Enthalpy

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

$H=U+pV\,$

Enthalpy used to be called "heat contents", which is why it is conventionally indicated by H. The term "enthalpy" was coined by the Dutch physicist Heike Kamerling Onnes.

The work term pV has dimension of energy, in SI units this is joule; H has consequently the same dimension.

Enthalpy is a function depending on the independent variables that describe the state of the thermodynamic system. Most commonly one considers systems that have three forms of energy contact with their surroundings, namely the reversible and infinitesimal gain of heat, DQ = TdS, loss of energy by mechanical work −DW = −pdV, and acquiring of substance, μ dn. The states of systems with three energy contacts are determined by three independent variables. Although a fairly arbitrary choice of three variables is possible, it is most convenient to consider H(S,p,n), that is, to describe H as function of entropy S, pressure p, and amount of substance n.

In thermodynamics one usually works with differentials (infinitesimal changes of thermodynamic variables). In this case

$dH=dU+pdV+Vdp\,$

The internal energy dU and the corresponding enthalpy dH are

$dU=TdS-pdV+\mu dn\;\Longrightarrow \;dH=TdS+Vdp+\mu dn$

The rightmost side is an equation for the characteristic function H in terms of the characteristic variables S, p, and n.

The first law of thermodynamics can be written—for a system with constant amount of substance—as

$DQ=dU+pdV\,$

If we keep p constant (an isobaric process) and integrate from state 1 to state 2, we find

$\int _{1}^{2}DQ=\int _{1}^{2}dU+\int _{1}^{2}pdV\;\Longrightarrow \;Q=U_{2}-U_{1}+p(V_{2}-V_{1})=(U_{2}+pV_{2})-(U_{1}+pV_{1})=H_{2}-H_{1}=\int _{1}^{2}dH,$

where symbolically the total amount of heat absorbed by the system, Q, is written as an integral. The other integrals have the usual definition of integrals of functions. The final equation (valid for an isobaric process) is

$H_{2}-H_{1}=Q.\,$

In other words, if the only work done is a change of volume at constant pressure, W = p(V₂ − V₁), the enthalpy change H₂ − H₁ is exactly equal to the heat Q transferred to the system.

As with other thermodynamic energy functions, it is neither convenient nor necessary to determine absolute values of enthalpy. For each substance, the zero-enthalpy state can be some convenient reference state.