Thermodynamics – Basic Principles

Logical and mathematical aspects of the basic concepts of thermodynamics are considered.
G. V. Skornyakov
FOREWORD
This treatise is in no way meant to serve as a help in gaining acquaintance with the theory of
thermal processes.
Discussion of the fundamentals of a theory can bear fruit only if led with competent enough people.
The author starts with a premise that the Reader embarking on a study of this book has a general knowledge of this theory within the program of the course of General
physics offered at a Physical Faculty of a University [1].
The major motivation that has prompted the Author to write this book was the inconsistency of the second law of thermodynamics as a law of Nature [2].
The logical structure of thermodynamics is often compared to that of geometry in the consistent and strict way it emerges from the two postulates (laws of thermodynamics).
The conclusions drawn in thermodynamics found convincing support in the truly immense variety of observations and deductions, so that one could hardly find today a physicist, chemist or biologist who would question the validity of thermodynamics.
Rather than being only a subject of scientific studies, thermal processes truly pervade all aspects of our life.
Thermodynamics is generally considered to be a scientific basis underpinning heatpower engineering, and conversion of heat to work, the main problem facing thermodynamics.
Conversion of heat to work by various heat engines had been enjoying worldwide industrial
application long before thermodynamics was formulated.
From the very beginning, the major motivation underlying thermodynamics had been a search for the most efficient methods that could be applied to this conversion.
But it is thermodynamics that grew to become an insurmountable monolithic wall separating the truly inexhaustible ocean of thermal energy surrounding us from the possibility of its use in technology.
Abandoning the second postulate as a universal law of Nature would at first glance seem to
imply a revision of all already well-established conceptions about the world surrounding us.
In actual fact, however, the situation is not that tragic. Indeed, the overwhelming majority (if not all) of the processes converting heat to work which were considered in thermodynamics relate to single-parameter systems.
For these processes, the second law certainly does hold. But if the number of external parameters of a system is larger than one, the applicability of the second law to it requires a rigorous proof. Said otherwise, the second law stated in its universally accepted form is nothing else than extension of the banality to the domain of Unknown.
The second law is a deep but regrettably not the only delusion in the present concepts bearing on the nature of thermal processes.
Another one is actual identification of the distribution function of a nonequilibrium system with that of probabilities.
It is a commonplace belief that the “physical essence” of the fundamental concepts of
thermodynamics is revealed by statistical physics.
The purpose of the molecular kinetics theory lies not only in explaining the concepts making up the framework of the phenomenological theory which had been thermodynamics from the very beginning, but in defining the limits of their applicability.
Thermodynamics does not formulate the equations governing the evolution of the state of a
thermodynamic system in time.
It only specifies the general principles this evolution has to obey in order to progress.
This characteristic feature of thermodynamics generated a certain feeling of dissatisfaction in many researchers. A number of concepts well established in thermodynamics (such as temperature, entropy) penetrated into the description of notoriously nonequilibrium
processes.
What is more, even formulation of the basic laws of hydrodynamics turned out to be impossible without their use.
Many concepts that originally had come from thermodynamics have so deeply penetrated into our consciousness as to become frequently used, so to say, by default.
It is an analysis of the fundamentals of thermodynamics that form the basement of the categories it involves that the present treatise is devoted to.
Particular emphasis is placed on the mathematics underlying the concepts employed in thermodynamics. No specific problems are considered….
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