# Intuitive understanding of enthalpy

1. Jun 24, 2010

### maxbashi

For most science concepts I try to intuitively understand what a quantity actually *is* but I'm having trouble understanding enthalpy. I understand the definition and how to work the standard problems you see involving H but I don't intuitively understand what it is.

In other words, why is it that H=E+PV? Since enthalpy is usually used to describe a general concept of "energy," (in a reaction), why add the PV work instead of just using E?

I hope you understand what I'm trying to say, any help would be appreciated.

2. Jun 25, 2010

### Topher925

Enthalpy isn't something that actually exists in nature, its a man made concept. It exists because one day someone got tired of writing U + pV all the time and decided to call it H. It has no specific meaning in nature.

3. Jun 25, 2010

### Ygggdrasil

The internal energy of a system (E) is an intuitive measure of the energy of a system because it is related to the amount of work done on/by the system and the amount of heat flowing in/out of the system. One useful property of E is that it is invariant under conditions of constant entropy (no heat flow) and constant volume (no work). Hence, we can write E as a function of entropy (S) and volume (V), E = E(S,V). However, most chemical systems are studied under conditions of constant pressure. It would, therefore, be useful to come up with a measure of potential energy that is a function of entropy and pressure, H = H(S,P). One particularly useful property of such a thermodynamic function would be that, under conditions of constant pressure, the change in this thermodynamic function depends only on the amount of heat flowing in/out of the system.

To derive this pressure-dependent function from E, we apply a Legendre transformation. That's where the +PV term comes from. The Gibbs free energy (G = G(T,P)) is derived in a similar way and is useful because it is constant under conditions of constant temperature and pressure.

N.B. these thermodynamic functions also depend on the number of particles in the system (N), but I'm ignoring these contributions for now for the sake of simplicity.