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Oct 8, 2022 at 22:28 comment added Chemomechanics @AndrewSteane I don't consider that nuance relevant to the context of this question, which is why the internal energy of the ideal gas isn't $PV=nRT$. $U=C_VT$ and $PV=nRT$ are arguably perfectly acceptable equations of state in this context.
Oct 8, 2022 at 22:14 comment added Andrew Steane Heat capacity of a diatomic gas depends on temperature so $U \ne C_V T$.
Oct 8, 2022 at 6:47 comment added alan.raceQs OK, I think I understand conceptually. So would it be correct to say that when heat is applied to a fixed volume of ideal gas some of the heat energy goes to increasing the linear momentum of the molecules which results in a rise in temperature and pressure and some of the heat energy goes to increasing the rotational momentum of the molecules which does not increase the temperature or pressure? And that ratio is reflected in the 5/2 ratio that we see for the internal energy from Kinetic theory. That makes sense, thanks.
Oct 8, 2022 at 0:57 history answered Chemomechanics CC BY-SA 4.0