How to define thermal energy

[Taylor_1989]

How would someone define thermal energy? My view is that it is the internal energy of the object e.g potential and kinetic energy. But from what I understand it can also be the energy transferred from one object to another, this is where I get confused.

Dose the term thermal energy aka heat have a board meaning to it, so to explain it you would have to use it in a specific context e.g thermal energy is the amount of energy transferred to the substance or it is the energy given to increase in kinetic energy of the molecules to increase the temp of a substance.

 

[haruspex]

It's kinetic energy (not potential), but only the disordered component. If you look at how all the atoms/molecules in a body are moving, there will be some co-ordinated components (linear and rotational) in which they are moving as one, plus their independent, disordered movements. The dividing line is not always clear, e.g. eddies in a river appear disordered at one scale but ordered at a finer scale.
Conduction can transfer this disordered energy from one body to another, but only to one that has less disordered motion.
More ordered energy can become disordered, e.g. on impact, or on dissipation of eddies.

 

[Rap]

It's also potential energy of the "disordered" kind. If two molecules of a gas exhibit a short-range repulsive force (e.g. a van der Waals gas), then the internal energy will also contain the potential energy due to those repulsive forces. The key word is "disordered". A better term is "unknown except statistically". Gross linear and rotational motion, potential energy of the whole object in an external field, these are not described statistically. Kinetic energy of individual particles, potential energy of one particle due to the position of other particles, these are described statistically, and are therefore thermal. If you had a gas of classical particles, and you knew the position and momentum of each one, and you knew how to calculate the result of a collision, you would have no thermal energy, only a collection of particles. You could calculate what the thermal energy would be if you didn't have that information, but that's another problem. In a more complicated way, the same is true in quantum mechanics - a pure state never becomes a mixed state.