Question

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 :

• A. 2P
• B. P
• C. P/2
• D. 4P

Answer 1

Answer: (A)

As P$=\frac{1}{3}\frac{mN}{V}{v}_{rms}^2...(i)$
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
$P^{\prime }=\frac{1}{3}\left(\frac{m}{2}\right)\times \frac{N}{V}\times (2v_{rms}{)}^2$
$=\frac{2}{3}\frac{mN}{V}{v}_{rms}^2=2P$ (Using (i))