Question

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then

• 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 $P_3>P_1,W<0$

In this figure, the curve ab represents isothermal expansion from $(P_1,V_1)$ to $(P_2,V_2)$.

As we compress the gas adiabatically it attains the state c.

So, $P_2>1$.

Total work$=W_{iso}+W_{iadia}$

The work done is specified so $W_{iso}⟶+ve,W_{iadia}⟶-ve$.

So, $W<0$ as $P_3>P_1,W<0.$