[Justme1]

Okay so I am sure this question has been asked a million times, but I have done reading and cannot find an answer that satisfies me. So I have trouble with this for a few reasons. The most common answers I see why internal energy cannot be absolute is that it could not be calculated or a system would still possess internal energy at absolute zero. So to address the first one, how come you cannot statistically calculate the internal energy of a system? I feel if you knew the basic properties of a system (P,V,n,T) you could calculate the bonding energies between atoms, you could calculate nuclear binding energies. Can't you statistically approximate the translation, rotation and vibration energies based on other values? Maybe I am wrong, but it seems like these are things wecould at least give estimations to. And most calculations, such as temperature of a body, are approximations, so how would this be any different?

To my next point, why can temperature be absolute, but not internal energy? It seems people argue since internal energy would never be zero, it could not be absolute, but we have never achieved absolute zero, so how can we definitively say absolute zero exists? If absolute zero did not exist wouldn't that make temperature only relative? Sorry if this is all babbling, but I was just wondering if anyone had any input.

[mjc123]

Let's take, for example, calculating the bonding energy between atoms. We can calculate the energy of a H₂ molecule on the assumption that the energy of two H atoms at infinite separation is zero. But this is just a convention - a logical one to use, perhaps, but still a convention, not an absolute fact. Suppose we considered those separate hydrogen atoms themselves. We could consider the potential energy of a proton and electron at infinite separation as zero, and the energy of the H atom as -1300 kJ/mol. Another convention. Which one is most useful depends on the problem we're considering. To use another example, for an astronomical problem (e.g. the energy with which an asteroid might hit the earth) we might say that the gravitational energy of two masses at infinite separation is zero, and as they approach each other the potential energy is -GMm/r. But for a simple terrestrial physics problem we might say that potential energy is zero at the earth's surface, and if we lift an object to a height h its potential energy is mgh. It's a question of what is most convenient. There is no absolute truth.
Kinetic energy is different, because being proportional to v² it can only be positive, and an object at rest has zero kinetic energy. When an object falls, and converts potential energy to kinetic energy, we can define the kinetic energy, and the change in potential energy, but there is still no absolute reference point for potential energy.
Now the temperature of a body is equivalent to the average kinetic energy of the molecules. It is therefore always positive and has a definable (if not practically attainable) zero. Any potential energy element in the internal energy, however, has no absolute reference point. Even if you could in principle calculate it precisely, it must always be referenced to some more-or-less arbitrary zero.

[Enthalpy]

Some thoughts, not ordered.

We have strong indications that dark matter and dark energy exist, they influence normal matter at least by gravitation hence have an effect on zero K internal energy but are not known in their nature nor full effects. And what if we discover a fifth force?

From time to time we discover a huge mass in our galactic supercluster (Relativity is very concrete here: because we fall freely, it's difficult to detect the effect). How should we know if we included all masses?

The nearby supernova 1987A changed the gravitational potential in our vicinity by 4.7mJ/kg (wow!) which we didn't notice at all (I speculate Lisa would have). If we don't notice such changes, I feel reasonable to live with relative energies.

I'm interested by thermo data at 298K 1atm, not at zero K. The transition between them is generally undocumented or inaccurate. I'm happy that people sometimes produce true measures converted to standard conditions, not to the zero K I can't use.

Rotations, vibrations and so on are vaguely estimated by software. Enthalpies of formation by software are far too inaccurate, even at zero K. Building a data system on that would be of no value to me.

Some weird effects exist at molecules' rotation and zero-point energy, for instance ortho- and para-hydrogen. I'm not sure that software can predict more complicated molecules properly.

No, we can't estimate the internal energy, because we have no means to compute a melting point nor a fusion enthalpy. This fails up to now, consistently and the big way, typically by 50K. So the internal energy of a solid at zero K is not predictable presently.

I doubt we can estimate the electron energy of heavy elements, and certainly not with the accuracy wanted by thermochemistry. 1kJ/mol is only 10meV. Better put the zero reference energy at a complete neutral atom than at separate electrons, protons,  neutrons.

"You could calculate nuclear binding energies", I doubt that one. Existing models are primitive and typically explain the general shape of the mass default curve. These days, experimenters discover things like "beryllium contains two alphas far from an other plus a diffuse neutron", or "we find more often a neutron close to a proton" and theory had predicted none of them. How could it have predicted the mass of the nuclides? Though, we're speaking of many eV error here, nothing that chemists want to accept in thermo calculations. Chemists better take an arbitrary reference that ignores nuclear forces, that is, complete atoms.

If willing to exaggerate further, protons and neutrons are composite particles, so we should compute energies starting from quarks and gluons. Worry: nobody can do it accurately now. The mass of lone protons and neutrons is known, but not of lone quarks since these do not exist, nor is their interaction energy known. So protons and neutrons are obviously less bad a zero reference than quarks and gluons.

And anyway, we ignore which particles are elementary. Where shall we stop?

Our mere incapacity to tell if we know all forces and if particles are elementary is a hint that energy is not absolute. If departure from some absolute reference were measurable, we could tell all that.