Advanced Topic 418 of 1102 Thermodynamics & Energetics
Maxwell Relations
Equalities between partial derivatives of thermodynamic potentials derived from state functions.
Practise Thermodynamics & Energetics All Thermodynamics & Energetics topics
In-depth explanation of Maxwell Relations
Maxwell relations are equalities between mixed second partial derivatives of thermodynamic potentials, which follow from the fact that the state functions are exact differentials. For example, the derivative of entropy with respect to volume at constant temperature equals the derivative of pressure with respect to temperature at constant volume. These identities allow quantities that are difficult to measure directly, such as entropy changes, to be expressed in terms of measurable properties like pressure, volume and temperature. They are routinely used to convert calorimetric or equation-of-state data into the desired thermodynamic quantities. Maxwell relations therefore reduce the amount of experimental work needed for thermodynamic analysis.
Going deeper: Maxwell Relations
Key ideas: They come from equality of mixed second derivatives of U, H, A and G. Four common ones relate entropy changes to measurable P, V and T derivatives. For example, the derivative of S with respect to P at constant T equals minus the derivative of V with respect to T at constant P.
Common mistakes and connections: Memorizing without understanding the source is risky. Use the thermodynamic square mnemonic only after knowing why they hold. They permit calculation of entropy from equation-of-state data and are crucial in deriving general thermodynamic identities.
Visualization of Maxwell Relations
A Maxwell relation says two mixed derivatives are equal: the entropy change with volume matches the pressure change with temperature, so the curves coincide. The interactive lesson shows this as a live animation or chart.
Worked example and use case
The Maxwell relation linking entropy and volume to pressure and temperature allows entropy changes in a gas to be computed from equation-of-state data.
Frequently asked questions about Maxwell Relations
What is Maxwell Relations?
Equalities between partial derivatives of thermodynamic potentials derived from state functions.
Is Maxwell Relations a beginner, intermediate or advanced topic?
Maxwell Relations is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Maxwell Relations?
Study these earlier topics in Thermodynamics & Energetics first: Thermodynamics of Dissolution, Gibbs-Helmholtz Equation, Van't Hoff Equation.
What comes after Maxwell Relations?
The next topics in Thermodynamics & Energetics are Residual Entropy.
Can I practise Maxwell Relations with quizzes?
Yes. The interactive lesson includes a self-check question on Maxwell Relations, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Maxwell Relations fits in Thermodynamics & Energetics
Maxwell Relations is topic 90 of 91 in Thermodynamics & Energetics.