|
|
Thermodynamic PotentialsIn thermodynamics, four quantities, measured in units of energy, are called thermodynamic potentials: | a href="/encyclopedia/Internal-energy" title="Internal energy">Internal energy | | The energy needed to create a system | | a href="/encyclopedia/Helmholtz-free-energy" title="Helmholtz free energy">Helmholtz free energy | | Also represented by A | | a href="/encyclopedia/Enthalpy" title="Enthalpy">Enthalpy | | | | a href="/encyclopedia/Gibbs-free-energy" title="Gibbs free energy">Gibbs free energy | | where T = temperature, S = entropy, P = pressure, V = volume Differential definitions The following differential relations hold for the four potentials: | i>dU | = | |TdS | - |PdV | | i>dF | = | - | SdT | - | PdV | | i>dH | = | |TdS | + |VdP | | i>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 -
+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.
|
 |