Thermodynamic processes

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Question

A gas at NTP is suddenly compressed to one-fourth of its original volume. It r is supposed to be $\frac{3}{2}$ , then the final pressure is______atmosphere.

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Solution

$\begin{array}{l} P V^{r} = Constant \\ \frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ} = {(\frac{V}{V / 4})}^{\frac{3}{2}} = 8 \end{array}$

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