Q110 / 150 · MHT CET 2022 (08 Aug Shift 1) · Physics

A polyatomic gas $\left(Y=\frac{4}{3}\right)$ is compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its volume adiabatically. If its initial pressure is $p$, its new pressure will be

  • A
    8p
  • Correct answer
    B
    16p
  • C
    2p
  • D
    6p

Solution

For an adiabatic process: $p V \gamma=$ constant Let initial pressure be $p$ and volume $V$, then the final pressure is $P$ and volume $\frac{V}{8}$. $\begin{aligned} & \Rightarrow p V^{4 / 3}=P\left(\frac{V}{8}\right)^{4 / 3} \\ & \Rightarrow P=8^{4 / 3} p=16 p \end{aligned}$

Hence, the correct answer is option: 'B'.

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