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Heat and work are forms of energy [1 cal = 4.184 J]. Energy [J] is a fundamental term that is used in physics and physical chemistry with various meanings [1]. These meanings become explicit in the following equations relating to systems at constant volume (dV = 0) or constant gas pressure (dp = 0). Energy is exchanged between a system and the environment across the system boundaries in the form of heat, deQ, total or available work, detW (or detW), and matter, dmatU (or dmatH) [2],

dU = (deQ + detW) + dmatU ; dV = 0 [Eq. 1a]
dH = (deQ + deW) + dmatH ; dp = 0 [Eq. 1b]

Whereas dU (or dH) describe the internal-energy change (or enthalpy change) of the system, heat and work are external energy changes (subscript e; et: external total; e: external excluding pressure-volume work), and dmatU (or dmatH) are the exchange of matter expressed in internal-energy (or enthaply) equivalents. In closed systems, dmatU = 0 (dmatH = 0). The energy balance equation [Eq. 1] is a form of the First Law of Thermodynamics, which is the law of conservation of internal-energy, stating that energy cannot be generated or destroyed: energy can only be transformed into different forms of work and heat, and transferred in the form of matter.

Notably, the term energy is general and vague, since energy may be associated with either the first or second law of thermodynamics. Work is a form of energy exchange [Eq. 1], but can be seen as exergy exchange in conjunction with deG = deW in a closed system [Eq. 3b].

An equally famous energy balance equation considers energy changes of the system only, in the most simple form for isothermal systems (dT = 0):

dU = dA + T∙dS = dU + dB [Eq. 2a]
dH = dG + T∙dS = dG + dB [Eq. 2b]

The internal-energy change, dU (enthalpy change, dH) is the sum of free energy change (Helmholtz energy, dA; or Gibbs energy = exergy change, dG) and bound energy change (bound energy, dB = T∙dS). The bound energy is that part of the energy change that is always bound to an exchange of heat.

A third energy balance equation accounts for changes of the system in terms of irreversible internal processes (i) occuring within the system boundaries, and reversible external processes (e) of transfer across the system boundaries (at constant gas pressure),

 dH = diH + deH [Eq. 3a]
 dG = diG + deG [Eq. 3b]

The energy conservation law of thermodynamics (first law) can be formulated as diH = 0 (at constant gas pressure), whereas the generally negative sign of the dissipated energy, diG ≡ diD ≤ 0, is a formulation of the second law of thermodynamics. Insertion into Eq. 3 yields,

 dH = deH [Eq. 4a]
 dG = diD + deW + dmatG [Eq. 4b]

When talking about energy transformations, the term energy is used in a general sense without specification of these various forms of energy.

Abbreviation: E; various [J]

Reference: Gnaiger 1993 Pure Appl Chem

Communicated by Gnaiger E 2018-12-29; last update: 2022-07-11


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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


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» Affinity
» Flux
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» Protonmotive force
» Mitochondrial membrane potential
» Chemical potential
» Faraday constant
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  1. Coopersmith J (2010) Energy, the subtle concept. Oxford Univ Press:400 pp. - »Bioblast link«
  2. Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«

MitoPedia concepts: Ergodynamics 

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