Enthalpy - Formal Definition

Formal Definition

The enthalpy of a homogeneous system is defined as:

where

H is the enthalpy of the system
U is the internal energy of the system
p is the pressure of the system
V is the volume of the system.

The enthalpy is an extensive property. This means that, for homogeneous systems, the enthalpy is proportional to the size of the system. It is convenient to introduce the specific enthalpy h =H/m where m is the mass of the system, or the molar enthalpy Hm = H/n, where n is the number of moles (h and Hm are intensive properties). For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems

where the label k refers to the various subsystems. In case of continuously varying p, T, and/or composition the summation becomes an integral:

where ρ is the density.

The enthalpy H(S,p) of homogeneous systems can be derived as a characteristic function of the entropy S and the pressure p as follows: we start from the first law of thermodynamics for closed systems for an infinitesimal process

Here, δQ is a small amount of heat added to the system and δW a small amount of work performed by the system. In a homogeneous system only reversible processes can take place so the second law of thermodynamics gives δQ = TdS with T the absolute temperature of the system. Furthermore, if only pV work is done, δW = pdV. As a result

Adding d(pV) to both sides of this expression gives

or

So

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