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Maxwell relations
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Equalities from the exactness of thermodynamic potentials.
Equalities among partial derivatives of thermodynamic potentials, such as (∂T/∂V)_S = −(∂P/∂S)_V, allow us to relate hard-to-measure quantities to measurable ones.
Find entropy changes from P–V–T data.
They follow from the exactness of state functions.
In more detail
Maxwell relations are equalities between partial derivatives of thermodynamic quantities, derived from the exactness of energy differentials. They relate hard-to-measure quantities to easily measured ones.
Real-world uses
- Physicists derive entropy changes from measured pressure and temperature data.
- They are used in chemical engineering to calculate thermodynamic properties.
- Chemists use Maxwell relations to relate quantities that are hard to measure, such as entropy changes, to easier ones like pressure.
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Frequently asked questions
Why are they useful?
They let us compute quantities such as entropy changes from measurable ones.
Where do they come from?
From the mathematics of exact differentials of thermodynamic potentials.
Why are these relations useful?
They let you calculate hard-to-measure derivatives from measurable quantities, which saves a great deal of experimental work.
Related topics in Heat & Thermodynamics
Statistical entropy · Free energy · Third law · Clausius–Clapeyron equation · Joule–Thomson effect · Heat death of the universe