Re: entropy - motivation for definition

[Michael Edmiston <edmiston@BLUFFTON.EDU>]

Mark Sylvester asked
> In Classical Thermodynamics, what is the motivation for the definition
of
> entropy as Q/T?

(1) It has the property of being a state function.

(2) It shows (I would say by design) the direction of spontaneous
irreversible change.  It is obvious thermal energy flows from the hotter
object to the colder object. But this cannot be concluded from the first
law.  Consider a system and its surroundings.  A change occurs that
results in thermal energy Q passing to/from the surroundings while it
passes from/to the system.

Let's say the surroundings are at lower T.  Q leaving the system (-) is
the same as Q entering the surroundings (+).  Since the surroundings has
a smaller T, Q/T for the surroundings has a larger absolute value than
abs(Q/T) for the system.  The total delta-S is delta-S(system) +
delta-S(surrounding).  The total delta-S will be positive.

The only way to get delta-S(total) equal zero is if the two temperatures
are the same... i.e. a reversible change.  For any spontaneous change
delta-S(total) will be positive.

I often hear that Q/T "explains" the spontaneous direction.  I would say
it doesn't explain it.  It was rigged to come out positive for
spontaneous change by defining it as Q/T and by knowing that
thermal-energy flows from hot to cold.

However, since it also turns out to be a state function, and can be
calculated from thermodynamic data tables, it can be calculated and used
to help determine spontaneous change for reactions we would not
otherwise know wihtout doing the experiment.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu