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

Question asked by Anton Hengst on Aug 18, 2020
Latest reply on Aug 27, 2020 by Ralph Nelson

Hello all! I have a quick and stupid thermodynamics 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 lowercase deltas in place of a proper inexact differential symbol). Finally, I understand that since h = u + PV and PV = N * Rhat * 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 his 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.