A monoatomic gas is suddenly compressed to $(1 / 8)^{ ext {th }}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is ( $\gamma=5 / 3$ )

Question

A monoatomic gas is suddenly compressed to $(1 / 8)^{	ext {th }}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is ( $\gamma=5 / 3$ )

Aicharya · Accepted Answer

$\frac{\mathrm{V}_2}{\mathrm{~V}_1}=\frac{1}{8}, \gamma=\frac{5}{3}$ For adiabatic process, $\begin{aligned} & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \ & 	herefore \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}ight)^\gamma=(8)^{5 / 3}=(2)^5=32 \end{aligned}$

A monoatomic gas is suddenly compressed to $(1 / 8)^{\text {th }}$ of its initial volume adiabatically. The…

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