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

Answer: (D)

less than $\frac{1}{2}$

Answer 2

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 $\frac{1}{{{(2)}^{1-\gamma }}}>\frac{1}{2}$