In thermodynamics, thermodynamic potentials are parameters associated with a thermodynamic system and have the dimensions of energy. They are called "potentials" because in a sense, they describe the amount of potential energy in a thermodynamic system when it is subjected to certain constraints. The different potentials correspond to different constraints to which the system may be subjected. The four most common thermodynamic potentials are: In thermodynamics, there are a large number of equations relating the various thermodynamic quantities. ... The laws of Thermodynamics in principle describe the specifics for the transport of heat and work in thermodynamic processes. ... Thermodynamic potentials Maxwell relations Bridgmans equations Exact differential (edit) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as pressure/volume or temperature/entropy. ... The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. ... This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... In thermodynamics the Gibbs free energy is a state function of any system defined as where G is the Gibbs free energy, measured in joules H is the enthalpy, measured in joules T is the temperature, measured in kelvins S is the entropy, measured in joules per kelvin... Maxwells relations are a set of equations in Thermodynamics which are derivable from the definitions of the four thermodynamic potentials. ... In Thermodynamics, Bridgmans Thermodynamic equations is actually a method of generating a large number of thermodynamic identities involving a number of thermodynamic quantities. ... In mathematics, both in vector calculus and in differential topology, the concepts of closed form and exact form are defined for differential forms, by the equations dα = 0 for a given form α to be a closed form, and α = dβ for an exact form, with α given and β... Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature on physical systems at the macroscopic scale. ...

Name	Formula	Natural variables
Internal energy
Helmholtz free energy
Enthalpy
Gibbs free energy

where T = temperature, S = entropy, P = pressure, V = volume. The Helmholtz free energy is sometimes denoted by the symbol F, but the use of A is preferred by IUPAC (See Alberty, 2001). N_i is the number of particles of type i in the system. For the sake of completeness, the set of all N_i are also included as natural variables, although they are sometimes ignored. The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. ... This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... In thermodynamics the Gibbs free energy is a state function of any system defined as where G is the Gibbs free energy, measured in joules H is the enthalpy, measured in joules T is the temperature, measured in kelvins S is the entropy, measured in joules per kelvin... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... For other senses of the term entropy, see entropy (disambiguation). ... Pressure (symbol: p) quantifies the intensity of a force acting on a surface in a direction perpendicular to that surface. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... The International Union of Pure and Applied Chemistry (IUPAC) is an international non-governmental organization devoted to the advancement of chemistry. ...

Description and interpretation

Thermodynamic potentials are very useful when calculating the expected results of a chemical reaction, or when measuring the properties of materials in a chemical reaction. The chemical reactions usually take place under some simple constraints such as constant pressure and temperature, or constant entropy and volume, and when this is true, there is a corresponding thermodynamic potential which 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 constraint.

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.

Just as a small increment of energy in a mechanical system is the product of a force times a small displacement, so an increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" which, when unbalanced, cause certain generalized "displacements" to occur, with their product being the energy transferred as a result. These forces and their associated displacements are called conjugate variables. For example, consider the PV conjugate pair. The pressure acts as a generalized force: Pressure differences force a change in volume, and their product is the energy lost by the system due to work. Here pressure is the driving force, volume is the associated displacement, and the two form a pair of conjugate variables. In a similar way, temperature differences drive changes in entropy, and their product is the energy transferred by heat transfer. The thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yielding an extensive energy. In physics and chemistry, an intensive quantity (also referred to as an intensive variable) is a physical quantity whose value does not depend on the amount of the substance for which it is measured. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ...

Differential definitions

Any differential change in the internal energy U of a system can be written as the sum of heat flowing into the system and work done on the system by the environment:

where δq is the infinitesimal heat flow into the system, and δw is the infinitesimal work done on the system. (Note that neither are exact differentials. Small changes are therefore represented with δ rather than d.)

Assuming only reversible mechanical work (PV work), we can express the internal energy change in terms of state functions and their differentials:

where T is temperature, S is entropy, P is pressure, and V is volume. Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... For other senses of the term entropy, see entropy (disambiguation). ... Pressure (symbol: p) quantifies the intensity of a force acting on a surface in a direction perpendicular to that surface. ... Volume, also called capacity, is a quantification of how much space an object occupies. ...

This leads to the standard differential form of the internal energy:

Applying Legendre transforms repeatedly, the following differential relations hold for the four potentials: In mathematics, two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: f and g are then said to be related by a Legendre transformation. ...

Note that 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. The above relations illustrate that when the natural variables of each potential are held constant, the change in the potential is zero. If we write the above four equations generally as

Then it is seen that

yielding expressions for T, P, S, and V in terms of derivatives of the potentials

Chemical reactions

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. Δ denotes the change in the potential and at equilibrium the change will be zero.

Most commonly one considers reactions at constant P and T, so the Gibbs free energy is the most useful potential in studies of chemical reactions.

Mnemonic device

A mnemonic used by physics students to remember the Maxwell relations in thermodynamics is "Good Physicists Have Studied Under Very Fine Teachers", which helps them remember the order of the variables in the square, in clockwise direction. Another mnemonic used here is "Valid Facts and Theoretical Understanding Generate Solutions to Hard Problems", which gives the letter in the normal left to right writing direction. Maxwells relations are a set of equations in Thermodynamics which are derivable from the definitions of the four thermodynamic potentials. ... Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature on physical systems at the macroscopic scale. ...

External links

• http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thepot.html

References

• Alberty, R. A. (2001). Use of Legendre transforms in chemical thermodynamics, Pure Appl. Chem., Vol. 73(8): 1349–1380.

• Lewis, Gilbert Newton; Randall, Merle: Revised by Pitzer, Kenneth S. & Brewer, Leo (1961). Thermodynamics, 2nd Edition, McGraw-Hill Book Co., New York, NY USA. ISBN 0071138099.