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## Hanyang University

Skip to 0 minutes and 1 secondLet'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.

Skip to 1 minute and 12 secondsInsert 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.

Skip to 2 minutes and 28 secondsSo 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.

# Thermodynamic potentials

Thermodynamic potential or fundamental function is a quantity used to represent the state of a system.

We have four fundamental functions: internal energy U, enthalpy H, Helmholtz free energy F, and Gibbs free energy G. They are “potential energy” defined as capacity to do work. Starting from the first and second laws of thermodynamics, we derive expressions for the differential form of four thermodynamic potentials. They are called fundamental equations.