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How many degrees of freedom does a monoatomic gas have?

According to my Thermal Physics textbook, there are $3N$ degrees of freedom for $N$ particles because the particle is free to move in the $x$, $y$, and $z$ directions.

Why doesn't the rotation/spin of the particle count as a degree of freedom? If we treat the atom as a classical particle, can't it also rotate in the same way that the Earth rotates/spins once per day along its axis?

behold, rotation!

I also understand that there are electronic degrees of freedom but those may only come into play at higher temperatures.

For context, I am learning about the equipartition theorem. Maybe this is the reason: the spin degree of freedom does exist, but it simply doesn't come into play here because the equipartition theorem only accounts for quadratic degrees of freedom.

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For a monoatomic gaseous atom, rotation of a particle about one's own axis is really insignificant since the rotational energy associated with this rotation is given by $E=\frac{1}{2}I\omega^2$ and I is the moment of inertia of the rotating particle given by $I=Mr^2$. Since for a gaseous atom, radius of atom is very,very small and hence $I$ and $E$ are extremely small and hence neglgible.

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  • $\begingroup$ Rotational energy might be insignificant but it will still rotate!! We are not measuring energy, we are measuring degrees of freedom. I and encountered the above reason many places but never convinced. $\endgroup$ Jul 2 at 2:54

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