In an adiabatic process, the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is
JEE MAIN 2020, Medium
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In adiabatic process
$PV ^{\gamma}= constant$
$P \left(\frac{ m }{\rho}\right)^{\gamma}= constant$
as mass is constant
$P \propto \rho^{\gamma}$
$\frac{P_{f}}{P_{i}}=\left(\frac{\rho_{f}}{\rho_{i}}\right)^{\gamma}=(32)^{7 / 5}=2^{7}=128$
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