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  4. If the absolute temperature of a gas is doubled and the pressure is reduced to one half, the volume of the gas will:

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Q. If the absolute temperature of a gas is doubled and the pressure is reduced to one half, the volume of the gas will:

KEAMKEAM 2005

Solution:

For a gas,
$ \frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}} $ (where $ {{T}_{2}}=2{{T}_{1}},{{P}_{2}}=\frac{1}{2},{{P}_{1}},{{V}_{2}}=? $ )
$ \frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}} $ = $ \frac{1}{2} $ $ \frac{{{P}_{1}}\times {{V}_{2}}}{2{{T}_{1}}} $
$ {{V}_{1}}=\frac{{{V}_{2}}}{4} $
$ \therefore $ $ {{V}_{2}}=4{{V}_{1}} $