Question:
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 $\mathrm{n}$ is:
Correct Option: , 4
Solution:
In adiabatic process
$\mathrm{PV} \gamma=$ constant
$\mathrm{P}\left(\frac{\mathrm{m}}{\mathrm{\rho}}\right)^{\gamma}=\mathrm{constant}$
as mass is constant
$P \propto \rho^{\gamma}$
$\frac{P_{f}}{P_{i}}=\left(\frac{\rho_{f}}{\rho_{i}}\right)^{\gamma}=(32)^{7 / 5}=2^{7}=128$