question_answer 31)

                  If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature \[({{27}^{o}}C)\] , find the temperature inside the refrigerator.                

Answer:

                  Co-efficient of performance \[\text{=}\,\frac{\text{Heat}\,\,\text{extracted}\,\,\text{from}\,\,\text{cold}\,\,\text{body}}{\text{Work}\,\,\text{done}}\]                 or \[E=\,\frac{{{Q}_{2}}}{W}\,=\,\frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}\]                 Since \[\frac{{{Q}_{1}}}{{{T}_{1}}}=\frac{{{Q}_{2}}}{{{T}_{2}}}\]                 \[\therefore \]\[E=\,\frac{{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}\]                 or \[5=\,\frac{{{T}_{2}}}{300\,-{{T}_{2}}}\,\] or \[{{T}_{2}}=250\text{ }K=23{}^\circ C.\]