At 10:51 AM 2001/06/21 +0200, Falk Koenemann wrote:
>Dugald, I must have left space for misunderstanding - my calculation was a
>consideration of the internal energy at constant state as the scale (ie.
>V) varies; no PdV-work is done. Mass is a variable in this case. ...
Neither P nor U/V can vary with scale at constant state. I doubt you have
disproven the first law of thermodynamics; there must be some mistake.
>... T, P, mass density or chemical composition at a point X all work by
>the same principle: we choose a point X in space which indicates the place
>of a thermodynamic system of arbitrary size. This system is finite and may
>enclose heterogeneities. But if we now let V approach zero (such that X does
>not leave V) we assume that the quantity under discussion approaches a
finite
>value. We then consider that value the density or chemical composition at X.
By the same dubious token (i.e., assuming that matter is homogeneous at the
atomic and subatomic scale), Cauchy contended that components of stress
approach finite values as V approaches zero.
>If stress is PdV-work the stress theory must be compatible with thermodynamic
>principles. Currently this is not the case.
Stress is not PdV work. Seems to me stress is simply a generalization of P
for solid systems in a state of homogeneous elastic strain (and fluid
systems while they are flowing at a constant and uniform rate of strain).
To my knowledge, none of the many attempts to reconcile stress/strain
theory with thermodynamic principles found it to be incompatible with them.
>> I would contend that P = f/A works for any thermodynamic system at
>> equilibrium or during any reversible process, but -P = dU/dV works only for
>> systems at constant mass and entropy.
>
>Can we directly measure U at all?
No. We can only measure a change in U indirectly, by integrating PdV work
(and/or VpP work) between two equilibrium states at constant mass and
entropy. So far as I can imagine, P = f/A must be implicit in any such
procedure that actually measures/monitors/controls P and V.
>> The forces applied to the outer surface of the system, whatever its
>> shape, must be mechanically balanced so as not to cause either linear or
>> angular acceleration of the system. This is the condition that restricts
>> the symmetry of stress to be not less than orthorhombic.
>
>Not quite. You recall the monoclinic symmetry of my predictions for simple
>shear fabrics... . The low symmetry is possible only because I include the
>bonds between system and surrounding into my calculations. The bonds certify
>that disequilibrium cannot exist in the elastic case (as long as you don't
>break any bonds). This gives you one more degree of freedom, and monoclinic
>symmetry for stress is possible (and, in my view, also observed).
This is a radical departure from the orthodox approach, and your claims are
very intriguing. If you can show (1) that your calculations are physically
and mathematically sound, and (2) that they lead to better explanations of
S-C fabric etc than the orthodox approach, I think you will be quite famous
whether or not Euler and Cauchy made mistakes.
Dugald M Carmichael Phone/V-mail: 613-533-6182
Dept of Geological Sciences and Geological Engineering
Queen's University FAX: 613-533-6592
Kingston ON K7L3N6 E-mail: [log in to unmask]
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