## isothermal reversible expansion

$\Delta U=q+w$

Hannah Guo 3D
Posts: 56
Joined: Fri Sep 29, 2017 7:06 am

### isothermal reversible expansion

In notes from a past lecture talking about isothermal reversible expansion, Lavelle gave an example and explained that in ideal gas, U(tot)=3/2nRT, which leads to deltaU=3/2nR deltaT=0. Can someone help me explain how to get the "3/2" for ideal gas? Thank you!

Kailey Brodeur 1J
Posts: 34
Joined: Thu Jul 27, 2017 3:00 am

### Re: isothermal reversible expansion

This is explained well in section 8.10 of the textbook, but basically, heat capacity at a constant volume is equal to change in internal energy over change in temperature. Change in internal energy is equal to (3/2)R(change in temp) for ideal gases. This formula arises from the molecular rotational energy that ideal gases possess. The changes in temp in the numerator and denominator cancel out, leaving us with the heat capacity of an ideal gas at constant volume is equal to (3/2)R.