How do you find the degrees of freedom
Posted: Sun Jan 24, 2016 6:58 pm
What exactly are the degrees of freedom for a gas molecule and how would one calculate this number for diatomic and monatomic ideal gases?
Re: How do you find the degrees of freedom
Posted: Sun Jan 24, 2016 8:11 pm
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).
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).