# Can internal energy be partitioned into well-defined components?

People often talk about different forms of energy like thermal energy, chemical energy, nuclear energy, etc. as belonging to the internal energy of a physical system. However, I can't really remember having encountered these in rigorous treatments of thermodynamics. I know that the amount of internal energy of a system is much less important than its changes and that we can neglect things like rest energy if they are irrelevant for the situation at hand. But it makes me really suspicous that the energy forms which I cited above don't seem to play a role at all in the equations.

So my question is: Can the internal energy $$U$$ of a physical system actually be partioned into well-defined components like thermal, chemical, nuclear, etc.? Maybe it can be done in some situations but not in all? Or maybe they lose their distinction as we become more rigorous?

• Nearly all of it (over 99%) is the energy of the gluon field inside protons and neutrons. – safesphere Jul 31 at 17:09

So my question is: Can the internal energy 𝑈 of a physical system actually be partioned into well-defined components like thermal, chemical, nuclear, etc.? Maybe it can be done in some situations but not in all? Or maybe they lose their distinction as we become more rigorous?

In its most basic form, the internal energy of an object can be partitioned into its kinetic and potential energies, that is, the kinetic and potential energies of the atoms and molecules at the microscopic level. Each of the forms of energy you describe, depending on how they are defined (and that varies since some common names of forms are not rigorously defined) may consist of combinations of internal kinetic and potential energy.

For example, the term "thermal energy" is typically (though not always) associated with temperature which, in turn, is typically associated with the internal kinetic energies of the motions atoms and molecules. The energy associated with intermolecular forces, such as the Van der Waals forces, is internal potential energy.

For chemical energy, the energy stored in the chemical bonds of a substance is often referred to as chemical potential energy.

In the case of nuclear energy, the energy that holds subatomic particles together, such as protons and neutrons, is often referred to as nuclear potential energy.

And so on.

Hope this helps.