Thermodynamics -- Energy of system in ideal cases

Question

In the books,it is stated that the energy of a gas system is purely Kinetic for an ideal monoatomic gas.
Why are energies such as nuclear energy not mentioned here?

John Rennie · Accepted Answer

The properties and behaviour of a gas (almost) never depend on its nuclear energy, so we (almost) never consider it.
For example if I am trying to design a steam engine then the kinetic energy of the gas molecules is vitally important because it determines the gas temperature and hence how the gas is going to behave in my steam engine. By contract the nuclear binding energy will have absolutely no effect on the functioning of my steam engine so I just ignore it.
I say almost because thermodynamics extends even to extreme cases like the interior of stars where the nuclear binding energy does make a difference. There might also be fringe cases like radon or other radioactive gases where the heat input from their decay might have to be considered. But for most thermodynamicists most of the time the nuclear binding energy can be safely ignored.

niels nielsen · Answer

Because for a monoatomic gas at pressures and temperatures such that the ideal gas law is a good approximation of its behavior, nuclear reactions do not take place and hence nuclear effects do not enter into the equation of state.
Furthermore, at those pressures and temperatures, the motions of the gas atoms are so slow relative to the speed of light that relativistic effects are far too small to measure- meaning that they don't have to be included in the equation of state either.

safkan · Answer

A good answer has been posted, and accepted. Yet, I have a couple of things to say about the subject matter that might shed additional light on this, as well as other "science".
What we teach in science classrooms is quite analytical and mathematical, and it is mostly quite appropriate and useful. However, what is mostly glossed over is the fact that before you can apply analytical and mathematical methods on a problem, you first need quite a long list of "simplifications", which are not yielded by the analysis itself.
Any system you try to understand is very deeply complex. As far as we can understand, the universe is a soup of quarks, leptons and bosons. We can not possibly solve that soup. So we head for simplifications.
A gas molecule... Well, it has all sorts of energies involved. Rotational, unless it is spherically symmetric. Its orbital states can also be excited. It may ionize and lose electrons, and then we have more "particles" in the "gas" to worry about.
Then, what you mentioned. Its nucleus may break down by radioactive decay. Two nuclei may collide with sufficient energy to cause fusion.
We can not possibly make sense of all that all at once. So, the simplifications begin, by limiting the domain of our analysis, but at the same time making the analysis possible. As such, we consider a simple case:

The nuclei of the molecules are stable (no radioactive decay).
Temperatures are low enough not to cause any fusion.
The molecules do not interact chemically (no chemical reactions).
Temperatures are low enough (much lower than the above) so that ionization may not happen. (No plasma state.)
The molecules do not have angular momentum, they are spherically symmetric. (This is easier to relax.)
The interaction range (somehow related to "size" of the molecules) is quite small compared to average spacing of molecules. (Do not have to deal with potential energy, can model the interaction as "free flight" + "collision".)

The list can be extended a bit, but you get the picture.
You can be sure that no real gas can satisfy all these conditions. Well, when people got to name this "gas", they called it an "ideal gas", because it exists only as an "idea".
What is the use, you can ask... Even if no gas completely satisfies these conditions, in most cases real gases in common conditions approximate this behavior quite well... To word that better, the ideal gas approximates real gases in common conditions quite well, and we get good predicitons about the behavior and parameters of the real gas by considering the "ideal gas".
The validity of the simplifications and assumptions are verified when predictions made by the simplified model are in sufficient agreement with observations and measurements to prove useful.
As you can see, this part of assumption/simplification and verification looks more like an art than a science. Well, it is, and it is not. This is putting the problem in a so-called "logic box". Once it is in there, you can attack it with your mathematical tools.
The art does not end there. Once you have satifcatory results, you modify your model by relaxing the assumptions. Like, the matter in the sun has some common behavior with the ideal gas, yet nuclear reactions are happening, and everything is ionized. You try to fit that on top of the exiting model. It sometimes works, and sometimes you need a completely new model. Life is not easy.
So, to circle back to the original question:
"Why are energies such as nuclear energy not mentioned here?"
The answer is rather short at this point: Simplicity.

Thermodynamics -- Energy of system in ideal cases

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