Chemistry - Thermodynamic potentials

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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	$F = U - T S$	Also represented by A
Enthalpy	$H = U + P V$
Gibbs free energy	$G = U + P V - T S$

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

$\left.\right.d\Phi=Adx+Bdy$

Then it is seen that

$A=\left(\frac{\partial \Phi}{\partial x}\right)_y$

$B=\left(\frac{\partial \Phi}{\partial y}\right)_x$

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

$+T=\left(\frac{\partial U}{\partial S}\right)_V =\left(\frac{\partial H}{\partial S}\right)_P$

$-P=\left(\frac{\partial U}{\partial V}\right)_S =\left(\frac{\partial F}{\partial V}\right)_T$

$+V=\left(\frac{\partial H}{\partial P}\right)_S =\left(\frac{\partial G}{\partial P}\right)_T$

$-S=\left(\frac{\partial G}{\partial T}\right)_P =\left(\frac{\partial F}{\partial T}\right)_V$

Furthermore, mathematically we have

$\left(\frac{\partial}{\partial y} \left(\frac{\partial \Phi}{\partial x}\right)_y \right)_x = \left(\frac{\partial}{\partial x} \left(\frac{\partial \Phi}{\partial y}\right)_x \right)_y$

which gives:

$\left(\frac{\partial A}{\partial y}\right)_x = \left(\frac{\partial B}{\partial x}\right)_y$

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.