show that RMS velocity of a gas molecule is directly proportional to square root of absolute temperature - Physics - Kinetic Theory of Gases and Radiation

Question

show that RMS velocity of a gas molecule is directly proportional
to square root of absolute temperature

Vaibhav Tiwari · Accepted Answer

Dear Student,
Expression for r m s velocity:
Let P = pressure exerted by one mole
of an ideal gas
V = volume of one mole of the
gas
T = absolute temperature
Pressure exerted by gas is given by, P =Mv23Vâ€‹
where M= mass of one mole(molecular
weight) of the gas
PV
=13Mv2  
 1
But for one mole of an ideal gas,PV=RT
RT=13Mv2  
 from equation 1v2=3RTMvrms=3RTM  
 2
represents expression for r m s velocity of gas molecules
As R and
M in
eqn-(2) are constant,
vrms α T
Regards

show that RMS velocity of a gas molecule is directly proportional to square root of absolute temperature.