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Enthalpy, H [J], can under conditions of constant gas pressure neither be destroyed nor created (first law of thermodynamics: diH/dt = 0). The distinction between enthalpy and internal-energy of a system is due to external pressure-volume work carried out reversibly at constant gas pressure. The enthalpy change of the system, dH, at constant pressure, is the internal-energy change, dU, minus reversible pressure-volume work,

dH = dU - dVW

Pressure-volume work, dVW, at constant pressure, is the gas pressure, p [Pa = J·m-3], times change of volume, dV [m3],

dVW = -p·dV [J]

The available work, deW, is distinguished from external total work, detW, [1]

deW = detW - dVW

The change of enthalpy of a system is due to internal and external changes,

 dH = diH + deH

Since diH = 0 (first law of thermodynamics), the dH is balanced by exchange of heat, work, and matter,

dH = (deQ + deW) + dmatH ; dp = 0 

The exchange of matter is expressed in enthalpy equivalents with respect to a reference state (formation, f, or combustion, c). The value of dH in an open system, therefore, depends on the arbitrary choice of the reference state. In contrast, the terms in parentheses are the sum of all (total, t) partial energy transformations,

dtH = (deQ + deW)

A partial enthalpy change of transformation, dtrH, is distinguished from the total enthalpy change of all transformations, dtH, and from the enthalpy change of the system, dH. In a closed system, dH = dtH. The enthalpy change of transformation is the sum of the Gibbs energy (free energy) change of transformation, dtrG, and the bound energy change of transformation at constant temperature and pressure, dtrB = T·dS,

dtrH = dtrG + dtrB

Abbreviation: H [J]

Reference: Gnaiger 1993 Pure Appl Chem

Communicated by Gnaiger E 2019-01-06


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  • Joule [J]; 1 J = 1 N·m = 1 V·C; 1 cal = 4.184 J
Fundamental relationships
» Energy
» Exergy
» Extensive quantity
» Force
» Pressure
» Intensive quantity
Forms of energy
» Internal-energy dU
» Enthalpy dH
» Heat deQ
» Bound energy dB
Forms of exergy
» Helmholtz energy dA
» Gibbs energy dG
» Work deW
» Dissipated energy diD


  1. Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«

MitoPedia concepts: Ergodynamics