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.

Dear Anton,

It is important in the sciences to always remember that we are just trying to make sense of observations. Thus, sometimes mathematical derivations come from different observed terms. It is always interesting to see how the mathematical manipulations and comparisons can reveal other things that might not have been noticed by the direct observations (or bias) of the experiments.

Gas phase interactions are different from the other phases,with that unique PV=nRT relationship. What you are seeing is the expression of the combination of the “internal” or intrinsic energy factors with the “external” or environmental factors. “PV” (and T) are external conditions, all related to the energy of the system and the atoms in it. In the Gas Laws we are relating the observed energy of the system (PVT) to the number of molecules ‘n’ with the derived constant ‘R’. Enthalpy is the heat energy in a system, not all of which is accessible. That is the specific internal energy ‘u’. The PV term expresses the accessible system energy as observed and related in the Gas Laws. COMBINED they express the total enthalpy of the molecule. Because we are expressing the energy in terms of heat, the temperature becomes another label for the heat energy in the equations.

Again, mathematical manipulations are always fun and internally consistent when done properly. Sometimes they can even uncover possible physical relationships that we didn’t originally observe. But in the end the primary importance of any mathematical expression is to model a real observation (experiment) accurately to allow us to predict future outcomes from different conditions. Keep in mind also where we get our symbols from. The ‘PV’ is not a ‘term’, but the expression of an observed Pressure and Volume in the system. Pressure, volume, and temperature (PVT) can all vary independently as well as being connected as expressed in the Gas Laws when part of a closed system.

Best regards,

Steven