Question

A gas is compressed adiabatically till its temperature is doubled. The ratio of his final volume to its initial volume will be

• A. between $ \frac{3}{2} $ and 2
• B. $ \frac{1}{2} $
• C. more than $ \frac{1}{2} $
• D. less than $ \frac{1}{2} $

Answer 1

The Correct Option is D

Using the relation. $ {{T}_{1}}{{V}_{1}}^{\gamma -1}={{T}_{2}}V_{2}^{\gamma -1} $ $ \frac{{{V}_{2}}}{V}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{1-\gamma }}={{\left( \frac{{{T}_{1}}}{2{{T}_{1}}} \right)}^{1-\gamma }} $ Or $ \frac{1}{{{(2)}^{1-\gamma }}}>\frac{1}{2} $