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  4. A polyatomic gas (γ=(4/3)) is compressed to (1/8) of its volume adiabatically. If its initial pressure is P0, its new pressure will be

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Q. A polyatomic gas $\left(\gamma=\frac{4}{3}\right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_{0}$, its new pressure will be

Thermodynamics

Solution:

For an adiabatic process,
$P V^{\gamma}=$ constant
$\therefore P\left(\frac{V_{0}}{8}\right)^{4 / 3}=P_{0}\left(V_{0}\right)^{4 / 3}$
or $P=P_{0}(8)^{4 / 3}=P_{0}(2)^{4}=16 P_{0}$