EXAMINATION II SOLUTIONS MAKING ICE a SYSTEM 106 g H20 STATES 1 100oC g STEAM 2 100oC liquid 3 0oC liquid 4 0oC solid 5 10oC solid ETH 2 ETH 1 mLV 106 540 540 x 106 calories ETH 3 ETH 2 mCliquid T3 T2 106 1 00 0 100 100 x 106 calories ETH 4 ETH 3 mLF 106 80 80 x 106 calories ETH 5 ETH 4 mCsolid T5 T4 106 0 50 10 0 0 50x106 calories So ETH 720 5x106 calories b By the FIRST LAW of THERMODYNAMICS Qi f ETH for this process Qi f 720 5x106 calories a NET HEAT TRANSFER of 720 5x106 calories from the SYSTEM is required for this process THERMODYNAMIC POTPOURRI a For an adiabatic process T2V2 1 T1V1 1 where for a diatomic IDEAL GAS 1 40 and for this process r V2 V1 1 5 T1 293 K yielding T2 T1 1 r 1 558 K b For this process GIVEN Wi f 0 Qi f 0 By the FIRST LAW of THERMODYNAMICS then ETH ETH f ETH i nCv Tf Ti 0 or Tf Ti where from the Equation of State for the IDEAL GAS Ti piVi nR 2 02x105 10 0x10 3 811 8 314 299 6 K c In this situation CARNOT 3 where CARNOT 1 TL TH TL 273 40 K 233 K TH 273 K yielding CARNOT 0 147 and 0 049 4 9 d The Coefficient of Performance for a CARNOT HEAT PUMP operating between reservoirs TL and TH is CARNOT TH TH TL and the function of the HEAT PUMP is to compensate for natural HEAT losses from the home due principally to conductive and air infiltration processes In this scenario for the HEAT PUMP CARNOT dQH dt dW dt dW dt dQH dt CARNOT where for TH 293 K TL 286 K CARNOT 41 86 and dW dt 35 kW 41 86 0 836 kW Since the GSHP is assumed to be a CARNOT HEAT PUMP 0 836 kW represents the MINIMUM RATE of ENERGY INPUT required to operate the GSHP Air sealing and upgrading the insulation will reduce the RATE of natural HEAT TRANSFERS between the house and the outside and therefore reduce the demand on the GSHP So dW dt will decrease CONCEPTUAL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 C D A C C B C D C D B B A B D
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