Question

If the energy input to a Carnot engine is thrice the work it performs then, the fraction of energy rejected to the sink is

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

If $Q_1$ is the energy input and $Q_2$ is the energy rejected to the sink, then work done $W=Q_1-Q_2$
Dividing by $Q_1$ on both sides, we get
$\frac{W}{Q_1}=1-\frac{Q_2}{Q_1}$ or
$\frac{Q_2}{Q_1}=1-\frac{W}{Q_1}$
As $Q_1=3W$ (given)
$\therefore \frac{Q_2}{Q_1}=1-\frac{W}{3W}$
$=1-\frac{1}{3}=\frac{2}{3}$
Thus the fraction of energy rejected to the sink is $\frac{2}{3}$.