Question

During an experiment, an ideal gas is found to obey an additional law $VP^2 =$ constant. The gas is initially at temperature $T$ and volume $V$. When it expands to a volume 2 V, the temperature becomes

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

Answer 1

Answer: (C)

$V P^{2}=$ constant or $P V^{1 / 2}=K$
$\frac{P V}{T}=$ constant
$\Rightarrow \frac{V}{T}\left(\frac{K}{V^{\frac{1}{2}}}\right)=$ constant
$\Rightarrow \frac{V^{\frac{1}{2}}}{T}=$ constant
or $\frac{(2 V)^{\frac{1}{2}}}{T'}=\frac{V^{\frac{1}{2}}}{T}$ or
$T'=T \sqrt{2}$.