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?
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).