Answer
$\dot{W}_{\text {in } \min }=12.1 W$
Work Step by Step
The maximum COP of this thermoelectric refrigerator is the COP of a Carnot refrigerator operating between the same temperature limits,
$$
\mathrm{COP}_{\max }=\mathrm{COP}_{\text {R.Carnot }}=\frac{1}{\left(T_H / T_L\right)-1}=\frac{1}{(293 \mathrm{~K}) /(268 \mathrm{~K})-1}=\mathbf{1 0 . 7 2}
$$ Thus, $$
\dot{W}_{\text {in, } \min }=\frac{\dot{Q}_L}{\mathrm{COP}_{\max }}=\frac{130 \mathrm{~W}}{10.72}=12.1 \mathrm{~W}
$$
