Q.Calculate the ratio of mean square speeds of molecules of a gas at 30 K and 120 K.

The root mean square (rms) speed of gas molecules is a way of characterising the typical speed of molecules in a gas, even though individual molecular speeds vary continuously across a whole distribution. It is defined as the square root of the average of the squared molecular speeds, and it emerges directly from combining the kinetic-theory pressure expression P = (1/3)(N/V) m <v^2> with the ideal gas equation, giving v_rms = sqrt(3RT/M0), where M0 is the molar mass of the gas and T its absolute temperature. …