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A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma=1.5$, then the final pressure is
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As the change is sudden, the process is adiabatic
$\begin{array}{ll}
\therefore & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\
\therefore & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left[\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right]^\gamma=\left[\frac{4}{1}\right]^{3 / 2}=\frac{8}{1}
\end{array}$
$\begin{array}{ll}
\therefore & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\
\therefore & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left[\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right]^\gamma=\left[\frac{4}{1}\right]^{3 / 2}=\frac{8}{1}
\end{array}$
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