Thermodynamic potential

A thermodynamic potential (in fact, rather energy than potential) is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. 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). Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, external forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mount Everest than it would at the bottom of the Mariana Trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. In a large system under even homogeneous external force, like the earth atmosphere under gravity, the intensive parameters ( p , T , ρ {displaystyle p,T, ho } ) should be studied locally having even in equilibrium different values in different places far from each other (see thermodynamic models of troposphere]. Five common thermodynamic potentials are: where T = temperature, S = entropy, p = pressure, V = volume. The Helmholtz free energy is in ISO/IEC standard called Helmholtz energy or Helmholtz function. It is often denoted by the symbol F, but the use of A is preferred by IUPAC, ISO and IEC. Ni is the number of particles of type i in the system and μi is the chemical potential for an i-type particle. For the sake of completeness, the set of all Ni are also included as natural variables, although they are sometimes ignored. These five common potentials are all energy potentials, but there are also entropy potentials. The thermodynamic square can be used as a tool to recall and derive some of the potentials. Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings: From these meanings (which actually apply in specific conditions, e.g. constant pressure, temperature, etc), we can say that ΔU is the energy added to the system, ΔF is the total work done on it, ΔG is the non-mechanical work done on it, and ΔH is the sum of non-mechanical work done on the system and the heat given to it.Thermodynamic potentials are very useful when calculating the equilibrium results of a chemical reaction, or when measuring the properties of materials in a chemical reaction. The chemical reactions usually take place under some constraints such as constant pressure and temperature, or constant entropy and volume, and when this is true, there is a corresponding thermodynamic potential that comes into play. Just as in mechanics, the system will tend towards lower values of potential and at equilibrium, under these constraints, the potential will take on an unchanging minimum value. The thermodynamic potentials can also be used to estimate the total amount of energy available from a thermodynamic system under the appropriate constraint. In particular: (see principle of minimum energy for a derivation) The variables that are held constant in this process are termed the natural variables of that potential. The natural variables are important not only for the above-mentioned reason, but also because if a thermodynamic potential can be determined as a function of its natural variables, all of the thermodynamic properties of the system can be found by taking partial derivatives of that potential with respect to its natural variables and this is true for no other combination of variables. On the converse, if a thermodynamic potential is not given as a function of its natural variables, it will not, in general, yield all of the thermodynamic properties of the system.