I would like to invite both teachers and students in physical chemistry
to think on the following serious problems. Older textbooks unanimously
deduce the so-called fundamental equation of chemical thermodynamics

dU = TdS - PdV             /1/

for a reversible change in a closed system and in the absence of any
non-expansion work. Perhaps recently P. Atkins has noticed some problem
in this deduction. In the fifth edition of his Phys. Chem. he does not
explain the problem but still adds an "amendment" - now the assumptions
are two - 1) no change of composition and 2) no non-expansion work.
Fortunately the "amendment" is easy to decipher. Let us heat (increase
the temperature in) a chemical system at equilibrium. The change is
reversible, no non-expansion work is done but........ if the reaction at
equilibrium is e.g. endothermic, the equilibrium shifts towards products
and therefore the composition changes. This is awkward - dependence of
thermodynamic functions on mole numbers is to be introduced later so at
this early stage it seems suitabe to forbid the chemical system to
change its composition. However a shrewd student may try to imagine a
reversible change in a chemical system involving no change of
composition - she/he would certainly fail - there can be no such change.
(The assumption can be justified to some extent, by using the concept of
partial derivatives, but then the deduction of /1/ is at least
misleading). The student would neither understand why the equation /1/
which is valid for nonchemical (by definition) changes should be called
"the fundamental equation of chemical thermodynamics".
Anyway, let us juxtapose the two assumptions. When the composition does
not change, can still the system do non-expansion work? If it can't, why
is the second (tautological?) assumption? Let us assume that the
chemical system contains a chemically neutral spring, and that the
sprind contracts and lifts a weight. So the composition of the system
may not change but still non-expansion work is done. Therefore the
second assumption is not tautological, but why is it necessary? Why
should  non-expansion work be initially forbidden and introduced later?
Is there a trick in this? Yes there is. The procedure guarantees that
later one introduces only that type of non-expansion work which suits
some purposes - e.g. does not contradict the second law of
thermodynamics.
Let us return to the spring - this type of non-expansion work is of
course not introduced later. Is that justified? Perhaps - spring-like
behavior is not typical of chemical systems. Isn't it? How about
conformational changes? It is demonstrated in Urry D.W. J.Phys.Chem. B
1997, 101, 11007-11028  that, on heating a polymer, it contracts and
lifts a weight. Also, the polymer does the same when the pH in the
system decreases. Is this type of non-expansion work introduced in
textbooks? No.
Another example. As we reduce the vapor volume in a liquid-vapor system,
e.g. with the help of a piston, the liquid rises and can lift a weight
(if the weight is lighter than the liquid and floats on the liquid
surface). Again non-expansion work is done by the (liquid-vapor) system
and again textbooks say nothing about it.
I hope at least some of the problems are clearly defined and
interesting.

Pentcho Valev





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