IntermediateTopic 44 of 105Thermodynamics & Fluids
Thermodynamic relations
Maxwell relations and property derivatives link measurable quantities.
In depth
Maxwell relations, e.g. (∂T/∂V)_S=-(∂P/∂S)_V, connect hard-to-measure derivatives with measurable ones. Clapeyron equation dP/dT=h_fg/(T v_fg) gives saturation pressure slopes. Helmholtz and Gibbs functions govern equilibrium. Joule-Thomson coefficient derived from them.
Key points
- Partial derivatives
- Property tables created from equations of state
- Clausius-Clapeyron for vapour pressure
ExampleSaturation pressure of water rises about 7% per kelvin near 100 °C.
What is Thermodynamic relations?
Maxwell relations and property derivatives link measurable quantities.
Why is it important to understand thermodynamic relations?
Maxwell relations and property derivatives let you calculate properties that are hard to measure from ones that are easy to measure, which is very useful in fluid data work.
What is a Maxwell relation?
An equality between second partial derivatives of thermodynamic potentials, which links properties such as pressure, temperature, volume and entropy.
Why are these relations useful?
They let you compute properties like entropy from easily measured quantities such as pressure, volume and temperature.
How is Thermodynamic relations used in practice?
Typical applications include finding the entropy change of a gas from measured pressure and temperature data, deriving the internal energy change from an equation of state and checking consistency in tabulated property data for a new fluid.
What should I learn before Thermodynamic relations?
Study "Chemical equilibrium" first (topic 43 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
What are the key points of Thermodynamic relations?
Partial derivatives. Property tables created from equations of state. Clausius-Clapeyron for vapour pressure.
Can you give an example of Thermodynamic relations?
Saturation pressure of water rises about 7% per kelvin near 100 °C.
What comes after Thermodynamic relations?
The next topic is "Fluid properties", which builds directly on this one.
How difficult is Thermodynamic relations?
It is classed as Intermediate in Thermodynamics & Fluids (topic 44 of 105). It is an intermediate topic. Work through the beginner topics in Thermodynamics & Fluids first.