A monoatomic gas having is stored in a thermally insulated container and the gas is suddenly compressed to of its initial volume. The ratio of final pressure and initial pressure is: ( is the ratio of specific heats of the gas at constant pressure and a

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Solution

Q.
A monoatomic gas having $γ = \frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to ${(\frac{1}{8})}^{th}$ of its initial volume. The ratio of final pressure and initial pressure is: ( $γ$ is the ratio of specific heats of the gas at constant pressure and at constant volume) [2025]

1 16

2 40

3 32

4 28

Ans.
(3)

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

$\Rightarrow \frac{P_{f}}{P_{i}} = {(\frac{V_{i}}{V_{f}})}^{γ} = {(8)}^{5 / 3} = 32$

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