Question

A gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and volume is reduced by $10\%$ . How much percentage of the gas has to leak for pressure to remain constant?

• A. $30\%$
• B. $40\%$
• C. $15\%$
• D. $25\%$

Answer 1

Answer: (D)

$V \, \propto \mu T,\frac{90}{100}$ $V \propto \mu ^{′}\frac{6 T}{5}$
$\frac{\mu ^{′}}{\mu }\times \frac{6}{5}=\frac{9}{10} \, or\frac{\mu ^{′}}{\mu }=\frac{9}{10}\times \frac{5}{6}=\frac{3}{4}$
Percentage of gas leaked out
$=\frac{\mu - \mu ′}{\mu }\times 100=\frac{4 - 3}{4}\times 100=25$ $\%$