A Carnot engine operates between two reservoirs at temperatures $600\text{ K}$ and $300\text{ K}$. If the engine performs $1000\text{ J}$ of work in each cycle, what is the amount of heat rejected to the cold reservoir?

Solution

1. The efficiency of a Carnot engine is given by $$\begin{array}{rl}\eta & =1-\frac{T_c}{T_h}\\ & =1-\frac{300\text{ K}}{600\text{ K}}\\ & =0.5\end{array}$$.
2. Efficiency is also defined as the ratio of work done to heat input, $\eta =\frac{W}{Q_h}$, so $0.5=\frac{1000\text{ J}}{Q_h}$, which gives $Q_h=2000\text{ J}$.
3. The heat rejected to the cold reservoir is $$\begin{array}{rl}{Q}_c& =Q_h-W\\ & =2000\text{ J}-1000\text{ J}\\ & =1000\text{ J}\end{array}$$.
4. Hence the answer is (B).