A Carnot engine is working between 300\ K and 600\ K has output 200\ J . What is the energy supplied to the engine ? a) 400\ J b) 800\ J c) 1200\ J d) 1600\ J

For a Carnot engine, the efficiency $\eta$ is given by: $$\eta =1-\frac{T_C}{T_H}$$ where $T_C=300\mathrm{K}$ (cold reservoir) and $T_H=600\mathrm{K}$ (hot reservoir).

Substitute the values: $$\eta =1-\frac{300}{600}=1-0.5=0.5$$

The efficiency is also defined as: $$\eta =\frac{W}{Q_H}$$ where $W=200\mathrm{J}$ (work output) and $Q_H$ is the energy supplied to the engine.

Rearrange to solve for $Q_H$: $$Q_H=\frac{W}{\eta }=\frac{200}{0.5}=400\mathrm{J}$$

Energy supplied to the engine: 400 J (Option a)