Q. Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$. The final pressure of gas will be (given $\gamma = 3/2$)
A) $1P$
B) $2P$
C) $4P$
D) $8P$
Explanation
(b) In isothermal process $P_{1}V_{1} = P_{2}V_{2}$
$\Rightarrow PV = P_{2} \times 4V\ \therefore P_{2} = \frac{P}{4}$
In adiabatic process
$P_{2}V_{2}^{\ \gamma} = P_{3}V_{3}^{\ \ \gamma} \Rightarrow \frac{P}{4} \times (4V)^{1.5} = P_{3}V^{1.5} \Rightarrow P_{3} = 2P$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.