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Re: TdS is not dQ or d(anything)



Pentcho wrote:

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.

So? What's wrong with reversible heating?

My definition of a reversible process is one which keeps the system
in quasi-equilibrium all along. This can be either a "work" or a
"heat" process (or some combination thereof; possibly including other
processes such as mass transfer).

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.

"Of course" is a very strong term.
Please give an example of a complex system for which entropy is *not*
a state function.

Let us test eq. /2/ by considering an analogous situation. We
have a large
group of people each of which possesses a certain amount of money. Let

M = SUM n_i m_i /6/

be the total amount of money in the group and n_i is the number of
people whose
money is m_i. Through exchanging money with the outside world M slightly
changes and the change can be expressed in two ways:

dM = SUM m_i dn_i + SUM n_i dm_i /7/

dM = SUM m_i dn_i /8/

In my view /8/ is correct whereas /7/ is meaningless.

Did you mean to write dM = SUM n_i dm_i for /8/?

Also, what happens if you allow the system to exchange not only money
but also people with the outside world? Then /7/ becomes meaningful.

And also, isn't n supposed to stand for energy levels in statistical
thermodynamics? But people are macroscopic while energy levels are
quantum mechanical, so I'm not sure this is the best analogy.

If so and if the analogy
is correct, statistical thermodynamics rests on a wrong foundation. The reason
is that heat is regarded as essentially different from work.

Once again I'd say "essentially different" may be too strong. We
agree that in the end heat and work are both forms of energy
transfer. We also agree that the distinction between them breaks down
at the microscopic level. We may even agree that the distinction
between them breaks down for many irreversible processes (eg. a
sliding block does both work and heat on a rough table by virtue of
the frictional force and the temperature differentials that result).

But I'm still not really sure what the problem is for macroscopic
reversible thermodynamics. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/