If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature $${27^ \circ }C,$$  the temperature inside the refrigerator is

Solution :
Here, Coefficient of performance $$\left( \beta \right) = 5$$
$$\eqalign{ & {T_1} = {27^ \circ }C = \left( {27 + 273} \right)K = 300\,K \cr & {\text{As,}}\,\beta = \frac{{{T_2}}}{{{T_1} - {T_2}}} \Rightarrow 5 = \frac{{{T_2}}}{{300 - {T_2}}} \cr & {\text{or}}\,\,1500 - 5{T_2} = {T_2}\,{\text{or}}\,6{T_2} = 1500 \cr & \therefore {T_2} = \frac{{1500}}{6} = 250\,K \cr} $$