Thermodynamics

480 | Thermodynamicsof the inner and outer surfaces of the bottom of the pan are104°C and 105°C, respectively, determine the rate of exergydestruction within the bottom of the pan during this process,in W. Take T 0 25°C.8–104 A crater lake has a base area of 20,000 m 2 , and thewater it contains is 12 m deep. The ground surrounding thecrater is nearly flat and is 140 m below the base of the lake.Determine the maximum amount of electrical work, in kWh,that can be generated by feeding this water to a hydroelectricpower plant. Answer: 95,500 kWh8–105E A refrigerator has a second-law efficiency of45 percent, and heat is removed from the refrigerated spaceat a rate of 200 Btu/min. If the space is maintained at 35°Fwhile the surrounding air temperature is 75°F, determine thepower input to the refrigerator.8–106 Writing the first- and second-law relations and simplifying,obtain the reversible work relation for a closed systemthat exchanges heat with the surrounding medium at T 0 in theamount of Q 0 as well as a heat reservoir at T R in the amount ofQ R . (Hint: Eliminate Q 0 between the two equations.)8–107 Writing the first- and second-law relations and simplifying,obtain the reversible work relation for a steady-flowsystem that exchanges heat with the surrounding medium atT 0 in the amount of Q . 0 as well as a thermal reservoir at T R ata rate of Q . R . (Hint: Eliminate Q. 0 between the two equations.)8–108 Writing the first- and second-law relations and simplifying,obtain the reversible work relation for a uniform-flowsystem that exchanges heat with the surrounding medium at T 0in the amount of Q 0 as well as a heat reservoir at T R in theamount of Q R . (Hint: Eliminate Q 0 between the two equations.)8–109 A 50-cm-long, 800-W electric resistance heatingelement whose diameter is 0.5 cm is immersed in 40 kg ofwater initially at 20°C. Assuming the water container is wellinsulated,determine how long it will take for this heater toraise the water temperature to 80°C. Also, determine the minimumwork input required and exergy destruction for thisprocess, in kJ. Take T 0 20°C.Water40 kgHeaterFIGURE P8–1098–110 A 5-cm-external-diameter, 10-m-long hot water pipeat 80°C is losing heat to the surrounding air at 5°C by naturalconvection at a rate of 45 W. Determine the rate at which thework potential is wasted during this process as a result of thisheat loss.8–111 Two rigid tanks are connected by a valve. Tank A isinsulated and contains 0.2 m 3 of steam at 400 kPa and 80 percentquality. Tank B is uninsulated and contains 3 kg of steamat 200 kPa and 250°C. The valve is now opened, and steamflows from tank A to tank B until the pressure in tank A dropsto 300 kPa. During this process 900 kJ of heat is transferredfrom tank B to the surroundings at 0°C. Assuming the steamremaining inside tank A to have undergone a reversible adiabaticprocess, determine (a) the final temperature in each tankand (b) the work potential wasted during this process.A0.2 m 3STEAM400 kPax = 0.8FIGURE P8–111B3 kgSTEAM200 kPa250°C8–112E A piston–cylinder device initially contains 15 ft 3 ofhelium gas at 25 psia and 70°F. Helium is now compressed ina polytropic process (PV n constant) to 70 psia and 300°F.Assuming the surroundings to be at 14.7 psia and 70°F,determine (a) the actual useful work consumed and (b) theminimum useful work input needed for this process.Answers: (a) 36 Btu, (b) 34.2 Btu8–113 A well-insulated 4-m 4-m 5-m room initially at10°C is heated by the radiator of a steam heating system. Theradiator has a volume of 15 L and is filled with superheatedvapor at 200 kPa and 200°C. At this moment both the inletand the exit valves to the radiator are closed. A 150-W fan isused to distribute the air in the room. The pressure of thesteam is observed to drop to 100 kPa after 30 min as a resultof heat transfer to the room. Assuming constant specific heatsfor air at room temperature, determine (a) the average temperatureof room air in 24 min, (b) the entropy change of thesteam, (c) the entropy change of the air in the room, and(d) the exergy destruction for this process, in kJ. Assume theair pressure in the room remains constant at 100 kPa at alltimes, and take T 0 10°C.Fan4 m × 4 m × 5 m10°CSteamradiatorFIGURE P8–113