The initial pressure and volume of an ideal gas are and . The final pressure of the gas when the gas is suddenly compressed to volume will be: (Given ratio of specific heats at constant pressure and at constant volume) [2023]

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Solution

Q.
The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

1 $P_{0} {(4)}^{1 / γ}$

2 $P_{0} {(4)}^{γ}$

3 $P_{0}$

4 $4 P_{0}$

Ans.
(2)

$As gas is suddenly compressed, the process is adiabatic.$

$Equation of gas for adiabatic process is P V^{γ} = constant$

$\Rightarrow P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

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

$\Rightarrow P_{2} = P_{0} {(4)}^{γ}$

$Option (2) is correct.$

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