Question

A gas is filled in a cylinder. Its temperature is increased by $20\%$ on kelvin scale and volume is reduced to $90\%$. How much percentage of the gas has to leak for pressure to remain constant?

• A. $20\%$
• B. $25\%$
• C. $30\%$
• D. $40\%$

Answer 1

The correct option is B $25\%$

$PV=nRT$ (i)
$P\left(\frac{90V}{100}\right)=n_{1}R(T+\frac{20}{100}T)$
or $\frac{9}{10}PV=\frac{6}{5}{n}_{1}RT$ .(ii)
Dividing (ii) by (i), we get

$\frac{6}{5}\frac{n_1}{n}=\frac{9}{10}$ or $\frac{n_1}{n}=\frac{9\times 5}{6\times 10}=\frac{3}{4}$ or $n_1=\frac{3}{4}$n

$\%$ of gas leaked $=\frac{n-n_1}{n}\times 100=(1-\frac{3}{4})\times 100=25\%$