Thermodynamic square

Born presented the thermodynamic square in a 1929 lecture.

A mnemonic used by students to remember the Maxwell relations (in thermodynamics) is "Good Physicists Have Studied Under Very Fine Teachers", which helps them remember the order of the variables in the square, in clockwise direction.

Another mnemonic used here is "Valid Facts and Theoretical Understanding Generate Solutions to Hard Problems", which gives the letter in the normal left-to-right writing direction.

Both times A has to be identified with F, another common symbol for Helmholtz free energy.

To prevent the need for this switch the following mnemonic is also widely used:"Good Physicists Have Studied Under Very Ambitious Teachers"; another one is Good Physicists Have SUVAT, in reference to the equations of motion.

One other useful variation of the mnemonic when the symbol E is used for internal energy instead of U is the following: "Some Hard Problems Go To Finish Very Easy".

Suppose for example one desires to compute the derivative of the internal energy

The following procedure should be considered: The Gibbs–Duhem equation can be derived by using this technique.

Notice though that the final addition of the differential of the chemical potential has to be generalized.

The thermodynamic square can also be used to find the first-order derivatives in the common Maxwell relations.