# Homework Help: How do I figure out the Degrees of Freedom?

1. May 8, 2010

### vorcil

How do i figure out the degrees of freedom of a certain object/gas

for example oxygen gas

i know it's 02

two oxygen molecules

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the degrees of freedom is supposibly 5

but how do you figure that out?

thanks

2. May 8, 2010

### Dickfore

monoatomic gases have 3 degs of freedoms, diatomic (or, in general all that lie on a common line) 5 and three and polyatomic (if they do not lie on a common line like CO2 for example) 6.

3. May 8, 2010

### vorcil

Yeah no, Not the answer i was looking for,

your answer, explains it empirically, you can't actually tell me why it is 3,5 ect...

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I've been reading about the Equipartition theorem, and it has to do with each form of energy a particle, or molecule can have, and the degrees of freedom is the sum of all the different forms of energy it can posses.

thanks for trying, but i'm needing a better explanation.

4. May 8, 2010

### jeppetrost

Monatomic can move in three dimensions, but any rotation doesn't really change how it looks (some quantum effect, I've heard). Hence 3 degrees of freedom.
Diatomic, like your oxygen molecule, can move in three dimensions and spin in two. Now why not three? Really, same explanation as before - the last axis spins the molecule, but you couldn't tell the difference anyway, so some quantum effect says it's not really a dergree of freedom. Hence 3 moving and 2 spinning = 5 degrees of freedom.

5. May 8, 2010

### Meithan

One way to look at degrees of freedom is to ask yourself: if I have a particle of the system (an atom, a molecule, anything), how many numbers do I have to give to specify its position / orientation (what we call the configuration)?

So for instance, for a gas of monoatomic particles, you need 3 numbers to specify the position (x, y and z) and it doesn't have any discernible orientation, so its total degrees of freedom is 3.

For a gas of diatomic particles, for each particle you need again 3 numbers to specify its position (this is usually always so), but this time you can orient it in space, and you need two angles to do this (one angle wouldn't be enough, since the orientation is in 3D). So it has 3+2 = 5 degrees of freedom.

Note that the previous example assumes that the distance between the atoms of the diatomic particle is fixed. If it's not, then we'd have an extra degree of freedom: the distance between them.