Thermodynamics

406 | Thermodynamics7–62C Starting with Eq. 7–34, obtain Eq. 7–43.7–63C What are P r and v r called? Is their use limited toisentropic processes? Explain.7–64C Can the entropy of an ideal gas change during anisothermal process?7–65C An ideal gas undergoes a process between two specifiedtemperatures, first at constant pressure and then at constantvolume. For which case will the ideal gas experience alarger entropy change? Explain.7–66 Oxygen gas is compressed in a piston–cylinder devicefrom an initial state of 0.8 m 3 /kg and 25°C to a final state of0.1 m 3 /kg and 287°C. Determine the entropy change of theoxygen during this process. Assume constant specific heats.7–67 A 1.5-m 3 insulated rigid tank contains 2.7 kg of carbondioxide at 100 kPa. Now paddle-wheel work is done onthe system until the pressure in the tank rises to 150 kPa.Determine the entropy change of carbon dioxide during thisprocess. Assume constant specific heats. Answer: 0.719 kJ/Khelium during this process, assuming (a) the process isreversible and (b) the process is irreversible.7–72 Air is compressed in a piston–cylinder device from90 kPa and 20°C to 400 kPa in a reversible isothermal process.Determine (a) the entropy change of air and (b) the work done.7–73 Air is compressed steadily by a 5-kW compressorfrom 100 kPa and 17°C to 600 kPa and 167°C at a rate of 1.6kg/min. During this process, some heat transfer takes placebetween the compressor and the surrounding medium at17°C. Determine the rate of entropy change of air during thisprocess. Answer: 0.0025 kW/K17°C600 kPa167°CAIRCOMPRESSOR5 kWCO 21.5 m 3100 kPa2.7 kgFIGURE P7–677–68 An insulated piston–cylinder device initially contains300 L of air at 120 kPa and 17°C. Air is now heated for15 min by a 200-W resistance heater placed inside the cylinder.The pressure of air is maintained constant during thisprocess. Determine the entropy change of air, assuming(a) constant specific heats and (b) variable specific heats.7–69 A piston–cylinder device contains 1.2 kg of nitrogengas at 120 kPa and 27°C. The gas is now compressed slowlyin a polytropic process during which PV 1.3 constant. Theprocess ends when the volume is reduced by one-half. Determinethe entropy change of nitrogen during this process.Answer: 0.0617 kJ/K7–70 Reconsider Prob. 7–69. Using EES (or other)software, investigate the effect of varying thepolytropic exponent from 1 to 1.4 on the entropy change ofthe nitrogen. Show the processes on a common P-v diagram.7–71E A mass of 15 lbm of helium undergoes a processfrom an initial state of 50 ft 3 /lbm and 80°F to a final state of10 ft 3 /lbm and 200°F. Determine the entropy change of100 kPa17°CFIGURE P7–737–74 An insulated rigid tank is divided into two equal partsby a partition. Initially, one part contains 5 kmol of an idealgas at 250 kPa and 40°C, and the other side is evacuated. Thepartition is now removed, and the gas fills the entire tank.Determine the total entropy change during this process.Answer: 28.81 kJ/K7–75 Air is compressed in a piston–cylinder device from100 kPa and 17°C to 800 kPa in a reversible, adiabaticprocess. Determine the final temperature and the work doneduring this process, assuming (a) constant specific heats and(b) variable specific heats for air. Answers: (a) 525.3 K,171.1 kJ/kg, (b) 522.4 K, 169.3 kJ/kg7–76 Reconsider Prob. 7–75. Using EES (or other)software, evaluate and plot the work done andfinal temperature during the compression process as functionsof the final pressure for the two cases as the final pressurevaries from 100 to 800 kPa.7–77 Helium gas is compressed from 90 kPa and 30°C to450 kPa in a reversible, adiabatic process. Determine the finaltemperature and the work done, assuming the process takesplace (a) in a piston–cylinder device and (b) in a steady-flowcompressor.7–78 An insulated rigid tank contains 4 kg of argon gas at450 kPa and 30°C. A valve is now opened, and argon isallowed to escape until the pressure inside drops to 200 kPa.