A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma=1.5$, then the final…

A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma=1.5$, then the final pressure is
  1. 4 times
  2. 1.5 times
  3. 8 times
  4. $\frac{1}{4}$ times

Solution

As the change is sudden, the process is adiabatic $\begin{array}{ll} \therefore & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\ \therefore & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left[\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right]^\gamma=\left[\frac{4}{1}\right]^{3 / 2}=\frac{8}{1} \end{array}$

Asked in: MHT CET 2023 (09 May Shift 2)

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