[Phys-l] modern vs classical thermodynamics

[John Denker <jsd@av8n.com>]

1) Once upon a time, an engineer was building a geothermal steam
  engine.  He needed to know the integral of 1/(1+x^2).  So he
  looked it up in a table of integrals.  And everybody lived
  happily ever after.

  Remark:  He did not need to calculate it /directly/ from the
  definition of Riemann integral.

2) The guy who prepared the table of integrals didn't do it by
  /direct/ use of the definition, either.  There are formulas
  and algorithms and theorems about integrals that are more
  appropriate than using the definition directly.

3) The guys who devised the aforementioned formulas etc. did
  sometimes use the definition of Riemann integral.

The moral of the story is:  In some cases you use the fundamental
definitions directly ... but in most cases you use the definitions
only very indirectly.

I wrote:

> > Classical thermodynamics has been obsolete for more than 100 years.

Evidently that statement is open to misinterpretation.  Sorry about
that.  Let me try to clarify what I mean.

On 01/27/2011 10:39 AM, LaMontagne, Bob wrote:

> Engineers still have to calculate exergy and the availability of
> energy when steam is supplied to a power plant or geothermal energy
> is used to produce electricity. The statistical definition of entropy
> may be more modern and may be more definitive, but it is not easy to
> use in many engineering applications.

Well, indeed it would be inconvenient to use the fundamental 
definition /directly/ in such applications ... but no engineer
would be dumb enough to do that.  Engineers are really good at
building black boxes out of black boxes, such that the top
level is many steps removed from the fundamental definitions.

Using "engineering" to argue against modern definitions is not
a good argument.

The valid engineering formulas that are found in classical thermo-
dynamics continue to be valid in modern (post-1898) thermodynamics. 
This is to be expected, in accordance with the correspondence
principle.  New theories are required to reproduce the main results
of the old theories.

On the other hand, there are some things that classical thermodynamics
gets wrong:
 *) This includes the third law, which is what stated the present
  discussion.

In addition:
 *) There are never-ending disputes about the classical definition 
  of "heat" ... which is important, because classical thermo defines 
  entropy in terms of heat.  (In contrast, in modern thermo there 
  is a much better definition of entropy, and no need to fuss over 
  heat.)

Furthermore, there are lots of cases where classical thermodynamics
has nothing to say, in which case using the modern theory is
/infinitely/ easier.
 *) This includes a wide range of far-from-equilibrium situations
  (such as arise in pulsed NMR experiments).
 *) This includes everything having to do with small systems. 
  Classical thermodynamics books generally say on page 1 that
  thermodynamics (i.e. classical thermodynamics) is applicable 
  only to macroscopic systems.

I've had physics professors tell me that my derivation of the Sackur
Tetrode equation is wrong because (a) it applies to small systems
(as well as large systems) and (b) it says that for small systems 
the entropy is not an extensive quantity.  I ask them how they know 
that the entropy has to be extensive.  They say "Everybody knows that.  
It says right here in the thermodynamics book that entropy is extensive." 
Well, first of all, don't believe everything you read in books, and 
secondly the book by its own terms doesn't apply to small systems.
You can't assume what it says about large systems applies to small
systems.

There is an important point here, because you can't assume that all
your engineering students are going to work on steam engines to the
exclusion of all else.  Steam engines were the trendy thing in the 
19th century, but the 19th century has been over for a while now.
In the 21st century, there are going to be more jobs in biomedical
engineering than in steam engineering.  For that, you want a theory
that can handle the thermodynamics of single molecules.

===========

There are two things that make modern thermodynamics difficult for 
the students:
 a) Sometimes they don't have a strong enough background in multi-
  dimensional calculus, and
 b) Sometimes they don't have a strong enough background in probability.

Problem (a) is the same for classical thermo and modern thermo,
so it cannot be used as an argument for or against either one.

Problem (b) is more of a problem for modern thermodynamics, but
there are two sides to this argument.  There are lots of reasons
why the students would be better off if they had a solid working
knowledge of probability.  Thermo is only one item on a list that
includes experimental design, data analysis, data compression and
communication, quantum mechanics, thermo, and lots of other things.  
So I reckon requiring probability for thermo doesn't really add 
to the students' workload.  That bandwagon is already in motion;  
the only question is whether you should climb aboard.

=============================

Bottom line:
  The arguments in favor of classical thermo are very weak.
  The arguments in favor of modern thermo are much stronger.