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Q.
If the pressure of a gas contained in a closed vessel is increased by $0.4\%$ when heated by $1\, K$, its initial temperature must be:
States of Matter
Solution:
Let initial temperature and pressure be $T_{1}$ and $P_{1}$
$P_{2}=\left(P_{1}+\frac{0.4}{100} P_{1}\right) T_{2}=\left(T_{2}+1\right)$
$\frac{P_{1}}{P_{2}}=\frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{100}{100.4}=\frac{T_{1}}{\left(T_{1}+1\right)} T_{1}=250\,K $