Room temperature $ = {t_1}{\,^ \circ }C$

For refrigerator,

$\frac{{Heat\,given\,to\,high\,temperature\,\left( {{Q_1}} \right)}}{{Heat\,taken\,from\,lower\,temperature\,\left( {{Q_2}} \right)}} = \frac{{{T_1}}}{{{T_2}}}$

$\frac{{{Q_1}}}{{{Q_2}}} = \frac{{{t_1} + 273}}{{{t_2} + 273}}$

$ \Rightarrow \frac{{{Q_1}}}{{{Q_1} - W}} = \frac{{{t_1} + 273}}{{{t_2} + 273}}\,\,or\,\,1 - \frac{W}{{{Q_1}}} = \frac{{{t_2} + 273}}{{{t_1} + 273}}$

$or\,\,\frac{W}{Q_1} = \frac{{{t_1} - {t_2}}}{{{t_1} + 273}}$

The amount of heat delivered to the room for each joule pf electrical energy $\left( {W = 1\,J} \right)$

${Q_1} = \frac{{{t_1} + 273}}{{{t_1} - {t_2}}}$