• # question_answer A gas at NTP is suddenly compressed to one-fourth of its original volume. If  $\gamma$ is supposed to be $\frac{3}{2}$, then the final pressure is                      A) 4 atmosphere B) $\frac{3}{2}$ atmosphere C) 8 atmosphere     D) $\frac{1}{4}$ atmosphere

Solution :

[c]        $P{{V}^{\gamma }}=\text{constant}\Rightarrow \frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}$     $\Rightarrow \frac{{{P}_{2}}}{1}={{\left( \frac{{{V}_{1}}}{{{V}_{1}}/4} \right)}^{3/2}}=8$ Þ ${{P}_{2}}=8\ atm$.

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