[disillusioned19]

Could anyone be so kind as to provide some reasoning behind the expression E(average) = (3/2)kT?

[Jorriss]

It can be shown from the Equipartition Theorem and can also be derived explicitly applying classical mechanics to ideal gas particles, iirc.

[Enthalpy]

It's because each degree of freedom stores kT/2 as a mean, and translations in space bring 3 degrees of freedom.
For a more detailed answer, equipartition and the like, sure.

3/2 is only for translations. If your gas molecules have several atoms, they can rotate, and as the rotations store energy, the internal energy exceeds (3/2)*kT, by again kT/2 for each degree of freedom.

Some exceptions:

- When a degree of freedom is grossly quantified, it stores little energy until the temperature is high enough. For instance N2 (stiff) and H2 (light) store no vibrational energy at room temperature, but Br₂ and CO₂ do.

- Each vibration mode stores kT instead of kT/2. That's because in the vibration, the speed stores kT/2 to put itself in equilibrium with the translations, and so does the elastic energy store kT/2, summing to kT.

[tomothyengel]

It's possible to derive that equation based on the ideal gas equation and the kinetic theory of gases. m is the mass of a gas particle and c² is the mean square speed of gas particles. Since an ideal gas has all of its internal energy in the form of translational kinetic energy. You can derive that the average energy of particles is a function of temperature alone. The kinetic theory of gases pressure-density equation can be derived using Newton's laws and equipartition theorem. I've attached a quick proof. Hope this helps. (: