A gas at temperature $250 K$ is contained in a closed vessel. If the gas is heated and the temperature rises by $1^{\circ} C,$ the percentage increase in its pressure is nearly

0.4 %

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0.6 %

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0.8 %

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1.0 %

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Solution

The correct option is A $0.4 %$
We know,
if mass and volume $(V)$ are constant,
$P \propto T$
$\Rightarrow \frac{P}{T} =$ constant
$\Rightarrow \frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$
$\Rightarrow \frac{P_{2}}{P_{1}} = \frac{T_{2}}{T_{1}}$
$\Rightarrow \frac{P_{2} - P_{1}}{P_{1}} = \frac{T_{2} - T_{1}}{T_{1}}$
$\Rightarrow \frac{P_{2} - P_{1}}{P_{1}} = \frac{1}{250}$
$\Rightarrow \frac{P_{2} - P_{1}}{P_{1}} % = \frac{100}{250} = \frac{2}{5} = 0.4 %$

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