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  4. In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be :

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Q. In a vessel, the gas is at pressure $P$. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be :

NEETNEET 2013Kinetic Theory

Solution:

As P$= \frac {1}{3} \frac {mN}{V}v^2_{rms} ...(i) $
where m is the mass of each molecule, N is the total number of molecules, V is the volume of the gas.
When mass of all the molecules is halved and their speed is doubled, then the pressure will be
$P'= \frac {1}{3} \bigg (\frac {m}{2}\bigg ) \times \frac {N}{V} \times (2v_{rms})^2$
$= \frac {2}{3} \frac {mN}{V}v^2_{rms}=2P $ (Using (i))