The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when the gas is suddenly compressed to volume V₀/4 will be:
(Given $γ$ = ratio of specific heats at constant pressure and at constant volume)

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P₀

4P₀

$P_{0} (4)^{γ}$

$P_{0} (4)^{1 / γ}$

answer is C.

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Detailed Solution

As the gas is compressed suddenly, the process will be adiabatic in nature.

Using the relation of ${PV}^{γ} = constant$ .

We get $\frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ}$

$\Rightarrow P_{2} = P_{0} {(\frac{V_{0}}{V_{0} / 4})}^{γ} = P_{0} 4^{γ}$

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