At 10:27 AM 12/11/00 -0700, Jim Green asked:
>
> Does an iceberg and, if melted, the water
from this iceberg weigh the same?
That's an interesting question. It is open to multiple interpretations,
depending on what assumptions one brings to the problem.
1) If we have an iceberg in the weightless environment of a space station,
it is weightless before melting and weightless afterward. So in this case
there is no change in weight.
2) The narrow wording of "ice" and "melting" is important.
2a) I will assume (for now) that melting was intended to refer to adding
energy to the substance at constant temperature and constant
pressure. This will increase the mass attributed to the substance.
In this narrow case it must do so; otherwise there would be violations of
the idea that re-arranging the contents of a black box cannot move the
centroid of the black box. See Misner/Thorn/Wheeler _Gravitation_ page
161; I can't immediately lay my hands on a more elementary discussion of
this important idea.
2b) If one slightly generalizes the question to cover evaporation of water
(rather than melting of ice) one could get the exact opposite answer.
Water has a finite vapor pressure at any nonzero temperature. If we allow
a glob of water to vaporize adiabatically, doing work against a flimsy
piston, the water will end up with less total energy.
============================
One should be very careful about taking the foregoing results out of their
narrow contexts.
Take-home messages include:
-- If somebody asks you for "the electron mass" you should assume they
are asking for an invariant quantity. Call it the "rest mass" if you don't
mind the pleonasm.
-- This (rest) mass is not the only contribution to what we call
"inertia". Neither is it the only source term for the gravitational field.
-- It is tempting to lump things together as "MassEnergy" but that
doesn't quite do it. It turns out that some types of energy are positive
source terms, while others are negative source terms for the gravitational
field.
-- For a single particle or rigid body, you can usually sort out what is
mass and what is energy, but for a relativistic fluid or solid, it may not
be worth the trouble to sort out which is which.
-- If we have a closed railroad car, anything that transfers mass and/or
energy from one end of the car will cause the car to recoil in such a way
that its centroid is unaffected by the transfer.