Question

An ideal gas having initial pressure $P$ volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $5.66V$, while its temperature falls to $T/2$. Find the number of degrees of freedom of the gas molecule.
(Take $(5.66{)}^{0.4}=2)$

• A. $2$
• B. $3$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

For an adiabatic process,
$T{V}^{\gamma -1}$ = constant
i.e. $T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$T{V}^{\gamma -1}=\frac{T}{2}(5.66V{)}^{\gamma -1}$
$\Rightarrow (5.66{)}^{\gamma -1}=2$
$\Rightarrow \gamma =1.4$
We know that, $\gamma =1+\frac{2}{f}$
$\therefore$ we get $f=\frac{2}{\gamma -1}=\frac{2}{0.4}=5$