## How do you find the degrees of freedom

isochoric/isometric:
isothermal:
isobaric:

Chu 3J
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Joined: Fri Sep 25, 2015 3:00 am

### How do you find the degrees of freedom

What exactly are the degrees of freedom for a gas molecule and how would one calculate this number for diatomic and monatomic ideal gases?

Chem_Mod
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### Re: How do you find the degrees of freedom

The degrees of freedom are the way something can move in space (pg 276).

Something that is amorphous will have 6 DoF's, because it can translate in three directions, and each rotation about one axis will have it "look" different than when it started.

So a perfect sphere will only have the three translations because if it's rotated about any of the axes it will look exactly the same.

For a linear molecule, 1 axis of rotation will have it look exactly the same, so 6-1=5 DoF's.

For a bent molecule, a rotation (anything between 0---->360 in each of these cases) about any axis will have it look different. 6-0= 6 DoF's.

Multiply that number by 1/2k*T an you have the kinetic energy for the atom (KE).

U=nR*KE

It's probably easier to memorize

monoatomic gas U=3/2nRT

Diatomic linear gas U=5/2nRT

(Which has a relationship with Cv as well).