Answer
$\dot{W}_{\text {out,max }}=364\text{ kW}$
Work Step by Step
The maximum thermal efficiency this thermoelectric generator can have is $$
\eta_{\text {th,max }}=1-\frac{T_L}{T_H}=1-\frac{295 \mathrm{~K}}{363 \mathrm{~K}}=0.1873
$$ Thus, $$
\dot{W}_{\text {ouț,max }}=\eta_{\text {th,max }} \dot{Q}_{\text {in }}=(0.1873)\left(7 \times 10^6 \mathrm{~kJ} / \mathrm{h}\right)=1.31 \times 10^6 \mathrm{~kJ} / \mathrm{h}=364\ \mathbf{k W}
$$
