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12.Kinetic Theory of Gases
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A gas is filled in a cylinder. Its temperature is increased by $20\%$ on kelvin scale and volume is reduced by $10\%$. How much percentage of the gas will leak out ...... $\%$
A
$30$
B
$40$
C
$15$
D
$25$
Solution
Let initial conditions $=V, T$
and final conditions $=V^{\prime} . \mathrm{T}^{\prime}$
By Charle's law $V$ $\propto$ $T$ [$P$ remains constant]
$\frac{\mathrm{V}}{\mathrm{T}}=\frac{\mathrm{V}^{\prime}}{\mathrm{T}^{\prime}} \Rightarrow \frac{\mathrm{V}}{\mathrm{T}}=\frac{\mathrm{V}^{\prime}}{1.2 \mathrm{T}^{\prime}} \Rightarrow \mathrm{V}^{\prime}=1.2 \mathrm{CV}$
But as per question, volume is reduced by $10 \%$ means $\mathrm{V}^{\prime}=0.9 \mathrm{V}$
So percentage of volume leaked out $=\frac{(1.2-0.9) \mathrm{V}}{1.2 \mathrm{V}} \times 100=25 \%$
Standard 11
Physics
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