Thermodynamic potentials

Let’s look at one of the most essential equations in thermodynamics. There are a number of state functions related to energy in thermodynamics. They are called thermodynamic potentials. The four most common thermodynamic potentials are U, H, G, and F. We only consider P - V work in energy functions for thermodynamic potentials in the following. The most fundamental potential is the internal energy U. dU is reversible heat + reversible work. And it is TdS - PdV. Let’s define enthalpy. H is U + PV. Expand the differential. Then it is dU + PdV + VdP. Insert the dU above, then, it becomes TdS + VdP. Gibbs free energy G is H - TS. Thus its differential is dH - TdS - SdT.

Insert the dH above, then, dG becomes - SdT + VdP. F is U - TS. So its differential is dU - TdS - SdT. Again, insert dU above, then dF becomes - SdT - PdV. The summary is shown. The total differential of thermodynamic potentials are like this. dU is TdS - PdV, dH is TdS + VdP, dF is - SdT - PdV, and dG is - SdT + VdP. Let’s first look at the property of G. The dependence of G on temperature and pressure can be graphically interpreted from the thermodynamic potential equation. G is H - TS. And its total differential dG is - SdT + VdP. At constant pressure, dG is - SdT.

So the dependence of G on T at constant pressure is - S. Let’s graphically represent it. It is one example of gibbs free energy versus temperature curve. The slope of this curve is - delta S. At constant temperature, dG is VdP. So the dependence of G on P at constant temperature is V. Let’s graphically represent it. It is one example of gibbs free energy versus pressure curve. The slope of this curve is delta V.