Question

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

• A. $1/2$
• B. More than $1/2$
• C. Less than $1/2$
• D. Between $1$ and $2$

Answer 1

The correct option is C Less than $1/2$

In adiabatic process, $T_2{V}_2^{\gamma -1}=T_1{V}_1^{\gamma -1}$

$\therefore \frac{V_2}{V_1}={\left(\frac{T_1}{T_2}\right)}^{\frac{1}{\gamma -1}}={\left(\frac{1}{2}\right)}^{\frac{1}{\gamma -1}}$

$\therefore \frac{V_2}{V_1}<\frac{1}{2}$ because $\gamma >1$