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I am a bit unclear on degrees of freedom in thermodynamics/stat mech, can someone critique my rational? Here I go:

Essentially, the equipartition theorem states that per each degree of freedom it has an energy of 1/2kT associated with it. So, for a monatomic gas, there are three degrees of freedom associated with the translational components of each atom (along X, Y, or Z). There are no rotational components since nearly all the mass of the atom is located at the center.

For a diatomic molecule, we can visualize it as simply being two atoms connected with a tiny spring. The molecule still has three translational degrees of freedom (X, Y and Z), but now we must consider the rotational and vibrational components. It won't rotate about its axis for the same reasons a single atom cannot. It can rotate about an axis perpendicular to the spring connecting the molecules though: if both our atoms are on the X-axis, then it can rotate about an axis pointing along either the Y-axis or the Z-axis. So, there are two rotational degrees of freedom. For vibrational, this is only along one axis (the X-axis), so there is only one vibrational degree of freedom. So, there are 3+2+1=6 degrees of freedom in a diatomic molecule.

For a triatomic molecule, we still have three translational degrees of freedom, but this time we have three rotational degrees of freedom and also three vibrational degrees of freedom.

Is my thinking correct? Thanks yall

IHateMayonnaise

EDIT: Also, unless we aren't talking about high temperatures, can the vibrational and rotational components be neglected?

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# Thermodynamics & Degrees of Freedom

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