A Carnot’s cycle is a reversible cycle. It can be described in the reverse direction. We can construct a device that can follow Carnot’s cycle in the reverse order. It absorbs Q2 amount of heat from the cold reservoir at T2, has work W done on it by an outside agency, and rejects Q1 amount of heat at the hot reservoir at T1. The device, known as a refrigerator, therefore cools the cold reservoir.
In a refrigerator heat energy flow from the cold reservoir (the inside of the refrigerator) to the hot reservoir (the outside of the refrigerator). The system is run by an outside energy source. The quality of a refrigerator is expressed in terms of the extracted heat, Q2, and the work done, W by an external agency. We, therefore, define the co-efficient of performance, C.O.P of a refrigerator as follows:
C.O.P = extracted heat/input work or C.O.P = Q2/W
From the above diagram showing heat flow in a refrigerator, we find that-
Q1 = Q2 + W
Thus the co-efficient of performance can be written as-
C.O.P = Q2/(Q1 – Q2)
In terms of the temperature of the cold reservoir, T2, and temperature of the hot reservoir T1, this reduces to-
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