Not all kinetic energy contributes to the heat capacity. Not
all of the heat capacity comes from kinetic energy. Not even close.
More generally, none of the following splits is the same as
T dS versus P dV.
- Locrian versus non-Locrian.
- Cramped versus uncramped.
- Kinetic versus potential energy.
- Overall motion of the center-of-mass versus
internal motion relative to the center-of-mass.