At present, thermodynamics tells chemists exactly which chemical reactions and under which conditions will take place spontaneously, and when some catalyst is needed to decrease kinetic barriers preventing the course of reactions. Thermodynamics allows for producing new chemical substances and identifying energy efficient manufacturing processes. It is an indispensable physicist's tool to understand the properties of systems under study, a biologist's tool to describe processes in cells, and an engineer's tool to design more efficient engines and motors.
At the same time, thermodynamics is a rigorous, excellently formalised and completed field of mathematics. David Hilbert, a famous German mathematician, said once that from among all the areas of physics, thermodynamics had been the easiest one for axiomatisation.
"In the faculties of physics, thermodynamics is often taught in combination with statistical physics," remarks Prof. Hołyst. "As a matter of fact, thermodynamics does not need statistical physics at all. That's why our textbook does not have it. We present thermodynamics as a consistent structure originating from the theory of differential forms."
The first part of the book introduces concisely the formalism of differential forms. Mastering mathematical foundations of thermodynamics allows one to notice interrelationships between various aspects of this discipline. "For example, there is no need to refer to non-measureable and therefore legendary entropy, if you know that all you can infer from entropy can be also inferred from Gibbs free energy that can be measured, for instance, by testing battery voltage," remarks Prof. Hołyst, adding: "We do our best to have the reader understand that conversion of entropy into free Gibbs energy is dictated by human comfort only. Ultimately, we learn thermodynamics to measure something."
Subsequent parts of the
|Contact: Robert Holyst|
Institute of Physical Chemistry of the Polish Academy of Sciences