Application
The experimental usefulness of these functions is restricted to conditions where certain variables (T, and V or external p) are held constant, although they also have theoretical importance in deriving Maxwell relations. Work other than pdV may be added, e.g., for electrochemical cells, or work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors.
In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.
| Name | Symbol | Formula | Natural variables |
|---|---|---|---|
| Helmholtz free energy | |||
| Gibbs free energy |
Ni is the number of molecules (alternatively, moles) of type i in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differentials for reversible processes are (assuming only pV work)
where μi is the chemical potential for the i-th component in the system. The second relation is especially useful at constant T and p, conditions which are easy to achieve experimentally, and which approximately characterize living creatures.
Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding.
An example is surface free energy, the amount of increase of free energy when the area of surface increases by every unit area.
The path integral Monte Carlo method is a numerical approach for determining the values of free energies, based on quantum dynamical principles.
Read more about this topic: Thermodynamic Free Energy
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