Question

The initial coordinates of any system are $p$ and $V$. If a gas $ \left( \gamma =\frac{5}{3} \right) $ is compressed to $ \frac{1}{8} $ of its original volume, then the pressure of the gas will be

• A. p
• B. 16p
• C. 4p
• D. 32p

Answer 1

Answer: (D)

$ {{p}_{1}}V_{1}^{\gamma }={{p}_{2}}V_{2}^{\gamma } $ constant
Here, $ {{p}_{1}}=p,{{V}_{1}}=V $ and $ {{V}_{2}}=\frac{V}{8} $
$ \therefore $ $ P{{V}^{\gamma }}={{p}_{2}}{{\left( \frac{V}{8} \right)}^{\gamma }} $
$ \Rightarrow $ $ {{p}_{2}}={{8}^{\gamma }}p={{8}^{5/3}}p=32p $