Re: Dissipation & Latent heat

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

As much as I, too, concur with the usefulness of the term 'dissipation'
in describing energy dissipating processes, I thought I would point out a
problem I perceived in John Barrer's earlier post.  It is possible that
what he wrote was just a harmless slip, or that I misinterpreted what he
wrote.  But it is also possible that it is a misconception.  I thought I
would address the issue on the outside chance that the latter case is the
case.

I'm referring to where John Barrer wrote:

>  ...      I suppose we could say "energy converted
> to increased internal kinetic energy which shows up as
                       ^^^^^^^
> a temperature rise", but I think Ediss is simpler and
> creates no difficulties within the context it is
> presented.  ...
> Comments?

It is in general *not* the case that when energy associated with
macroscopic degrees of freedom (i.e. kinetic energy of the motion of the
center of mass, gravitational potential energy of a macroscopic system in
an external gravitational field, Hookeian elastic energy of macroscopic
deformation, etc.) is dissipated into internal energy associated with a
system's microscopic degrees of freedom that energy becomes only internal
*kinetic* energy.  It is only in the special case where the system
happens to be a noninteracting ideal gas that the internal energy
increase is merely kinetic.  The usual case has a comparable amount of
internal energy in the form of kinetic energy of the individual
constituent particles *and* in the form of potential energy associated
with the interactions among the nearby particles.  In fact, for most
insulating solids near room temperature (i.e. far enough above the Debye
temperature to behave classically but cool enough to still be quasi-
harmonic) the Dulong-Petit law is pretty accurate and it divides the
internal energy of thermal excitation (above the absolute zero
temperature ground state) into *equal* parts kinetic energy and
increased potential energy of the constituent particles.

Somewhat related to this issue is a misconception that one sometimes
encounters related to the latent heat of transformation of a system (of
particles that can adequately be described by classical statistical
mechanics) that undergoes a 1st order phase transition.  (I'm definitely
*not* accusing John of holding this latter misconception here.  It's just
that I had just thought of a pet peeve in the context of the previous
discussion.)  One sometimes hears it said that when ice melts at its
melting point the water molecules in the liquid acquire a greater kinetic
energy than they had in the solid.  Or when liquid water evaporates at
some fixed temperature on the liquid/vapor coexistence curve (say, the
boiling point, for convenience) one sometimes hears it said--even among
physics teachers (as well as students)--that the molecules of the vapor
have acquired a greater kinetic energy than they had when they were a
part of the liquid.  This is *not* the case.  For such 1st order phase
transformations (done isothermally) the latent heat of transformation
goes *entirely* into a combination of increased *potential* energy of the
particles and into maybe some external work on the system's environment
as the system expands (if it expands)--*not* into increased kinetic
energy.

In fact, when the phase transformation is not constrained to be
isothermal, such as when evaporative cooling (in temperature) takes
place, then the kinetic energy of the particles involved in the process
actually *decreases* as the transformation takes place upon the
absorption of the latent heat.  In this case the latent heat is the
difference between the (sum of any work done on the environment and an)
increase in potential energy and the decrease in kinetic energy.  If the
transformation takes place adiabatically then there is no net absorption
of latent heat from an external thermal reservoir at all, but rather,
the system's kinetic energy of its particles decreases by as much as
their potential energy increases (and any possible external work is done
on the environment) as the transformation proceeds.  This is typical for
an endothermic process driven by an internal increase in entropy (where
the higher entropy phase also has a higher potential energy).

David Bowman
David_Bowman@georgetowncollege.edu