For a one phase single component system, a variety of thermodynamic variables, such as three pairs of natural variables(P~V, T~S, & �~N), eight thermodynamic potentials (U, H, G, A, O, ?, ?, & F), their six first order and twenty-four second order partial derivatives (-P, V, T, -S, �, -N and CPN, CVN, OPN, OVN, JTN, JSN, RTN, RSN, CP�, CV�, OP�, OV�, JT�, JS�, RT�, RS�, ?PT, ?VT, GPT, GVT, ?PS, ?VS, GPS, & GVS), were arranged at vertexes of a concentric multi-polyhedron (a cube sandwiches between a pair of octahedrons and it is surrounded by a 26-face polyhedron or rhombicuboctahedron) based on considerations of their physical meanings, such as a neighbor relationship among correlated (corresponding and/or conjugate) variables, the criteria for spontaneous changes & equilibria, the Ehrenfest classification of phase transitions, and symmetry in thermodynamics. It could be found out by this diagram that some quite confused similar derivatives could be easily distinguished by their variable neighbor relationship, that more than ten families of thermodynamic relations (Legendre transforms, Identity equations, Maxwell equations, Maxwell-II & III equations, fundamental equations, important Jacobian equations, Gibbs-Helmholtz equation family. CPN-type variable family, CPN~CVN relation family, two groups of concise relations among 24 CPN-type variables) could be symmetrically expressed by specific movable patterns, that any derivatives, such as Bridgman's equations, Shaw's formulas, Koenig's results etc., could be derived and expressed in terms of T, P, V, S, a, ?T & CP on the spot by using the fixed diagram as a map and selecting specific movable patterns plus symmetrical operations as different routes to get their destinations, that the symmetry emphasized by Callen in thermodynamics has been visually revealed in development of this foolproof graphic method, and that the thermodynamic symmetry is not as perfect as the geometric symmetry of the polyhedrons is because of F(T,P,�)=0 at a corner of the cube. This generalized elegant diagram might be considered as a model rather than a mnemonic device since it has profoundly distinguished, expressed, derived, and developed a variety of thermodynamic relations, and especially because it has virtually revealed the thermodynamic symmetry being a C3 symmetry about the special conjugate U~F pair as a C3 axis, which pivots at F=0, and displaying C4 & s symmetries on three U-containing squares, where the U, H, G, & A square is most important and useful.

Thermodynamic concentric multipolyhedron diagram and its applications

244th National Meeting (2012)

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.