Q152 / 160 · WBJEE 2011 · Physics
An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume \(\left(\gamma=1.4\right.\) and \(\left.2^{-14}=0.38\right)\). The ratio of the final to initial pressure is
- A\(0.76: 1\)
- Correct answerB\(1: 1\)
- C\(0.66: 1\)
- D\(0.86: 1\)
Solution
Hints: 
\(\begin{aligned} & \mathrm{P}_{\mathrm{f}} \mathrm{V}^\gamma=\left(2 \mathrm{P}_{\mathrm{i}}\right)\left(\frac{\mathrm{V}}{2}\right)^\gamma \\ & \frac{\mathrm{P}_{\mathrm{f}}}{\mathrm{P}_{\mathrm{i}}}=2\left(\frac{\gamma}{2 \gamma}\right)^\gamma=2(2)^{-\gamma} \\ & =2 \times 0.38=0.76 \\ & \end{aligned}\)
\(\begin{aligned} & \mathrm{P}_{\mathrm{f}} \mathrm{V}^\gamma=\left(2 \mathrm{P}_{\mathrm{i}}\right)\left(\frac{\mathrm{V}}{2}\right)^\gamma \\ & \frac{\mathrm{P}_{\mathrm{f}}}{\mathrm{P}_{\mathrm{i}}}=2\left(\frac{\gamma}{2 \gamma}\right)^\gamma=2(2)^{-\gamma} \\ & =2 \times 0.38=0.76 \\ & \end{aligned}\)
Hence, the correct answer is option: 'B'.