Interpreting the Carnot corollaries Dotted line defines combined system Hot reservoir First,two power cycles R and I; Then Let R operate as a refrigeration cycle; WR W SameW Q and Qc Hot reservoir:no change Oc=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=WR2->7R1=R2 So,2nd law places limits on the performance W<W-→1<R 上游充通大 Apr/5 Wed,2017 6 SHANGHAI JIAO TONG UNIVERSITY
Apr/5 Wed, 2017 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 B→∞；Y→∞ Heat pump cycle: -to deliver energy OH to the hot reservoir 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 Apr/5 Wed,2017 7 SHANGHAI JIAO TONG UNIVERSITY
Apr/5 Wed, 2017 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 0 COPI<COPR WR R W WR1=WR2 2c Cold reservoir 2c ↓ reversible irreversible COPR1=COPR2 上游文通大学 Apr/5 Wed,2017 8 SHANGHAI JIAO TONG UNIVERSITY
Apr/5 Wed, 2017 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