MEEN 315 SECTION 503 PRINCIPLES OF THERMODYNAMICS Spring 2013 Homework 10 DUE April 16 2013 1 A power plant generates 150 MW of electrical power It uses a supply of 1000 MW from a geothermal source and rejects energy to the atmosphere Find the power to the air and how much air should be flowed to the cooling tower kg s if its temperature cannot be increased more than 10 C Finally if you assume the power plant operates on a Carnot Cycle and the atmosphere is 20 C assume the heat rejection occurs at constant temperature what is the temperature of the geothermal source 2 We wish to produce refrigeration at 20 F A reservoir is available at 400 F and the ambient temperature is 80 F as shown to the right Thus work can be done by a cyclic heat engine operating between the 400 F reservoir and the ambient This work is used to drive the refrigerator Determine the ratio of the heat transferred from the 400 F reservoir to the heat transferred from the 20 F reservoir assuming all processes are reversible 3 A farmer runs a heat pump with a motor of 2 kW It should keep a chicken hatchery at 30 C which loses energy at a rate of 0 5 kW per degree difference to the colder ambient Tamb The heat pump has a coefficient of performance that is 50 of a Carnot heat pump What is the minimum ambient temperature for which the heat pump is sufficient 4 Consider a Carnot heat pump cycle executed in a steady flow system in the saturated liquid vapor mixture region of R 134a The R 134a is flowing at a rate of 0 264 kg s It is known that the maximum absolute temperature in the cycle is 1 25 times the minimum absolute temperature and the net power input to the cycle is 7 kW If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process determine the ratio of the maximum and minimum pressures in the cycle HINT Recall that hfg hg hf 5 In a Carnot engine with water as the working fluid the high temperature is 450 F and as QH is received the water changes from saturated liquid to saturated vapor The water pressure at the low temperature is 14 7 psia Find TL cycle thermal efficiency heat added per lbm and entropy s at the beginning of the heat rejection process A power plant generates 150 MW of electrical power It ses a supply of 1000 MW from a geothennal source and rejects energy to the atmosphere Find the to the air and how much air should be flowed to the cooling tower kg s if its temperature cannot be increased more than 100 e Finally if you assume the power plant operates on a Carnot Cycle and the atmosphere is 20 C assume the heat rejection occurs at constant temperature what is the temperature of the geothermal source r 1 xy LV gov Q 1 Q 1J H y l O c r I oor t r IO c cI t J t y T Q 111 C r Q c r T Qf vv I COO r r Jo I t 1000 M h t i M Ii V Q Q Re C w i AJe ecf fo 6 i cr I J s t J If E M 8 rn M v C9 EV r Vte 6 cvw i J kod A 1 Q T I We wish to produce refrigeration at 20 F A reservoir is available at 400 F and the ambient temperature is 80 F as sho n to the right Thus work can be done by a cyclic heat engine operating between the 400 f reservoir and the ambient This ork is used to drive the refrigerator Determine the ratio of the heat transferred from the 400 F reservoir 10 the heat transferred from the 20 F reservoir assuming all processes are reversible 1 T LJ rt 1 tiE T t tiE THJu f 1 I 00 F v iJ r GJ ti 1 iD R C O R 6 I SqO 4 5vvYIf t f QL J R fr j It E rL W fiE WN E Wr 1 c l or Wit f te t A I f roc s ies So 1 R Q 8E QI j f f l p CJ L1 lit Q r I Q t f e ws A farmer runs a heat pump with a motor of 2 kW It should keep a chicken hatchery at 30 C which loses energy at a rate of 0 5 kW per degree difference to the colder ambient Tomb The heat pump has a coefficient of performance that is 50 of a Carnol heat pump What is the minimum ambient temperature for which the heat pump is sufficient c t k IA t J rt Q 11 fj 11 t J V l art o To cil 2 0 ZOf c j c O Oe C 1i QL T To I f 111 I Q I I QI a VI 01 0 W Dei T W tr I LJ lL lot 1 VI TL Ttt IL gO J It oc t 1 q o Consider a Carnot heat pump cycle executed in a steady flow system in the saturated liquid vapor mixture region ofR 134a The R J343 is flowing at 3 rate 0 0 264 kg so t is known that the maximum absolute temperature in the cycle is 1 25 limes the minimum absolute temperature and the net power input to the cycle is 7 kW If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process determine the ratio of the maximum and minimum pressures in the cycle HINT Recall that hfg hg hf T I I ofp VIUS Wl 1 GH O J P i lolls 1 1 l L C 1 1 1 P I r f 01 ClL VV C QI t M d d W r Tot 1 1 J i k4 ek Q I QIi I l Iii IN i rii I ITIt li IT t k r W W k f T txiJLe A II T L l K l r v e f J E It s r 1 1 PIf C 11 1 I 1 f J 1 0 s L I l 1 P L a In a Carnot engine with water the working t1uid the high temperature is 450 p and as QH is received the water changes from saturated liquid to saturated vapor The water pressure at the low temperature is 14 7 psia Find T L cycle thennal efficiency heat added per Ibm and entropy s at the beginning of the heat rejection process 1 1 1 n r Lt Q IS jVlcec tJCA fer n L y ck kJ tS V 1 0 1 f sG t V c f r HE Pl JTI 14 j t t Jl l Q J s f r tf t 1 t I J Ii 2 …