Complete the account of where the Maxwell relations come from.
Each Maxwell relation follows from the equality of ______ second derivatives of a thermodynamic potential. Their practical value is that the left-hand side involves ______, which no instrument measures directly, while the right-hand side needs only ______ measurements.
Word bank: mixed · entropy · pressure, volume and temperature · first
Hints
- The derivation uses the fact that the order of partial differentiation does not matter.
- The whole point is to replace something unmeasurable with something measurable.
Show the answer
Each Maxwell relation follows from the equality of mixed second derivatives of a thermodynamic potential. Their practical value is that the left-hand side involves entropy, which no instrument measures directly, while the right-hand side needs only pressure, volume and temperature measurements.
Because is the same taken in either order, the relations come free from the structure of the potentials. Their value is entirely practical: they make entropy accessible through ordinary mechanical measurements.
Practise Thermodynamic Potentials and Maxwell Relations
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