Falk,
>1. Equivalence of f/A and dU/dV. Assume shape of V is spherical.
>Assume: f = 5, f/A = P is scale-independent.
>Assume that f/A and U/V are equivalent for the case r = 1.
>Calculate U/V and f as V approaches zero at constant P.
>
>Hence U/V is scale-dependent. This is physically impossible.
>Furthermore, as V vanishes, so does f, but f vanishes faster than r.
I'm not sure what's been demonstrated here -- all you seem to have shown is
that area doesn't equal volume.
Please enlighten me on the following points:
1) Pressure is dU/dV, not U/V, so I don't see why U/V is of any relevance
to this argument.
2) Your column calculating U/V assumes that U is constant. You define an
exact initial value for U, but none of your equations constrain subsequent
values (unless somehow you're assuming that all of your states are related
by compression?). So, it seems that you're stuffing more and more energy
into a smaller and smaller volume, while simultaneously saying that the
pressure is constant. On the face of it, this does not make much sense.
3) A simplifying feature of using flat surfaces is that it's easy to
resolve force vectors into normal and parallel components. When you're
using the surface of a sphere, this would seem to make balance-of-force
computations much more difficult to do correctly.
Rich Ketcham
______________________________
Dr. Richard Ketcham
Research Scientist
Manager, High-Resolution X-Ray Computed Tomography Facility
Department of Geological Sciences, C1110
University of Texas
Austin, TX 78712-1101
Office: (512) 471-0260 Fax: (512) 471-9425
Email: [log in to unmask]
http://www.ctlab.geo.utexas.edu
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