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A vessel is filled with a gas at a pressure of $76 c m$ of mercury at a certain temperature. The mass of the gas is increased by $50 %$ by introducing more gas in the vessel at the same temperature. The resultant pressure of the gas is

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$112 c m$ of mercury

$76 c m$ of mercury

$108 c m$ of mercury

$114 c m$ of mercury

answer is D.

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Detailed Solution

Pressure exerted by gas.

$P = \frac{1}{2} \frac{M}{V} {v^{2}}_{a v}$

Since the temperature $T$ is kept constant, $v_{a v}^{2}$ and $V$ are also constant.

$∴ P \propto M$ or $\frac{P_{2}}{P_{1}} = \frac{M_{2}}{M_{1}}$

According to the question,

$∴ \frac{P_{2}}{76} = \frac{[M_{1} + (\frac{50}{100}) M_{1}]}{M_{1}} = \frac{3}{2} \Rightarrow P_{2} = \frac{3}{2} x 76 = 114 c m$

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