## Description

The bound energy change in a closed system is that part of the total energy change that is always bound to an exchange of heat,

```dB = dU - dA [Eq. 1]
```
```∆B = ∆H - ∆G [Eq. 2]
```

The free energy change (Helmoltz or Gibbs; dA or dG) is the total energy change (total inner energy or enthalpy, dU or dH) of a system minus the bound energy change.

Therefore, if a process occurs at equilibrium, when dG = 0 (at constant gas pressure), then dH = dB, and at deW = 0 (dH = deQ + deW; see energy) we obtain the definition of the bound energy as the heat change taking place in an equilibrium process (eq),

```dB = T∙dS = deQeq [Eq. 3]
```

Abbreviation: B [J]

## History

• From Kubo 1976 North-Holland: "Free energy" is due to H. van Helmholtz (1882), and means that part of the internal energy that can be converted into work, as seen in the equation dF = dA for an isothermal quasi-static process. It was customary to call the remaining part, TdS, of the internal energy, dU = dF+TdS, the gebundene Energie (bound energy), but this is not so common now.
• The term bound energy helps to resolve one of the historic battles in thermodynamics .