Question

# When a gas in enclosed in a closed vessel was heated so as to increase its temperature by $$25^o C$$ its pressure was seen to have increased by 10% The initial temperature of the gas was nearly

A
500C
B
227C
C
273C
D
250C

Solution

## The correct option is D $$250^\circ C$$Given, Percentage increase in pressure is $$10$$% Increase in temperature is $${{25}^{o}}C$$ For constant volume, $$P\,\,\alpha \,T$$ $$\dfrac{{{P}_{2}}}{{{P}_{1}}}=\dfrac{{{T}_{2}}}{{{T}_{1}}}$$ $$\Rightarrow \dfrac{1.1{{P}_{1}}}{{{P}_{1}}}=\dfrac{\left( {{T}_{1}}+25 \right)}{{{T}_{1}}}$$ $$\Rightarrow {{T}_{1}}=\dfrac{25}{0.1}=250{{\,}^{o}}C$$ Hence, initial temperature is $${{250}^{o}}C$$Physics

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