Question

A gas undergoes a cyclic process $a\to b\to c\to a$ which is as shown in the $PV$ diagram. The process $a\to b$ is isothermal , $b\to c$ is adiabatic and $c\to a$ is a straight line on the $P-V$ diagram. Work done in process $ab$ and $bc$ is $5\text{J}$ and $4\text{J}$ respectively. Calculate the efficiency of the cycle, if the area enclosed by the diagram $\text{abca}$ in the figure is $3\text{J}$.

• A. $0.4$
• B. $0.6$
• C. $0.75$
• D. $0.8$

Answer 1

The correct option is B $0.6$

From the data given in the question,
Work done during process $ab$ $\left(W_{ab}\right)=5\text{J}.....\left(1\right)$
Work done during process $bc$ $\left(W_{bc}\right)=4\text{J}$
Total work done during the cycle $a\to b\to c\to a$
$\left(W\right)=\text{Area enclosed by the graph}=3\text{J}......\left(2\right)$

Using first law of thermodynamics for process $ab$, we get
$Q_{ab}=\Delta U_{ab}+W_{ab}$
For an isothermal process, $\Delta T=0$
$\Rightarrow \Delta U_{ab}=0$
From $\left(1\right)$, we get, $Q_{ab}=5\text{J}.....\left(3\right)$ {heat absorbed}
$Q_{bc}=0$ {adiabatic}
and in process $ca$, heat is rejected.

Hence, from $\left(2\right)$ and $\left(3\right)$, we get
Efficiency of cycle $\eta =\frac{\text{Work output}}{\text{Heat input}}=\frac{W}{Q_{ab}}=\frac{3}{5}=0.6$
Thus, option (b) is the correct answer.