Q66 / 90 · JEE Main 2023 (13 Apr Shift 2) · Physics

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.)

Correct answer
A
$P_{0} (4)^{γ}$
B
$4 P_{0}$
C
$P_{0}$
D
$P_{0} (4)^{\frac{1}{γ}}$

Solution

As the gas is suddenly compressed the process is adiabatic.
So, $P V^{γ} = constant$
$\Rightarrow P_{0} V_{0}^{γ} = P \cdot {(\frac{V_{0}}{4})}^{γ}$
$\Rightarrow P = 4^{γ} \cdot P_{0}$

Hence, the correct answer is option: 'A'.

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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 V04 will be:(Given γ= ratio of specific heats at constant pressure and at constant volume.)

Solution

Relevant Questions

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.)