The temperature inside a refrigerator is $t_2 \,^o C$ and the room temperature is $t_1\,^o C.$ The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be
NEET 2016, Medium
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Temperature inside refrigerator $ = {t_2}{\,^ \circ }C$
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 $\left( {W = 1\,J} \right)$
${Q_1} = \frac{{{t_1} + 273}}{{{t_1} - {t_2}}}$
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