Question

A gas undergoes a cyclic process $a-b-c-a$ which is as shown in $PV$ diagram. The process $a-b$ is isothermal, $b-c$ is adiabatic and $c-a$ is a straight line on $P-V$ diagram. Work done in process $ab$ and $bc$ is $5J$ and $4J$ respectively. If the area enclosed by the diagram $abca$ in the figure is $3J$, choose the correct statements.

• A. The efficiency of cycle is $0.6$
• B. Workdone during process $c-a$ is $-6J$
• C. Change in Internal energy during process $b-c$ is $2J$
• D. Change in Internal energy during process $c-a$ is $2J$

Answer 1

The correct option is B Workdone during process $c-a$ is $-6J$

For process $ab$
Work done $W_{ab}=5J$
Internal energy $\Delta U_{ab}=0$ (isothermal process)
$\Rightarrow Q_{ab}=\Delta U_{ab}+W_{ab}=5J$ (from 1st law)

For process $bc$
$W_{bc}=4J$ and $Q_{bc}=0$ (adiabatic process)

$\Rightarrow \Delta U_{bc}=Q_{bc}-W_{bc}=-4J$ (from 1st law)

For cyclic process, $abca$,
$\Delta U_{ab}+\Delta U_{bc}+\Delta U_{ca}=0$
$\Rightarrow \Delta U_{ca}=4J$
Also,
$W_{ab}+W_{bc}+W_{ca}=3J$ (Area under $PV$ graph)
$\Rightarrow 5+4+W_{ca}=3$
$\Rightarrow W_{ca}=-6J$

For process $ca$
$Q_{ca}=W_{ca}+U_{ca}=4-6=-2J$

Efficiency of cycle, $\eta =\frac{\text{net work done}}{\text{net heat supplied to system}}$
$\eta =\frac{W_{\text{net}}}{Q_{ab}}=\frac{3}{5}=0.6$