|
In thermodynamics, four quantities, measured in units of energy, are called thermodynamic potentials:
where T = temperature, S = entropy, p = pressure, V = volume
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
- <math>\left.\right.d\Phi=Adx+Bdy<math>
Then it is seen that
- <math>A=\left(\frac{\partial \Phi}{\partial x}\right)_y<math>
- <math>B=\left(\frac{\partial \Phi}{\partial y}\right)_x<math>
yielding expressions for T, P, S, and V in terms of derivatives of the potentials
- <math>
+T=\left(\frac{\partial U}{\partial S}\right)_V
=\left(\frac{\partial H}{\partial S}\right)_P
<math>
- <math>
-P=\left(\frac{\partial U}{\partial V}\right)_S
=\left(\frac{\partial A}{\partial V}\right)_T
<math>
- <math>
+V=\left(\frac{\partial H}{\partial P}\right)_S
=\left(\frac{\partial F}{\partial P}\right)_T
<math>
- <math>
-S=\left(\frac{\partial F}{\partial T}\right)_P
=\left(\frac{\partial A}{\partial T}\right)_V
<math>
Furthermore, mathematically we have
- <math>
\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
<math>
which gives:
- <math>
\left(\frac{\partial A}{\partial y}\right)_x
=
\left(\frac{\partial B}{\partial x}\right)_y
<math>
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
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.
| 
