Re: Dissipation & Latent heat

[John Denker <jsd@MONMOUTH.COM>]

At 04:46 PM 3/16/00 -0500, David Bowman wrote a very very nice note:

> It is in general *not* the case that when energy associated with
> macroscopic degrees of freedom ...
> is dissipated ... that energy becomes only internal
> *kinetic* energy.

Right.  Good point.

> 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.

Right.

>   The usual case has a comparable amount of
> internal energy in the form of kinetic energy [and] potential
> energy  ... Debye ... quasi-harmonic

Right again.

To generalize the idea...  One must decide what to say about the common and
important case of _radiative_ cooling.  Is photon energy kinetic or
potential or both or neither?

> ... Dulong-Petit ...

That's a subtle point.  An ideal gas would follow the right functional form
to agree with the D-P law, but it would be off by a factor of two.  I'd
never thought about that before.

> One sometimes hears it said that ... when liquid water evaporates ...
> 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.

> when evaporative cooling (in temperature) takes
> place, then the kinetic energy of the particles involved in the process
> actually *decreases*

Right.  Moisten your finger and blow on it.  You can feel the decrease in
kinetic energy.  Heat is not the same as temperature!

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

To continue the discussion:

People may be wondering what is the difference between the thermal
potential energy referred to above, and ordinary nonthermal energy.  For
instance, when the rail cars collide, the energy that departs the
macroscopic kinetic degrees of freedom could be transferred to
  a) thermal potential energy, such as the latent heat of melted ice in
the "draft gears", or
  b) nonthermal potential energy, such as winding a clockworks spring
somewhere in the mechanism.

Both of these occur at constant temperature, yet one is considered thermal
and the other nonthermal.  What's the difference?

Answer:  The the thermal potential energy is more random than the
nonthermal potential energy (just as thermal kinetic energy is more random
than nonthermal kinetic energy).

This is perhaps best visualized by considering a magnetic resonance
experiment.

1) Initially all the spins are in a low-temperature low-energy state, all
pointing down along the minus-Z axis.

2) Then we put in a pi/2 pulse, tipping all the spins into the XY plane
where they will precess.  This state has higher energy.  If we do it right,
at this point the state has _not_ increased its entropy, so this is
nonthermal potential energy.  All the energy is free energy.  We can get
all the energy back if we want, and use it to do useful work, with no
limits on the thermodynamic efficiency.

3) But if we wait*, the spins will _spread out_ in the XY plane.  That
increases the entropy, at constant energy.  The nonthermal energy becomes
thermal energy.  The free energy becomes less than the total
energy.  Thereafter, we cannot freely use the energy to do useful work.  We
can perhaps use some of it by connecting the spin system to a heat
engine.  The thermodynamic efficiency is limited, in ways that depend on
the temperature of the heat-sink on the other side of the heat engine.

(* Note this scenario involves waiting for a time long compared to T2 but
short compared to T1.)

=====

To apply this concept to latent heat:  isothermal melting or isothermal
evaporation involves transferring energy to the _thermal_ potential
energy.  We are not free to use this energy the way we would use the
potential energy in a spring.