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  4. A gas for which γ =1.5 is suddenly compressed to the (1/4) th of the initial volume. Then the ratio of the final to the initial pressure is

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Q. A gas for which $\gamma =1.5$ is suddenly compressed to the $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

Here, $\gamma =1.5, \, V_{2}=\frac{1}{4}V_{1}; \, \frac{p_{2}}{p_{1}}=?$
As compression is sudden/adiabatic,
$\therefore \, \, p_{2}V_{2}^{\gamma }=p_{1}V_{1}^{\gamma }$
$\frac{p_{2}}{p_{1}}=\left(\frac{V_{1}}{V_{2}}\right)^{\gamma }=\left(4\right)^{1.5}=8$