full load, and its operation at part load is negligible. If the cost
of electricity is $0.075/kWh, determine the amount of energy
and money this facility will save by purchasing the high-
efficiency motor instead of the standard motor. Also, deter-
mine if the savings from the high-efficiency motor justify the
price differential if the expected life of the motor is 10 years.
Ignore any possible rebates from the local power company.
7–158 The space heating of a facility is accomplished by nat-
ural gas heaters that are 80 percent efficient. The compressed
air needs of the facility are met by a large liquid-cooled com-
pressor. The coolant of the compressor is cooled by air in a
liquid-to-air heat exchanger whose airflow section is 1.0-m
high and 1.0-m wide. During typical operation, the air is
heated from 20 to 52°C as it flows through the heat exchanger.
The average velocity of air on the inlet side is measured to be
3 m/s. The compressor operates 20 hours a day and 5 days a
week throughout the year. Taking the heating season to be 6
months (26 weeks) and the cost of the natural gas to be
$1.00/therm (1 therm 100,000 Btu 105,500 kJ), deter-
mine how much money will be saved by diverting the com-
pressor waste heat into the facility during the heating season.
7–159 The compressors of a production facility maintain the
compressed-air lines at a (gage) pressure of 850 kPa at 1400-
m elevation, where the atmospheric pressure is 85.6 kPa. The
average temperature of air is 15°C at the compressor inlet and
25°C in the compressed-air lines. The facility operates 4200
h/yr, and the average price of electricity is $0.07/kWh. Taking
the compressor efficiency to be 0.8, the motor efficiency to be
0.93, and the discharge coefficient to be 0.65, determine the
energy and money saved per year by sealing a leak equivalent
to a 5-mm-diameter hole on the compressed-air line.
Review Problems
7–160 A piston–cylinder device contains steam that under-
goes a reversible thermodynamic cycle. Initially the steam is
at 400 kPa and 350°C with a volume of 0.3 m^3. The steam is
first expanded isothermally to 150 kPa, then compressed adi-
abatically to the initial pressure, and finally compressed at
the constant pressure to the initial state. Determine the net
work and heat transfer for the cycle after you calculate the
work and heat interaction for each process.
7–161 Determine the work input and entropy generation
during the compression of steam from 100 kPa to 1 MPa in
414 | Thermodynamics
(a) an adiabatic pump and (b) an adiabatic compressor if the
inlet state is saturated liquid in the pump and saturated vapor
in the compressor and the isentropic efficiency is 85 percent
for both devices.
7–162 A rigid tank contains 1.5 kg of water at 120°C and
500 kPa. Now 22 kJ of shaft work is done on the system and
the final temperature in the tank is 95°C. If the entropy change
of water is zero and the surroundings are at 15°C, determine
(a) the final pressure in the tank, (b) the amount of heat
transfer between the tank and the surroundings, and (c) the
entropy generation during this process. Answers:(a) 84.6 kPa,
(b) 38.5 kJ, (c) 0.134 kJ/K
7–163 A horizontal cylinder is separated into two compart-
ments by an adiabatic, frictionless piston. One side contains
0.2 m^3 of nitrogen and the other side contains 0.1 kg of
helium, both initially at 20°C and 95 kPa. The sides of the
cylinder and the helium end are insulated. Now heat is added
to the nitrogen side from a reservoir at 500°C until the pres-
sure of the helium rises to 120 kPa. Determine (a) the final
temperature of the helium, (b) the final volume of the nitro-
gen, (c) the heat transferred to the nitrogen, and (d) the
entropy generation during this process.Turbine1 MPa100 kPaPump1 MPa100 kPaFIGURE P7–161N 2
0.2 m^3Q
He
0.1 kgFIGURE P7–1637–164 A 0.8-m^3 rigid tank contains carbon dioxide (CO 2 )
gas at 250 K and 100 kPa. A 500-W electric resistance heater
placed in the tank is now turned on and kept on for 40 min
after which the pressure of CO 2 is measured to be 175 kPa.
Assuming the surroundings to be at 300 K and using constant
specific heats, determine (a) the final temperature of CO 2 ,
(b) the net amount of heat transfer from the tank, and (c) the
entropy generation during this process.CO 2
250 K
100 kPaW·eFIGURE P7–1647–165 Helium gas is throttled steadily from 500 kPa and
70°C. Heat is lost from the helium in the amount of 2.5 kJ/kg
to the surroundings at 25°C and 100 kPa. If the entropy of
the helium increases by 0.25 kJ/kg K in the valve, deter-
mine (a) the exit pressure and temperature and (b) the