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Q.
If the energy input to a Carnot engine is thrice the work it performs then, the fraction of energy rejected to the sink is
Thermodynamics
Solution:
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 $Q_{1}=3 W$ (given)
$\therefore \frac{Q_{2}}{Q_{1}}=1-\frac{W}{3 W}$
$=1-\frac{1}{3}=\frac{2}{3}$
Thus the fraction of energy rejected to the sink is $\frac{2}{3}$.