## Ideal Gas Internal Energy

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

Simmi Diwanji 2B
Posts: 32
Joined: Fri Sep 28, 2018 12:20 am

### Ideal Gas Internal Energy

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

Jennifer Su 2L
Posts: 47
Joined: Wed Nov 21, 2018 12:20 am

### Re: Ideal Gas Internal Energy

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

jonathanjchang2E
Posts: 61
Joined: Fri Sep 28, 2018 12:26 am

### Re: Ideal Gas Internal Energy

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.