Re: TdS is not dQ or d(anything)

[Pentcho Valev <pvalev@BAS.BG>]

Carl Mungan wrote:

> Furthermore, if we restrict ourselves to reversible processes between
> equilibrium states, why do you object to dbar_Q = TdS? (I agree that
> this restriction leaves out a lot of interesting physical situations
> however.) Carl

Let me try to contribute. From the ideal gas law and the first law we can
deduce, for an ideal gas,

dQ/T = Cv (dT/T) + nR (dV/V)              /1/

Obviously dQ/T is an exact differential (INT dQ/T = 0) but there is a subtlety
that needs to be explained. One has taken dW = -PdV which means that the
system is IN EQUILIBRIUM all along. But the process is not necessarily
reversible - the system is allowed to absorb, slowly though, heat from
surroundings at a higher temperature. This is the origin of one of the lines
of confusion in thermodynamics. The definition dS = dQrev/T gives the
impression that, at least for an ideal gas, the entropy is a state function
only if the system undergoes a reversible process. On the other hand, the
nature of the ideal gas as reflected by eq. /1/ guarantees that the entropy,
if defined by dS = dQ/T, will also be a state function provided the system is
in equilibrium all along. Textbooks define dS = dQrev/T, then apply dS = dQ/T
and poor students learn.
   The problem is that dQrev/T (or dQ/T for a system at equilibrium) is
declared as an exact differential (the entropy is declared as a state
function) for systems different from ideal gas. Here a typical thermodynamic
argument is operating: "The entropy IS a state function, everybody knows it is
and if you say it isn't, you are mad". However common sense leads to the
opposite assumption. The ideal gas differs from all other systems in that
there is no interaction between the particles. So, if you have discovered some
property of the ideal gas, you should suspect that it is most probably due to
this lack of interaction and would no longer hold in systems where the
interaction is strong. By the way, there are easy ways of checking whether the
entropy is a state function for more complex systems - it isn't of course.

Pentcho