peaceharris said:
Do you agree with people who say that the thermosphere is very hot?
Dear Peaceharris,
Your have posed four questions:
1) Do I agree that the thermosphere is hot?
2) Would a jar of boiling water placed in the thermosphere freeze to ice?
3) Do I agree that particles in outer space have high velocity because
they are the ones on the tail of the Boltzmann distriubution that
lies aove the escape velocity?
4) Is it meaningless to ascribe a high temperature to particles having a
high velocity?
Oh dear, this post may be a bit long! As a preface to my answers, let me
recall that my reply to the original post about the units of temperature
was couched in the terminology of classical thermodynamics, in which the state
functions (e.g. energy, entropy, enthalpy, fugacity, free energy, etc.)
refer to systems
in equilibrium. Moreover, I avoided all mention of
statistical mechanics (which is just a mechanistic
interpretation of
classical thermodynamics) because it was not needed. To answer your questions,
one needs to consider the distribution functions that arise in statistical
mechanics, where temperature can be regarded as a parameter in a function
determining the distribution of some quantity (e.g velocity or energy or
quantum state etc) among a number of particles. An important remark here is
that if temperature is so regared, then it is nonsense to ascribe a
temperature to any particular particle; i.e. we must always bear this in
mind. So now to my answers.
1) The thermosphere is
not in thermodynamic equilibrium (and never
will be in my lifetime!), so to speak of a temperature in the usual
sense is meaningless. So what do people mean by hot (2000 C in this
case)? According to the text in the web-site, "temperature is a measure
of how fast particles move" (This is of course not a very good definition.
It is like saying that money is a measure of the value of cheese.), so
they must be using the velocity distribution of the particles to define
a temperature, i.e. they are asking "What temperature would a Boltzmann
distribution have to have in order to
fit the
observed
distribution of velocities?" The answer is apparently T=2000 C. I
can agree with this kind of parlance but one must realize that this
is not
the temperature. If a system is not in equilibrium, there can
be as many temperatures as
there are quantities for which a distribution can be determined, and
all of these can be different! Even
negative temperatures can
be observed by playing this game! (I can give you an example in
another post if you are interested.) At equilibrium, all of these
temperatures would be equal.
2) Are you so sure that boiling water would freeze in the thermosphere?
I have no idea, not being an atmospheric physicist but consider this:
You are on your way to a wedding at 10:00 am dressed in your best
black suit. An alien specimen collector snaps you up, puts you in
a big closed jar of air and places you in the thermosphere directly
above the spot upon which you were walking. Will you freeze? I think
not---you will probably be fried in the sunshine. And if instead, you
were plucked from the street on returning from the wedding at 11 pm? Then
I think you would freeze in the dark shadow of the earth. Maybe this
latter situation was your point: the "hot" particles would not prevent
your freezing. True, but not because they are not hot but because there
simply aren't enough of them---they would have to compete with the
rate at which the boiling water is losing energy owing to radiative
cooling (infra-red radiation).
3) Suppose you are in the thermosphere and you measure the velocity
of those molecules leaving the Earth that reach you. Yes, you would
find some molecules with high velocity but you would find many many
more with low velocity, namely those that do
not have
escape velocity but which are fast enough to have reached your
position (remember that gravity is a
very long range force).
(In order to have reached you, they had to overcome the gravitational
force and have therefore a smaller velocity than when they started
their journey)
If you play the fitting game with your observed distribution, you
might find a "temperature" which was not too different from the
original temperature of the molecules nearer the earth. Note that
many of the molecules reaching you would have
zero velocity.
But there is an even more important consideration: are there any
other processes that could produce fast particles? I can think of
one at least. The web-site mentioned that the oxygen and nitrogen
molecules were good at converting "heat" into velocity. How
do they do this? One way would be for a molecule to absorb radiation
from the sun and thus go from its ground state into a highly
excited electronic state. If the latter were not stable with respect
to
molecular dissociation, the two atoms (e.g two N atoms from
nitrogen) would then fly apart with a high velocity. I don't know if
such a process is important in the thermosphere but it is certainly
well-known in the laboratory and would merit your investigation before
you place too much faith in your escape velocity theory.
4) I agree with you. It is meaningless to talk of the temperature of a
particle (in the context of our discussion here).
