Design Energy Conversion Devices Practice Test

A small heat engine is proposed to convert thermal energy $\rightarrow$ mechanical work for a demonstration vehicle. The hot reservoir is at $T_{hot} = 600,\text{K}$ and the cold reservoir is at $T_{cold} = 300,\text{K}$. The engine must achieve an efficiency of at least $\eta \ge 55%$ to meet the project goal.

Based on the Carnot limit $\eta_{max} = 1 - \dfrac{T_{cold}}{T_{hot}}$, is the goal achievable in principle?

(You do not need detailed thermodynamics beyond the Carnot formula.)

A camping stove add-on is a thermoelectric generator that converts thermal → electrical energy. The stove provides thermal input power $P_{in}=150\ \text{W}$. The thermoelectric module has efficiency $\eta=5%$. The device must provide at least $P_{out}\ge 10\ \text{W}$ to charge a battery.

Which modification would most directly help meet the 10 W electrical output requirement, assuming the efficiency stays the same unless stated?