Thermodynamics

418 | Thermodynamicsare 104°C and 105°C, respectively, determine the rate ofentropy generation within bottom of the pan, in W/K.500 W104°CFIGURE P7–1877–188 A 1200-W electric resistance heating element whosediameter is 0.5 cm is immersed in 40 kg of water initially at20°C. Assuming the water container is well-insulated, determinehow long it will take for this heater to raise the watertemperature to 50°C. Also, determine the entropy generatedduring this process, in kJ/K.7–189 A hot-water pipe at 80°C is losing heat to the surroundingair at 5°C at a rate of 2200 W. Determine the rate ofentropy generation in the surrounding air, in W/K.7–190 In large steam power plants, the feedwater is frequentlyheated in closed feedwater heaters, which are basicallyheat exchangers, by steam extracted from the turbine atsome stage. Steam enters the feedwater heater at 1 MPa and200°C and leaves as saturated liquid at the same pressure.Feedwater enters the heater at 2.5 MPa and 50°C and leaves10°C below the exit temperature of the steam. Neglecting anyheat losses from the outer surfaces of the heater, determine(a) the ratio of the mass flow rates of the extracted steam andthe feedwater heater and (b) the total entropy change for thisprocess per unit mass of the feedwater.7–191 Reconsider Prob. 7–190. Using EES (or other)software, investigate the effect of the state ofthe steam at the inlet of the feedwater heater. Assume theentropy of the extraction steam is constant at the value for 1MPa, 200°C and decrease the extraction steam pressure from1 MPa to 100 kPa. Plot both the ratio of the mass flow ratesof the extracted steam and the feedwater heater and the totalentropy change for this process per unit mass of the feedwateras functions of the extraction pressure.7–192E A 3-ft 3 rigid tank initially contains refrigerant-134aat 100 psia and 100 percent quality. The tank is connected bya valve to a supply line that carries refrigerant-134a at 140psia and 80°F. The valve is now opened, allowing the refrigerantto enter the tank, and is closed when it is observed thatthe tank contains only saturated liquid at 120 psia. Determine(a) the mass of the refrigerant that entered the tank, (b) theamount of heat transfer with the surroundings at 110°F, and(c) the entropy generated during this process.7–193 During a heat transfer process, the entropy change ofincompressible substances, such as liquid water, can be determinedfrom S mc avg ln(T 2 /T 1 ). Show that for thermalenergy reservoirs, such as large lakes, this relation reduces toS Q/T.7–194 The inner and outer glasses of a 2-m 2-m doublepanewindow are at 18°C and 6°C, respectively. If the glassesare very nearly isothermal and the rate of heat transfer throughthe window is 110 W, determine the rates of entropy transferthrough both sides of the window and the rate of entropygeneration within the window, in W/K.18°C 6°CQAIRFIGURE P7–1947–195 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 120-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 air in 30 min, (b) the entropy change of the steam,(c) the entropy change of the air in the room, and (d) theentropy generated during this process, in kJ/K. Assume the airpressure in the room remains constant at 100 kPa at all times.7–196 A passive solar house that is losing heat to the outdoorsat 3°C at an average rate of 50,000 kJ/h is maintainedat 22°C at all times during a winter night for 10 h. The houseis to be heated by 50 glass containers, each containing 20 Lof water that is heated to 80°C during the day by absorbingsolar energy. A thermostat controlled 15 kW backup electricresistance heater turns on whenever necessary to keep thehouse at 22°C. Determine how long the electric heating systemwas on that night and the amount of entropy generatedduring the night.7–197E A 15-ft 3 steel container that has a mass of 75 lbmwhen empty is filled with liquid water. Initially, both the steeltank and the water are at 120°F. Now heat is transferred, and