Gujarati
Hindi
12.Kinetic Theory of Gases
normal

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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