Robert J. Twiss wrote:
>
> Classical thermodynamics (really more appropriately called thermostatics,
> because quantities are assumed not to change with time) does not take shear
> stresses into account because it deals only with pressure,
> <SNIP>
> ... .
A recent posting suggested, I believe,
that questioning the existence of
isovolumetric deformation by induction
from thermodynamic laws was specious. It
was misguided by confusion about what
'classical thermodynamics' is. This note
is for any students who may have been
mislead by this.
Why use 'classical' ?
The term 'classical' means measurable
with instruments in the laboratory or
observable with the senses in the field.
It was prepended to distinguish the
abstract theory Gibbs developed from the
more concrete, statistical theory he
later created. This emphasizing of
physical operations is valuable in
keeping abstract theories scientific.
Its heritage can be traced through
physicists to Einstein & through
philosophers to Hume.
Why use 'dynamics' ?
Dynamics had become exciting even to
mathematicians after the publication of
Lagrange's analysis of Newton's
mechanics. When Gibbs was writing his
work, Hamilton had just transformed
Lagrange's differential equations into a
equivalent set, using what we today call
the Legendre transformation.
Incorporating heat led naturally to
'thermo-dynamics', though its
formulation proved surprisingly
difficult.
Why not use 'thermostatics' ?
A subset of this theory, when frictional
dissipation along a path is negligible,
became richer than the original. An
elegant theorem that states such a
(reversible) path connecting two states
exists. This freed Gibbs from finding
it, and led to a theory using variables
of state rather than paths. The word
'static' was associated with states,
because time was needed for laboratory
instruments to measure unique
magnitudes: hence states connecting
paths are 'static'.
To illustrate the reversible path, whose
existence was proven, writers of texts
borrowed from calculus the technique of
dividing the path into segments bounded
by 'static' points. The limit produced a
curve of static points, termed
'quasi-static'. This unhappy &
unnecessary technique has confused some
geologists, who might reasonably but
incorrectly conclude that rocks can't
preserve equilibrium paths. (Cf. Zeno's
paradox.)
Is elasticity outside the range of
thermodynamic theory?
Classical thermodynamics is applicable
to all macroscopic phenomena, and the
theory is complete for elastic states.
Before classical thermodynamics is used,
its definition of work is augmented
according to the phenomena studied. For
a gas, the product of a mean pressure in
& volume decrease of an insulated system
is work; for an elastic substance, the
work effected in three different
directions is summed by calculating the
trace of the direct product of an
appropriate stress & strain tensor.
PS. Some thermodynamic theorems fail
when the sources of external energy,
such as gravitational bodies, move. For
this reason texts use the term 'internal
energy' when developing the complete
theory. The classical thermodynamics of
equilibrium states is complete; the
study of paths without equilibrium
states is now an active field of
investigation.
Respectfully,
Bruce Bathurst
|