Question

An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done by gas during the whole process is $W$. Then identify the correct statement.

• A. $P_3>P_1,W>0$
• B. $P_3<P_1,W<0$
• C. $P_3>P_1,W<0$
• D. $P_3=P_1,W=0$

Answer 1

The correct option is C $P_3>P_1,W<0$

The two processes are shown in the following $P-V$ diagram.


As slope of adiabatic curve is greater than that of isothermal process curve, adiabatic curve will lie above the isothermal curve.
$\Rightarrow$For isothermal process$(1\to 2)$, For adiabatic process $(2\to 3)$

From, the shown graph it is clear that pressure $P_3$ is greater than $P_1$.
$\therefore P_3>P_1$

Area under the curve for adiabatic process $(2\to 3)$ is greater than area under curve for isothermal process $(1\to 2)$
$\because (2\to 3)$ gives a $-ve$ work done by gas (due to compression) and $(1\to 2)$ gives a $+ve$ work done by gas (due to expansion)
$\Rightarrow \text{Negative Work}>\text{Positive Work}$
Hence net work done by gas during whole process is $-ve$.
$\therefore W<0$