A closed vessel of fixed volume contains a mass m of an ideal gas, the root mean square speed being v. Additional mass m of the same gas is pumped into the vessel and the pressure rises to 2 P, the temperature remaining the same as before. The root mean square speed of the molecule now is

PV=(m/M)RT(M= molecular mass )       ....(1)P′V=(2m/M)RT                                             ....(2)           From eqs. (1) and (2),P′P=21Now,   Vrms=3Pρ=3P(m/V)            ....(3)and     vrms′=3P′(2m/V)                           ...(4)From eqs. (3) and (4),vrms′vrms=12P′P=12(2)=1vrms′=vrms