Thermodynamics

420 | Thermodynamicswater pipe heats the water from 16 to 43°C. Taking the densityof water to be 1 kg/L, determine the electric power inputto the heater, in kW, and the rate of entropy generation duringthis process, in kW/K.(b) In an effort to conserve energy, it is proposed to pass thedrained warm water at a temperature of 39°C through a heatexchanger to preheat the incoming cold water. If the heatexchanger has an effectiveness of 0.50 (that is, it recoversonly half of the energy that can possibly be transferred fromthe drained water to incoming cold water), determine the electricpower input required in this case and the reduction in therate of entropy generation in the resistance heating section.kPa. The mechanical efficiency between the turbine and thecompressor is 95 percent (5 percent of turbine work is lostduring its transmission to the compressor). Using air propertiesfor the exhaust gases, determine (a) the air temperature atthe compressor exit and (b) the isentropic efficiency of thecompressor. Answers: (a) 126.1°C, (b) 0.642Turbine400°CAir, 70°C95 kPa0.018 kg/sCompressorExh. gas450°C0.02 kg/s135 kPaFIGURE P7–210ResistanceheaterFIGURE P7–2077–208 Using EES (or other) software, determine thework input to a multistage compressor for agiven set of inlet and exit pressures for any number of stages.Assume that the pressure ratio across each stage is identical andthe compression process is polytropic. List and plot the compressorwork against the number of stages for P 1 100 kPa,T 1 17°C, P 2 800 kPa, and n 1.35 for air. Based on thischart, can you justify using compressors with more than threestages?7–209 A piston–cylinder device contains air that undergoesa reversible thermodynamic cycle. Initially, air is at 400 kPaand 300 K with a volume of 0.3 m 3 Air is first expandedisothermally to 150 kPa, then compressed adiabatically to theinitial pressure, and finally compressed at the constant pressureto the initial state. Accounting for the variation of specificheats with temperature, determine the work and heattransfer for each process.7–210 Consider the turbocharger of an internal combustionengine. The exhaust gases enter the turbine at 450°C at a rateof 0.02 kg/s and leave at 400°C. Air enters the compressor at70°C and 95 kPa at a rate of 0.018 kg/s and leaves at 1357–211 Air is compressed steadily by a compressor from100 kPa and 20°C to 1200 kPa and 300°C at a rate of 0.4kg/s. The compressor is intentionally cooled by utilizing finson the surface of the compressor and heat is lost from thecompressor at a rate of 15 kW to the surroundings at 20°C.Using constant specific heats at room temperature, determine(a) the power input to the compressor, (b) the isothermal efficiency,and (c) the entropy generation during this process.7–212 A 0.25-m 3 insulated piston–cylinder device initiallycontains 0.7 kg of air at 20°C. At this state, the piston is freeto move. Now air at 500 kPa and 70°C is allowed to enterthe cylinder from a supply line until the volume increases by50 percent. Using constant specific heats at room temperature,determine (a) the final temperature, (b) the amount ofmass that has entered, (c) the work done, and (d) the entropygeneration.Air0.25 m 30.7 kg20°C Air500 kPa70°CFIGURE P7–2127–213 When the transportation of natural gas in a pipelineis not feasible for economic reasons, it is first liquefied usingnonconventional refrigeration techniques and then transportedin super-insulated tanks. In a natural gas liquefaction plant,the liquefied natural gas (LNG) enters a cryogenic turbine at40 bar and 160°C at a rate of 55 kg/s and leaves at 3 bar. If