Thermodynamics

414 | Thermodynamicsfull load, and its operation at part load is negligible. If the costof electricity is $0.075/kWh, determine the amount of energyand money this facility will save by purchasing the highefficiencymotor instead of the standard motor. Also, determineif the savings from the high-efficiency motor justify theprice 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 naturalgas heaters that are 80 percent efficient. The compressedair needs of the facility are met by a large liquid-cooled compressor.The coolant of the compressor is cooled by air in aliquid-to-air heat exchanger whose airflow section is 1.0-mhigh and 1.0-m wide. During typical operation, the air isheated from 20 to 52°C as it flows through the heat exchanger.The average velocity of air on the inlet side is measured to be3 m/s. The compressor operates 20 hours a day and 5 days aweek throughout the year. Taking the heating season to be 6months (26 weeks) and the cost of the natural gas to be$1.00/therm (1 therm 100,000 Btu 105,500 kJ), determinehow much money will be saved by diverting the compressorwaste heat into the facility during the heating season.7–159 The compressors of a production facility maintain thecompressed-air lines at a (gage) pressure of 850 kPa at 1400-m elevation, where the atmospheric pressure is 85.6 kPa. Theaverage temperature of air is 15°C at the compressor inlet and25°C in the compressed-air lines. The facility operates 4200h/yr, and the average price of electricity is $0.07/kWh. Takingthe compressor efficiency to be 0.8, the motor efficiency to be0.93, and the discharge coefficient to be 0.65, determine theenergy and money saved per year by sealing a leak equivalentto a 5-mm-diameter hole on the compressed-air line.Review Problems7–160 A piston–cylinder device contains steam that undergoesa reversible thermodynamic cycle. Initially the steam isat 400 kPa and 350°C with a volume of 0.3 m 3 . The steam isfirst expanded isothermally to 150 kPa, then compressed adiabaticallyto the initial pressure, and finally compressed atthe constant pressure to the initial state. Determine the network and heat transfer for the cycle after you calculate thework and heat interaction for each process.7–161 Determine the work input and entropy generationduring the compression of steam from 100 kPa to 1 MPa in1 MPa1 MPa(a) an adiabatic pump and (b) an adiabatic compressor if theinlet state is saturated liquid in the pump and saturated vaporin the compressor and the isentropic efficiency is 85 percentfor both devices.7–162 A rigid tank contains 1.5 kg of water at 120°C and500 kPa. Now 22 kJ of shaft work is done on the system andthe final temperature in the tank is 95°C. If the entropy changeof water is zero and the surroundings are at 15°C, determine(a) the final pressure in the tank, (b) the amount of heattransfer between the tank and the surroundings, and (c) theentropy generation during this process. Answers: (a) 84.6 kPa,(b) 38.5 kJ, (c) 0.134 kJ/K7–163 A horizontal cylinder is separated into two compartmentsby an adiabatic, frictionless piston. One side contains0.2 m 3 of nitrogen and the other side contains 0.1 kg ofhelium, both initially at 20°C and 95 kPa. The sides of thecylinder and the helium end are insulated. Now heat is addedto the nitrogen side from a reservoir at 500°C until the pressureof the helium rises to 120 kPa. Determine (a) the finaltemperature of the helium, (b) the final volume of the nitrogen,(c) the heat transferred to the nitrogen, and (d) theentropy generation during this process.QN 20.2 m 3FIGURE P7–163He0.1 kg7–164 A 0.8-m 3 rigid tank contains carbon dioxide (CO 2 )gas at 250 K and 100 kPa. A 500-W electric resistance heaterplaced in the tank is now turned on and kept on for 40 minafter which the pressure of CO 2 is measured to be 175 kPa.Assuming the surroundings to be at 300 K and using constantspecific heats, determine (a) the final temperature of CO 2 ,(b) the net amount of heat transfer from the tank, and (c) theentropy generation during this process.CO 2250 K100 kPa·W e100 kPaPumpTurbine100 kPaFIGURE P7–161FIGURE P7–1647–165 Helium gas is throttled steadily from 500 kPa and70°C. Heat is lost from the helium in the amount of 2.5 kJ/kgto the surroundings at 25°C and 100 kPa. If the entropy ofthe helium increases by 0.25 kJ/kg K in the valve, determine(a) the exit pressure and temperature and (b) the