Applying symmetry of partial derivatives to the thermodynamic potentials allows one to derive a set of relations named for this physicist. For 10 points each:
[10e] Name this Scottish formulator of a thought experiment in which the second law of thermodynamics is violated by a namesake “demon.” This physicist unified classical electromagnetism into a set of four equations.
ANSWER: James Clerk Maxwell
[10h] Name this operation that may be thought of as the continuous analogue of a power series. Mellin derived a formula for the inverse of this operation that takes the limit of an integral over a vertical contour.
ANSWER: Laplace transform [accept inverse Laplace transform]
[10h] Two answers required. Maxwell’s relations may be used to express the second-order derivatives of these two thermodynamic potentials as negative partial derivatives of entropy, with temperature held constant. This works because temperature is a natural variable for both of these quantities.
ANSWER: Gibbs free energy AND Helmholtz free energy [accept equivalents like Gibbs and Helmholtz free energies; prompt on G AND F or G AND A; prompt on free energies]
[10e] This function of negative s times t is the kernel of the Laplace transform. The Euler-Mascheroni constant appears when taking the Laplace transform of this function’s inverse, the natural logarithm.
ANSWER: exponential function [or e to the x; accept anything indicating that e is being raised to a power; accept negative exponential]
[10m] This quantity is a natural variable of all four main thermodynamic potentials, reflecting its appearance in the derivation of the Gibbs–Duhem equation. This quantity is conjugate to particle number.
ANSWER: chemical potential [prompt on mu]
[10m] The Euler–Mascheroni constant is denoted by this letter. Applying the Laplace transform to a power generates a function denoted by the uppercase version of this letter that has poles at the nonpositive integers.
ANSWER: gamma
<JC, Physics>