## Utotal of Ideal Gas

Janice Xiao 1I
Posts: 52
Joined: Thu Jul 13, 2017 3:00 am

### Utotal of Ideal Gas

What is the significance of the 3/2 in Utotal=3/2*nRT?

Shannon Wasley 2J
Posts: 71
Joined: Fri Sep 29, 2017 7:06 am
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### Re: Utotal of Ideal Gas

The molar heat capacity for a monatomic gas at constant volume, C (v,m) is 3/2R. Therefore when we use the equation q = nC(m)deltaT, we get q = n 3/2RdeltaT, when we plug in our molar heat capacity for a monatomic gas. Since this molar heat capacity is at constant volume, delta V = 0 and therefore w = 0. So delta U is equal to n 3/2RdeltaT. The value of the molar heat capacity changes based on whether it is for constant volume or constant pressure and if it is atoms, linear or nonlinear molecules. These values can be found on page 281 in the book.

Danah Albaaj 1I
Posts: 50
Joined: Fri Sep 29, 2017 7:07 am

### Re: Utotal of Ideal Gas

It has to do with the kinetic energy of the ideal gas. I recommend reading section 8.7 where it goes into great detail on how the numbers come into play through the use of Boltzmann's constant and the Ideal Gas Law alongside the equipartition theorem. Professor Lavelle also briefly went over it while deriving the equation for reversible, isothermal expansion work during lecture 7.