Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Thermodynamics: Dismal Swamp of Obscurity
Posted:
Sep 29, 2017 2:21 PM


Clifford Truesdell, The Tragicomical History of Thermodynamics, 18221854, p. 6: "Finally, I confess to a heartfelt hope  very slender but tough  that even some thermodynamicists of the old tribe will study this book, master the contents, and so share in my discovery: Thermodynamics need never have been the Dismal Swamp of Obscurity that from the first it was and that today in common instruction it is; in consequence, it need not so remain." [...] p. 333: "Clausius' verbal statement of the "Second Law" makes no sense, for "some other change connected therewith" introduces two new and unexplained concepts: "other change" and "connection" of changes. Neither of these finds any place in Clausius' formal structure. All that remains is a Mosaic prohibition. A century of philosophers and journalists have acclaimed this commandment; a century of mathematicians have shuddered and averted their eyes from the unclean." https://www.amazon.com/TragicomicalThermodynamics18221854MathematicsPhysical/dp/1461394465
Truesdell is exaggerating perhaps? See this:
Wikipedia: "The second law of thermodynamics states that the total entropy can only increase over time for an isolated system, meaning a system which neither energy nor matter can enter or leave. The total entropy can remain constant in ideal cases where the system is in a steady state (equilibrium) or undergoing a reversible process." https://en.wikipedia.org/wiki/Second_law_of_thermodynamics
There is an omission that makes the above formulation of the second law meaningless (not even wrong). The entropy increase is only defined for processes that BEGIN AND END IN EQUILIBRIUM STATES. Scientists who study different processes and claim that the entropy increases simply don't know what they are talking about.
Let us imagine that the condition
BEGIN AND END IN EQUILIBRIUM STATES
is resuscitated and strictly obeyed. Will there be much improvement? No, because processes in an isolated system that begin and end in equilibrium states don't exist:
Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 4: "Even deliberate attempts at careful formulation of the Second Law sometimes end up in a paradox. One sometimes finds a formulation which admits that thermodynamics aims only at the description of systems in equilibrium states, and that, strictly speaking, a system does not always have an entropy during a process. The Second Law, in this view, refers to processes of an isolated system that begin and end in equilibrium states and says that the entropy of the final state is never less than that of the initial state (Sklar 1974, p. 381). The problem is here that, by definition, states of equilibrium remain unchanged in the course of time, unless the system is acted upon. Thus, an increase of entropy occurs only if the system is disturbed, i.e. when it is not isolated." http://philsciarchive.pitt.edu/313/
Pentcho Valev



