Obtain the Coefficient of performance (COP). `(beta)`.

Explanation

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)`
From the equation `Q_(L)+W=Q_(H)`
`beta=(Q_(L))/(Q_(H)-Q_(L)), beta = (1)/((Q_(H))/(Q_(L))-1)" " ...(1)`
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))`