In thermodynamics, four quantities, measured in units of energy, are called thermodynamic potentials:

Internal energy	U	The energy needed to create a system
Helmholtz free energy	F = U - TS	Also represented by A
Enthalpy	H = U + PV
Gibbs free energy	G = U + PV - TS

where T = temperature, S = entropy, P = pressure, V = volume

Contents

1 Differential definitions 2 Chemical reactions 3 External links 4 References

Differential definitions

The following differential relations hold for the four potentials:

dU	=		TdS	-	PdV
dF	=	-	SdT	-	PdV
dH	=		TdS	+	VdP
dG	=	-	SdT	+	VdP

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

Furthermore, mathematically we have

which gives:

which are known as Maxwell's relations

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.

	Constant V	Constant P
Constant S	ΔU	ΔH
Constant T	ΔF	ΔG

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.

External links

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

References

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