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 $\gamma=$ ratio of specific heats at constant pressure and at constant volume)
JEE MAIN 2023, Medium
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As gas is suddenly compressed, the processes is adiabatic.
Equation of gas for adiabatic process is
$PV ^\gamma=\text { constant. }$
$\Rightarrow P _1 V _1^\gamma= P _2 V _2^\gamma$
$\Rightarrow P _0 V _0^\gamma= P _2\left(\frac{ V _0}{4}\right)^\gamma$
$\Rightarrow P _2= P _0(4)^\gamma$
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