Ideal Gas Internal Energy

[Simmi Diwanji 2B]

Does anyone remember the explanation for why in the equation: Utotal = 3/2 nRT there is a 3/2 coefficient?

[Jennifer Su 2L]

I believe he said we don't have to worry about deriving it! He didn't explain how he got 3/2 nRT.

[jonathanjchang2E]

The 3/2 coefficient comes from the equipartition theorem which states, "The average value of each quadratic contribution to the energy of a molecule in a sample at a temperature T is equal to (1/2)kT" and since there are three translational modes of motion, each giving a quadratic contribution, the equation for internal energy ends up being 3 x (1/2)kT or U=(3/2)kT.