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  4. When a gas filled in a closed vessel is heated by raising the temperature by 1° C, its pressure increase by 0.4 %. The initial temperature of the gas is K.

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Q. When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ} C$, its pressure increase by $0.4 \%$. The initial temperature of the gas is ____$ K$.

JEE MainJEE Main 2022Kinetic Theory

Solution:

$pV = nRT$
$\Delta P . V = nR \Delta T$
$\Rightarrow \frac{\Delta P }{ P }=\frac{\Delta T }{ T }=\frac{0.4}{100} $
$\Rightarrow T =\frac{100 \times 1}{0.4}=250\, K$