Q136 / 150 · MHT CET 2021 (23 Sep Shift 2) · Physics
An ideal gas at pressure ' $p$ ' is adiabatically compressed so that its density becomes twice that of the initial. If $\gamma=\frac{c_p}{c_v}=\frac{7}{5}$, then final pressure of the gas is
- A$\mathrm{p}$
- B$2 \mathrm{p}$
- C$\frac{7}{5} \mathrm{p}$
- Correct answerD$2.63 p$
Solution
Since density become twice, its volume will become half.
$$
\therefore \frac{\mathrm{V}_1}{\mathrm{~V}_2}=2
$$
$\therefore$ For adiabatic process we have
$$
\begin{aligned}
& \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\
& \therefore \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)^\gamma=(2)^{7 / 5}=(2)^{1.4}=2.63
\end{aligned}
$$
Hence, the correct answer is option: 'D'.