Root mean square velocity of gas is given as

v_rms =

where R=gas constant whose value is 8.31 J/mol K.

T=temperature of gas.

M= molar mass of molecule of gas

Squaring both side of equation (I) we are removing the square root and

we will get mean square velocity which is,

So, mean square speed is directly proportional to temperature as for a

given gas its molar mass will not change.