Answer to Question #243226 in Mechanical Engineering for Imms(ENG)

Question #243226

Prove that the COP of a reversible refrigerator operating between two given temperature is the maximum.


1
Expert's answer
2021-09-28T00:54:48-0400


Considering two thermal energy reservoirs, one at a higher temperature of"T_H" compared to the other at "T_L" , if we operate a reversible refrigeration cycle between the reservoirs then its coefficient of performance is given by,


"COP_{R,rev}=T_L\/T_H-T_L"


This is the basically the maximum COP a refrigeration cycle can achieve operating between two thermal energy reservoirs at "T_H" and "T_L" .Since a Carnot refrigerator is a reversible refrigeration cycle the above expression for"\\space COP_{R,rev}" is valid for the reversed Carnot cycle.


If we consider any other reversible refrigeration cycle operating between the same two temperature limits it should have a similar COP as given by the above expression.Now considering a reversed Brayton cycle which is a reversible cycle (all processes are internally reversible) operating between two TERs at "T_H" and "T_L".




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