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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?

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$40 %$

$25 %$

$30 %$

$20 %$

answer is B.

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Detailed Solution

$P V = n R T$ ……(i)

$P (\frac{90 V}{100}) = n_{1} R (T + \frac{20}{100} T)$

or $\frac{9}{10} P V = \frac{6}{5} n_{1} R T$

or $\frac{9}{10} P V = \frac{6}{5} n_{1} R T$ ……(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 $= \frac{n - n_{1}}{n} \times 100 = (1 - \frac{3}{4}) \times 100 = 25 %$

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