Question

The efficiency of a Carnot engine is $0.6$. It rejects total $20J$ of heat. The work done in $\left(J\right)$ by the engine is

Answer 1

Heat rejected, $Q_r=20J$

Efficiency, $\eta =0.6$

The efficiency of the engine, $\eta =\frac{W}{Q}$

$0.6=\frac{\text{Work done}}{Q_{\text{input}}}=\frac{Q_{\text{input}}-Q_{\text{reject}}}{Q_{\text{input}}}$

$0.6=1-\frac{Q_r}{Q_i}$

$0.6=1-\frac{20}{Q_i}$

$Q_i=50$

$W=Q_i-Q_r=30J$

Final answer: $30$