The average kinetic energy of the molecules of an ideal gas is directly proportional to what?

1 Answer
Jun 6, 2017

Answer:

The energy is proportional to the absolute temperature.

Explanation:

An immediate deduction of kinetic theory is the pressure expression,

#p = (mnv^2)/3#

Where #m# is mass of a gas molecule, #n# is no. of molecules per unit volume and #v# is the rms speed.

Thus, #n = N/V# where #N# is number of molecules.

Making this substitution,

#pV = (mNv^2)/3#

But, #(mv^2)/2 = E# is kinetic energy of a molecule.

Therefore, #pV = (2NE)/3#

But, from ideal gas equation,

#pV = muRT# where, #mu = N/N_A# is the number of moles.

Using these results,

#muRT = (2NE)/3#

#implies (NRT)/N_A = (2NE)/3#

Which finally gives,
#E = (3kT)/2#

Where, #k = R/N_A# is the Boltzmann constant.

Thus the energy is proportional to the temperature.

This the the kinetic interpretation of temperature.