Q. An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume $\left( \gamma = 1.4\ and\ 2^{- 1.4} = 0.38 \right).$ The ratio of the final to initial pressure is
A) 0.76:1
B) 1:1
C) 0.66:1
D) 0.86:1
Explanation
(a) According to question
$p_{f}V^{\gamma} = \left( 2p_{i} \right)\left( \frac{V}{2} \right)^{\gamma}$
$\frac{P_{f}}{P_{i}} = 2\left( \frac{V}{2V} \right)^{\gamma} = 2(2)^{- \gamma}$
$= 2 \times 0.38 = 0.76$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.