I am reading many online references, but I cannot understand where the concept enthalpy comes from and what it represents.

The Spanish Wikipedia article states it is the Legendre transformation of internal energy.

The English Wikipedia article says it is internal energy plus pV.

I remember a teacher talking about how it was just defined, because the internal energy + pV product was found in many chemical reactions, and someone decided to just give it a name, so it would simplify calculations.

I understand it is something that makes sense, being it a state function.

Also, I can see a utility in it, since it will be equal to a heat transfer during a constant pressure process. And that helps the calculations.

Also, it is stated (in different sources, including the English Wikipedia article for enthalpy) that the internal energy term can be interpreted as the energy required to “create” the system, and the pV term as the work that would be required to “make room” for the system.

My two questions about enthalpy are:

  1. How was it defined? As the Legendre transformation of U, or directly as U + pV? They may happen to be the same mathematical thing, but... what is the real origin (chemistry, thermodynamics, ... how and why)?
  2. If it somehow represents the energy to “create” a system (what does that mean: put a bunch of separated atoms together by giving them some linking energy?) and the work required to “make room” for that system (what does that mean: it's not the same to put a system into an iron block than putting it into an air block, it would require a different amount of work to push those different things away. And for the void/emptiness... well, would that take energy at all, if it is already void?)
  • $\begingroup$ I don't have time to write a full answer right now, but the way I think about enthalpy is that it is simply a more appropriate/convenient way to quantify the 'energy' of a thermodynamic system that has some level of compressibility. I.e. where some of the energy can be stored as compressible potential energy, as well as thermal. $\endgroup$
    – Time4Tea
    Aug 20, 2019 at 14:04
  • $\begingroup$ In the same way as a falling ball has both kinetic energy and gravitational potential energy - I could create an energy variable that combines those two together. $\endgroup$
    – Time4Tea
    Aug 20, 2019 at 14:05
  • $\begingroup$ @Time4Tea Thank you, I am still in doubt about both questions. If you find some time to elaborate on your comments, I will appreciate. All the best. $\endgroup$ Aug 25, 2019 at 8:14

1 Answer 1


Imagine doing chemistry from a physics point of view. You know the energy of various bound states, so you can calculate the change in energy when $2H_2 + O_2$ combine to make $2H_2O$. You multiply by the numbers in your sample, then use the heat capacity ( in $k$ units of course) to calculate the temperature rise.

And the experiment finds a different, lower answer. Your calculation was wrong.

A chemist would have looked up the enthalpy change of the reaction and gotten the experimental value.

Most chemical systems are intimately tied to an environment. Physics experiments work hard to achieve complete energy isolation, so we think in terms of accounting for energy. Lots of chemistry is done connected to the atmosphere, at constant pressure. There, enthalpy is the right form of “free” energy to calculate with.

Our original experiment resulted in hot water vapor that expanded to reach atmospheric pressure, in the process cooling down and dropping in temperature. You can consider that a transfer of energy from the thermal kT form to the mechanical PV form. Or you can consider it as constant enthalpy, which is easier to calculate with.


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