Biological Membranes - A. N. Ogurtsov 2012

Electrogenesis of Biomembranes
Nonequilibrium Thermodynamics of Biomembranes
Thermodynamic Potentials

In Thermodynamics, special system state Functions are introduced, the decrease of which in a reversible process running at a constant specific pair of thermodynamic parameters equals the maximum useful work.

By analogy with mechanics, where the work of constant potential forces is determined by the path-independent potential difference of these forces between the initial and final states of the system, in thermodynamics these functions are called thermodynamic potentials. They are a special case of the so-called characteristic functions.

A characteristic function is a state function by means of which (and its partial derivatives of various orders with respect to corresponding variables) all thermodynamic Properties of the system (p,V,T,S,...) can be expressed most simply and explicitly.

Natural variables are thermodynamic parameters at constant values of which the decrease in the thermodynamic potential during a reversible process equals the maximum work.

Depending on the process conditions, there are four thermodynamic potentials:

1) the isochoric-isothermal potential—Helmholtz Free energy A;

2) the isobaric-isothermal potential—Gibbs free energy G;

3) the isochoric-isoentropic potential—internal energy U;

4) the isobaric-isoentropic potential—enthalpy H.

The dependence of thermodynamic potentials on their natural variables is described by the fundamental equation of thermodynamics, which combines the First and Second laws. This equation can be written in four equivalent forms

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(for closed systems only, in which solely mechanical expansion work is performed).

The relationship between thermodynamic potentials

G = U - TS + pV = H - TS = A + pV

is clearly illustrated in Figure 164.

Figure 164 - Diagram of relations between thermodynamic potentials

For systems of variable composition, the number of moles of the system components is also a state parameter.

The chemical potential of a component μ_і is defined as the derivative of the thermodynamic potential with respect to the number of moles of that i-th component, serving as the partial molar property of the thermodynamic potential

where n_j is the constant quantity of all components except the one whose variation is being considered (j ≠ i).

Unlike U,H,A,G, the quantity μ strictly corresponds to METABOLISM/2.html">THE CONCEPT OF potential, since by definition a potential does not depend on The amount of substance, whereas U,H,A,G are extensive properties.

Using the chemical potential, the fundamental equation of thermodynamics can be rewritten as