Enthalpy

In thermodynamics, enthalpy is the sum of the internal energy U of a system and the product of pressure p and V of the system,

$H=U+pV\,$

Enthalpy used to be called "heat content", which is why it is conventionally indicated by H.

The work term pV has dimension energy, in SI units joule, and H has the same dimension. Enthalpy is a state function, a property of the state of the thermodynamic system and its value is determined entirely by the temperature T, pressure p, and composition N_A, N_B, ... (molar amounts of substances A, B, ... ) of the system and not by its history.

Internal energy

Often one considers a system with thermal conducting walls, so that (small) amounts of heat ΔQ can go through the wall in either direction: if ΔQ > 0, heat enters the system and if ΔQ < 0 heat leaves the system. Also one usually considers one manner of performing (small) amount of work ΔW by or on the system:

$\Delta W=pdV\,$

If dV > 0 the volume of the system increases and work is performed by the system, if dV <0, work is performed on the system, hence the internal energy increase of the system by the work term obtains a minus sign:

$dU=\Delta Q-\Delta W\,\quad \quad \quad \ (1)$

Notes:

• Other forms of work are possible, for instance magnetization ΔW = H•dM, inner product of magnetic field (a vector) H—not to be confused with enthalpy H—with small change in molar magnetization dM (also a vector).
• The symbol Δ indicates a small quantity (sometimes called an inexact differential), not necessarily a differential. The symbol d indicates a differential of a differentiable function

$dF(x_{0})\equiv \lim _{x\rightarrow 0}{\frac {F(x_{0}+x)-F(x_{0})}{x}}x$

• Remarkable about equation (1) is that the sum of two small quantities (inexact differentials)

gives a differential of a state function. This is why equation (1) is the first fundamental law (postulate) of thermodynamics

To be continued