The molecules of a given mass of a gas have root mean square speeds of 100 ms-1 at 270C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 1270C and 2.0 atmospheric pressure?

We know that for a given mass of a gas vrms =  3RTMwhere R is gas constant, T is temperature in kelvin and M is molar mass of the gas.Clearly for a given gas, vrms ∝ T, as R, M are constants.Hence, (vrms)1(vrms)2 = T1T2 ---------(i)Given, (vrms)1 = 100 m/sT1 = 270C = 27 + 273 = 300 KT2 = 1270C = 127+273 = 400 K∴ From Eq. (i) 100(vrms)2 = 300400 = 32⇒ (vrms)2 = 2×1003 = 2003m/s