Josiah Willard Gibbs in his papers used the term fundamental functions.
Effects of changes in thermodynamic potentials can sometimes be measured directly, while their absolute magnitudes can only be assessed using computational chemistry or similar methods.
[3] One main thermodynamic potential that has a physical interpretation is the internal energy U.
It is the energy of configuration of a given system of conservative forces (that is why it is called potential) and only has meaning with respect to a defined set of references (or data).
For example, the working fluid in a steam engine sitting on top of Mount Everest has higher total energy due to gravity than it has at the bottom of the Mariana Trench, but the same thermodynamic potentials.
Five common thermodynamic potentials are:[4] where T = temperature, S = entropy, p = pressure, V = volume.
The set of all Ni are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change.
Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings like the below: From these meanings (which actually apply in specific conditions, e.g. constant pressure, temperature, etc.
[10] Using IUPAC notation in which the brackets contain the natural variables (other than the main four), we have: If there is only one species, then we are done.
For the most simple case, a single phase ideal gas, there will be three dimensions, yielding eight thermodynamic potentials.
(Neither δQ nor δW are exact differentials, i.e., they are thermodynamic process path-dependent.
This leads to the standard differential form of the internal energy in case of a quasistatic reversible change:
If the system has more external variables than just the volume that can change, the fundamental thermodynamic relation generalizes to:
[12] Applying Legendre transforms repeatedly, the following differential relations hold for the four potentials (fundamental thermodynamic equations or fundamental thermodynamic relation): The infinitesimals on the right-hand side of each of the above equations are of the natural variables of the potential on the left-hand side.
If we define Φ to stand for any of the thermodynamic potentials, then the above equations are of the form:
where {yi ≠ j} is the set of all natural variables of Φ except yj that are held as constants.
This yields expressions for various thermodynamic parameters in terms of the derivatives of the potentials with respect to their natural variables.
can be integrated: Note that these measurements are made at constant {Nj } and are therefore not applicable to situations in which chemical reactions take place.
We may take the "cross differentials" of the state equations, which obey the following relationship:
it follows from Euler's homogeneous function theorem that the internal energy can be written as:
Thus, there is another Euler relation, based on the expression of entropy as a function of internal energy and other extensive variables.
[11][18][19] Equating any thermodynamic potential definition with its Euler relation expression yields:
It follows that for a simple system with I components, there will be I + 1 independent parameters, or degrees of freedom.
For example, a simple system with a single component will have two degrees of freedom, and may be specified by only two parameters, such as pressure and volume for example.
The law is named after Josiah Willard Gibbs and Pierre Duhem.
As the internal energy is a convex function of entropy and volume, the stability condition requires that the second derivative of internal energy with entropy or volume to be positive.
[20] The same concept can be applied to the various thermodynamic potentials by identifying if they are convex or concave of respective their variables.
The stability conditions impose that isothermal compressibility is positive and that for non-negative temperature,
[21] Changes in these quantities are useful for assessing the degree to which a chemical reaction will proceed.
The relevant quantity depends on the reaction conditions, as shown in the following table.