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  4. If pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1° C , its initial temperature must be

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Q. If pressure of a gas contained in a closed vessel is increased by $0.4\%$ when heated by $ 1^{\circ} C $ , its initial temperature must be

AMUAMU 2008

Solution:

$ \frac{pV}{T}= $ constant; $V =$ constant
$ \therefore \frac{p}{T}= $ constant
$ \therefore \frac{p}{T}=\frac{100.4\,p}{100}\times \frac{1}{(T+1)} $
$ \frac{1}{T}=\frac{100.4}{100}\times \frac{1}{(T+1)} $
$ \frac{1}{T}=\frac{100.4}{100T+100} $
$T = 250 \,K$