Interpreting the Carnot corollaries Dotted line defines combined system 行中中年者中年车年年香小华中小小小票自车车小年有中小中小年中中非年华果车中车年小中中年华华车车车青有 Hot reservoir First,two power cycles R and I; >OH Then Let R operate as a refrigeration cycle; WR W SameW QH and Qc Hot reservoir:no change Qc=CH-WR Oc=CH-WI Cold reservoir Combined system: W cle <0 (single reservoir) Similarly:for two reversible cycles R1 and R2 WI-WR<0 WR1=W2->7R1=1R2 So,2nd law places limits on the performance Wi<WR---->m<n 上游充通大 April 17,2018 6 SHANGHAI JIAO TONG UNIVERSITY
April 17, 2018 6 Interpreting the Carnot corollaries First, two power cycles R and I; Then Let R operate as a refrigeration cycle; Same WR , QH , and QC Hot reservoir: no change Combined system: W W I R I R W W R1 R2 R1 R2 Similarly: for two reversible cycles R1 and R2 So, 2nd law places limits on the performance
Refrigeration and Heat Pump Cycles Hot CH= reservoir c+Weyele Refrigeration cycle: -to remove energy Qc from the cold Boundary Weyele OH-Oc reservoir Coefficient Of Performance >COP Cold reservoir Qe B Weycle CH-Qc e→0， B→∞；Y→∞ Heat pump cycle: -to deliver energy QH to the hot reservoir W cycle =0 Transfer Qc from cold reservoir CH to hot reservoir without W input Wcycle Cn-Qc (normally 2~4) Violate Clausius statement for fixed values of Q and Q: Y=B+1 上泽通大学 April 17,2018 7 SHANGHAI JIAO TONG UNIVERSITY
April 17, 2018 7 Refrigeration and Heat Pump Cycles Refrigeration cycle: —to remove energy QC from the cold reservoir Heat pump cycle: — to deliver energy QH to the hot reservoir Coefficient Of Performance COP for fixed values of QL and QH : 1 (normally 2~4) Wcycle 0 β∞; γ∞ Wcycle = 0 Transfer QC from cold reservoir to hot reservoir without W input Violate Clausius statement
Corollaries for reverse cycles and Interpreting The COP of an irreversible refrigeration (heat pump)cycle is always less than the COP of a reversible refrigeration cycle when each operates between the same two thermal reservoirs. All reversible refrigeration (heat pump)cycles operating between the same two thermal reservoirs have the same coefficient of performance. CH=Oc+WR OH=Qc+WI WI>WR Hot reservoir ↓ COPI<COPR WR R W WR1 WR2 2c Cold reservoir 2c reversible irreversible COPR1 COPR2 上游文通大学 April 17,2018 8 SHANGHAI JIAO TONG UNIVERSITY
April 17, 2018 8 Corollaries for reverse cycles and Interpreting reversible irreversible WI > WR COPI < COPR WR1 = WR2 COPR1 = COPR2 • The COP of an irreversible refrigeration (heat pump) cycle is always less than the COP of a reversible refrigeration cycle when each operates between the same two thermal reservoirs. • All reversible refrigeration (heat pump) cycles operating between the same two thermal reservoirs have the same coefficient of performance. 1 2