Re: [Phys-l] heat +- impulse

[John Denker <jsd@av8n.com>]

On 11/05/2007 03:25 PM, LaMontagne, Bob wrote:
> > -----Original Message-----
> > From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> > bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> >
> > There is one school of thought that says
> >      -P dV _is_ the work and
> >       T dS _is_ the heat
> > in this context.  Just the other day I saw somebody write
> >       dE = heat + work
> > with this meaning.  
>
> I don't really follow this way of formulating work - what if we have a
> resistor immersed in water? Usually the rise in the internal energy of
> the water is attributed to electrical "work" being done because a
> temperature difference is not involved (since the resistor is basically
> kept at the same temperature as the water bath).

Ah, well, that illustrates my point that people have a 
devil of a time figuring out what is "heat" and what is
"work", especially when dissipation is involved.

I don't want to get involved in a holy war about terminology,
but let us observe in passing that according to *some*
schools of thought, a resistor that can be immersed in water 
would be called a "heater".  If you to the store and ask for 
an "immersion heater", that's what you get.

That school of thought has some merit, i.e. some basis in real
objectively-observable physics.  In particular, if we consider
the *state* of the water, as described by state variables E, T,
S et cetera, the change in state of the water (under the influence
of the immersion device) is well described by the T dS term in
the equation
     dE = -P dV + T dS                [1]

Now, we previously identified T dS as the heat-related term, so
there is some consistency here;  the immersion heater contributes
via the heat-related term.

  I remain quite aware that according to another school of thought,
  the term "heat" is vehemently restricted to something that happens
  at a spatial boundary, whereas T dS has got nothing to do with
  boundaries.  dS is a gradient in abstract state-space, not in 
  ordinary position-space.

I can happily remain neutral in the terminological holy wars,
because I don't need to know the definition of heat and/or work ... 
all I need to know is the energy and the entropy.  

In the case of the immersion heater, I don't really need eqn [1] 
at all anyway.  It seems vastly more sensible to use
    dH = Cp dT     at at constant pressure       [2]
especially since the Cp of water is well known.  And dH is not
much different from dE in this case.

Equation 2 comes from differentiating w.r.t (T)  ... in contrast
to equation 1 which involves differentiating  w.r.t (S).  The
fact that we have a free choice of variables is discussed at
  http://www.av8n.com/physics/thermo-laws.htm#sec-heat-capacity

> > In my experience, instead of trying to quantify "heat", it has
> > always been easier to quantify other things instead, usually
> > energy and entropy.  
>
> Do you have a macroscopic definition of S2 - S1 that does not involve
> the heat associated with reversible processes connecting the end states?

That's an easy question :-).  The answer is no, I don't have a
macroscopic definition of S.  And I don't want one.

I have only one definition of S.  It is a microscopic definition.  
In this case it reduces to 
     S[P] = sum Pi log (1/Pi)                [3]
     http://www.av8n.com/physics/thermo-laws.htm#sec-quantify-s

I have macroscopic ways of _calculating_ S, but a calculation
must not be mistaken for a definition.  As a corollary of the
trustworthy microscopic definition, one obtains, under mild
restrictions, the useful macroscopic expression
      dS = (1/T) Cp dT    at constant pressure      [4]
which you can compare to equation [2] above; see also
  http://www.av8n.com/physics/thermo-laws.htm#eq-s-vs-t





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

As a minor tangent:

> reversible processes connecting the end states

People talk a lot about "reversible processes connecting
end states" but I've never understood why the word "reversible"
appears there.  If the laws of thermodynamics make any 
sense, they must apply perfectly well to irreversible
paths, not just reversible paths.  The immersion heater,
for example, is about as irreversible as anything could 
possibly be.




Extra credit question:
  What do you call the only flounder spirit?