Derive an expression for co-efficient of performance of refrigerator.

1.	Derive an expression for co-efficient of performance of refrigerator.
Answer» Solution :Coefficient of performance (COP)`(beta)`: COP is a MEASURE of the efficiency of a REFRIGERATOR. It is defined as the ratio of heat extracted from the cold BODY (sink) to the EXTERNAL work DONE by the compressor W. COP `= beta = (Q_(L))/W`...(1) From the equation `Q_(L)+W=Q_(H)` `beta = (Q_(L))/(Q_(H) - Q_(L))` `beta = (1)/((Q_(H))/(Q_(L)) - 1)`...(2) But we know that `(Q_(H))/(Q_(L)) = (T_(H))/(T_(L))` Substituting this equation into equation (1) we get `beta = (1)/((T_(H))/(T_(L)) - 1) = (T_(L))/(T_(H) - T_(L))`

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