Several times during the year papers purporting to explain entropy pictorially are published in the Journal of Chemical Education. All such attempts are doomed to fail. The problem is that the thermodynamic quantities, S, U, H, A, and G, are mathematical functions. Mathematical functions cannot interact at all with a thermodynamic system. The change of the values of these thermodynamic functions for thermodynamic systems is determined from experimental measurements of observable quantities such as temperature, pressure, volume, emf, position in a gravitational field, concentration, etc. Usually an integration follows the actual measurements. Predictions may follow from the knowledge of these thermodynamic quantities.

The first law of thermodynamics defines the energy function as

dU = DQ - DW (1)

where DQ is the differential quantity of heat absorbed by the system for some differential change of state, and DW is the differential work done by the system on the surroundings (this definition is used because it is the system and not the surroundings that is of interest). Please note that we use capital D in eq 1 to indicate an inexact differential because Q and W are effects and not functions; that is, the value of the integral of DQ or DW depends on the path, and their cyclic integral is not zero. The value of the cyclic integral of dU starting from some state of a system and returning to the exact same state is zero. This shows that U is a function of the appropriate independent measurable quantities.

Similarly, the entropy function is defined by the following equation in differential form

dS = DQ_rev/T (2)

where DQ_rev is the differential quantity of heat absorbed by the system along a reversible path. The cyclic integral of dS is also zero. This result shows that S is a function of suitable independent variables.

When eqs 1 and 2 are combined for a system of constant mass and the work is limited to PV work, the result is

dU = TdS - PdV (3)

Here the independent variables are S and V. The other thermodynamic functions are defined when the independent variables are indicated as follows: U = U(S,V), H = H(S,P), A = A(T,V), and G = G(T,P).

When entropy is introduced in terms of statistical mechanics, it is still a function as described above.

The subject matter of a course in thermodynamics depends on the instructor, the student, and the textbook. We do not intend to dictate how the subject should be taught. We only ask that the instructor keep in mind that the thermodynamic quantities are really mathematical functions. It has been our experience that such questions as "What is entropy?" and "What is enthalpy?" disappear when the concept of functions is introduced. It is also our experience that for many students a course in thermodynamics confronts them for the first time with the abstract quantities and abstract thinking that are an integral part of thermodynamics.