# Why do internal energy/heat and enthalphy differ? What is the physical significance of the $PV$ term for enthalphy of an ideal gas? [duplicate]

Let it be noted that this is not a duplicate of this downvoted-to-hell question, simply because I hope to ask it better!

I've been reading a thermo textbook and I've got a simple question.

The enthalpy of an ideal gas is $$h = u + PV$$. I understand that the specific internal energy, $$u$$, is the sum of all rotational, vibrational, translational, electronic/nuclear bonding, and lattice (ignored for ideal gasses, I presume) energies of the substance per unit mass. I further understand that $$w + q =\Delta u$$ for specific transferred work and heat $$w$$ and $$q$$, implying that $$\delta w + \delta q = du$$ (forgive my deltas in place of a proper inexact differential symbol). Finally, I understand that since $$h = u + PV$$ and $$PV = N\hat{R}T$$, for a constant amount of ideal gas, $$PV$$ is solely a function of temperature. It can be demonstrated that for an ideal gas, $$u$$ is also a function solely of temperature, so that means $$h$$ is as well.

So what's the difference between $$u$$ and $$h$$? Clearly, it's that $$PV$$ term, but what does that physically represent? I don't grok it.

All incoming energy, whether mechanical or thermal, goes into a change of $$u$$--that makes sense. Add energy to a gas, it's going to vibrate/translate/rotate more & maybe change its bonding state. Say you adiabatically compress your gas. You do work on it and $$u$$ and $$T$$ rise, but $$PV$$ stays constant. Adiabatically unconfine the gas and the same thing occurs the other way. But $$h$$ still varies because $$u$$ does, it's not conserved over adiabatic actions.

So the "energy" of the $$PV$$ term represents something somehow separate to internal energy, inherent to the system, invariate to mechanical work done on it... unless that work ends up raising the temperature? What is this term physically represent? Where does it exist? Why bother with the enthalpy concept at all? I don't get it & I know I'm missing something fundamental.

• Enthalpy is just a convenient function to work with in solving many kinds of thermo problems, particularly those that take place at constant pressure, so $P\Delta V$ is the work done. My advice is not to drive yourself crazy trying to assign a deeper meaning to the PV. As you get more experience solving thermo problems, you will see how enthalpy comes in. Otherwise, I think you will be wasting your valuable time obsessing over this. Commented Aug 18, 2020 at 21:14
• @chetmiller I couldn’t write a better answer.
– Karsten
Commented Aug 19, 2020 at 13:21
• Well, can be done in more straightforward way. U is total mass energy inherent to an object and H is mass energy of object that is compressed (or perhaps stretched). Commented Aug 19, 2020 at 16:32