Two vessels of the same volume and filled with the same gas at the same temperature. If the pressure of the gas in these vessel be in the ratio 1:2, then state : (i) the ratio of the rms speeds of the molecules, (ii) the ratio of the number of molecules.

Explanation

If average kinetic energy = E
then `E=(1)/(2)Mv^(2)=(3)/(2)PV`
(a) `therefore (E_(1))/(E_(2))=(P_(1))/(P_(2))=(1)/(2)`
Ratio of average KE is `(1)/(2)`
(b) Again, by gas law, `PV=nRT`
`therefore (P_(1))/(P_(2))=(n_(1))/(n_(2))` when V and T are kept constant.
`therefore (n_(1))/(n_(2))=(1)/(2)`, Ratio of number of molecules `= (1)/(2)`