The coefficient of performance of a refrigerator is 5 . If the temperature inside freezer is $-20^{\circ} \mathrm{C}$, the temperature of the surrounding to which is rejects heat is: (1) $21^{\circ} \mathrm{C}$ (2) $31^{\circ} \mathrm{C}$ (3) $41^{\circ} \mathrm{C}$ (4) $11^{\circ} \mathrm{C}$

Solution: (2)

$
\begin{array}{l}
\operatorname{cop}=\frac{\mathrm{q}_{1}}{w}=\frac{\mathrm{q}_{2}}{\mathrm{q}_{1}-\mathrm{q}_{2}}=\frac{\mathrm{T}_{\mathrm{c}}}{\mathrm{T}_{\mathrm{H}}-\mathrm{T}_{\mathrm{C}}}=5 \\
\mathrm{~T}_{\mathrm{C}}=5 \mathrm{~T}_{\mathrm{H}}-5 \mathrm{~T}_{\mathrm{c}} \\
6 \mathrm{~T}_{\mathrm{c}}=5 \mathrm{~T}_{\mathrm{H}} \\
\mathrm{T}_{\mathrm{H}}=\frac{6}{5} \times 253 \mathrm{k}=303.6 \mathrm{k}=30.6^{\circ} \mathrm{C}=31^{\circ} \mathrm{C}
\end{array}
$