Question

A gas is found to obey $P^{2} V=$ constant. The initial temperature and volume of gas are $T_{0}$ and $V_{0}$. If the gas expands to volume $3 V_{0}$, then the final temperature of gas is $\sqrt{n} T_{0}$. Find $n$.

Answer 1

$P^{2} V=$ Constant
Also, $\frac{P V}{T}=$ Constant
$\Rightarrow \frac{T^{2}}{V^{2}} V=$ Constant
$\therefore T^{2} V^{-1}=$ Constant
$\therefore T_{f}^{2}=T_{0}^{2}\left(\frac{3 V_{0}}{V_{0}}\right) $
$\Rightarrow T_{f}=\sqrt{3} T_{0}$