if knock is to be avoided. The cold
ambient air enters the aftercooler at 30°C and leaves at 40°C.
Disregarding any frictional losses in the turbine and the compressor and
treating the exhaust gases as air, determine (a) the temperature of the
air at the compressor outlet and (b) the minimum volume flow rate of
ambient air required to avoid knock.
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5–200
Steam is accelerated by a nozzle steadily from a low velocity to a
velocity of 210 m/s at a rate of 3.2 kg/s. If the temperature and
pressure of the steam at the nozzle exit are 400°C and 2 MPa, the exit
area of the nozzle is (a) 24.0 cm2 (d) 152 cm2 (b) 8.4 cm2 (e) 23.0 cm2
(c) 10.2 cm2
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5–201
Steam enters a diffuser steadily at 0.5 MPa, 300°C, and 122 m/s at a
rate of 3.5 kg/s. The inlet area of the diffuser is (a) 15 cm2 (d) 150
cm2 (b) 50 cm2 (e) 190 cm2 (c) 105 cm2
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5–202
An adiabatic heat exchanger is used to heat cold water at 15°C entering
at a rate of 5 kg/s by hot air at 90°C entering also at a rate of 5
kg/s. If the exit temperature of hot air is 20°C, the exit temperature
of cold water is (a) 27°C (d) 85°C (b) 32°C (e) 90°C (c) 52°C
Get 5.202 exercise solution
5–203
A heat exchanger is used to heat cold water at 15°C entering at a rate
of 2 kg/s by hot air at 100°C entering at a rate of 3 kg/s. The heat
exchanger is not insulated and is losing heat at a rate of 40 kJ/s. If
the exit temperature of hot air is 20°C, the exit temperature of cold
water is (a) 44°C (d) 72°C (b) 49°C (e) 95°C (c) 39°C
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5–204
An adiabatic heat exchanger is used to heat cold water at 15°C entering
at a rate of 5 kg/s by hot water at 90°C entering at a rate of 4 kg/s.
If the exit temperature of hot water is 50°C, the exit temperature of
cold water is (a) 42°C (d) 78°C (b) 47°C (e) 90°C (c) 55°C
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5–205
In a shower, cold water at 10°C flowing at a rate of 5 kg/min is mixed
with hot water at 60°C flowing at a rate of 2 kg/min. The exit
temperature of the mixture is (a) 24.3°C (d) 44.3°C (b) 35.0°C (e)
55.2°C (c) 40.0°C
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5–206
In a heating system, cold outdoor air at 10°C flowing at a rate of 6
kg/min is mixed adiabatically with heated air at 70°C flowing at a rate
of 3 kg/min. The exit temperature of the mixture is (a) 30°C (d) 55°C
(b) 40°C (e) 85°C (c) 45°C
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5–207
Hot combustion gases (assumed to have the properties of air at room
temperature) enter a gas turbine at 1 MPa and 1500 K at a rate of 0.1
kg/s, and exit at 0.2 MPa and 900 K. If heat is lost from the turbine to
the surroundings at a rate of 15 kJ/s, the power output of the gas
turbine is (a) 15 kW (d) 60 kW (b) 30 kW (e) 75 kW (c) 45 kW
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5–208
Steam expands in a turbine from 4 MPa and 500°C to 0.5 MPa and 250°C at
a rate of 1350 kg/h. Heat is lost from the turbine at a rate of 25 kJ/s
during the process. The power output of the turbine is (a) 157 kW (d)
287 kW (b) 207 kW (e) 246 kW (c) 182 kW
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5–209
Steam is compressed by an adiabatic compressor from 0.2 MPa and 150°C
to 2.5 MPa and 250°C at a rate of 1.30 kg/s. The power input to the
compressor is (a) 144 kW (d) 717 kW (b) 234 kW (e) 901 kW (c) 438 kW
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5–210
Refrigerant-134a is compressed by a compressor from the saturated vapor
state at 0.14 MPa to 1.2 MPa and 70°C at a rate of 0.108 kg/s. The
refrigerant is cooled at a rate of 1.10 kJ/s during compression. The
power input to the compressor is (a) 5.54 kW (d) 7.74 kW (b) 7.33 kW (e)
8.13 kW (c) 6.64 kW
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5–211
Refrigerant-134a expands in an adiabatic turbine from 1.2 MPa and 100°C
to 0.18 MPa and 50°C at a rate of 1.25 kg/s. The power output of the
turbine is (a) 46.3 kW (d) 89.2 kW (b) 66.4 kW (e) 112.0 kW (c) 72.7 kW
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5–212
Refrigerant-134a at 1.4 MPa and 90°C is throttled to a pressure of 0.6
MPa. The temperature of the refrigerant after throttling is (a) 22°C (d)
80°C (b) 56°C (e) 90°C (c) 82°C
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5–213
Air at 20°C and 5 atm is throttled by a valve to 2 atm. If the valve is
adiabatic and the change in kinetic energy is negligible, the exit
temperature of air will be (a) 10°C (d) 20°C (b) 14°C (e) 24°C (c) 17°C
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5–214
Steam at 1 MPa and 300°C is throttled adiabatically to a pressure of
0.4 MPa. If the change in kinetic energy is negligible, the specific
volume of the steam after throttling is (a) 0.358 m3/kg (d) 0.646 m3/kg
(b) 0.233 m3/kg (e) 0.655 m3/kg (c) 0.375 m3/kg
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5–215
Air is to be heated steadily by an 8-kW electric resistance heater as
it flows through an insulated duct. If the air enters at 50°C at a rate
of 2 kg/s, the exit temperature of air is (a) 46.0°C (d) 55.4°C (b)
50.0°C (e) 58.0°C (c) 54.0°C
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5–216
Saturated water vapor at 50°C is to be condensed as it flows through a
tube at a rate of 0.35 kg/s. The condensate leaves the tube as a
saturated liquid at 50°C. The rate of heat transfer from the tube is (a)
73 kJ/s (d) 834 kJ/s (b) 980 kJ/s (e) 907 kJ/s (c) 2380 kJ/s
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