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  4. On increasing the temperature of a gas filled in a close container by 1oC , its pressure increases by 0.4%, initial temperature of the gas is:

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Q. On increasing the temperature of a gas filled in a close container by $ {{1}^{o}}C $ , its pressure increases by 0.4%, initial temperature of the gas is:

Rajasthan PMTRajasthan PMT 1996

Solution:

According to pressure law $ \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}} $ $ \Rightarrow $ $ \frac{P}{P+\frac{P\times 0.4}{100}}=\frac{x+273}{x+274} $ $ \frac{250}{251}=\frac{x+273}{x+274} $ $ \therefore $ $ x=-{{23}^{o}}C=250K $