Question

During an experiment an ideal gas is found to obey an additional law $V{P}^2=$ constant. The gas is initially at temperature $T$ and volume $V$. When it expands to volume $2V$, the final temperature is:

• A. $T/2$
• B. $2T$
• C. $\sqrt{2}T$
• D. $T/\sqrt{2}$

Answer 1

The correct option is C $\sqrt{2}T$

For $n$ moles of an ideal gas,
$PV=nRT...\left(i\right)$
Also, given: $V{P}^2=$ constant $...\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$,
$V{\left(\frac{nRT}{V}\right)}^2=$ constant
$\Rightarrow \frac{n^2{R}^2{T}^2}{V}=$ constant
$\Rightarrow \frac{T^2}{V}=$ constant.
$\Rightarrow \frac{T_1^2}{V_1}=\frac{T_2^2}{V_2}$
$\Rightarrow \frac{T^2}{V}=\frac{T_2^2}{2V}$
$\Rightarrow T_2^2=2T^2$
$\Rightarrow T_2=\sqrt{2}T$