Re: Density of hydrogen on Jupiter

On 4 Feb, 21:36, tadchem <tadc...@xxxxxxxxxxx> wrote:

Does the word "adiabatic" mean anything to you? There is a
gravitational gradient present. Kinetic energy will vary with
gravitational potential, regardless of temperature, because the fluid
is free to move.

I repeat: we are assuming a state of *equilibrium* , i.e. a (quasi)
steady state. Nothing is macroscopically moving or otherwise changing.
For a collisional gas and in the absence of any heat sources or sinks,
this also logically implies that the temperature is constant
throughout the volume, which in turn implies a 1/r^2 density
dependence as pointed out.

In gas clouds there are spatial variations in
temperature. Planets and stars are condensed phases where the
compressibility never follows the gas laws.


As you can easily show over the virial theorem (which says that the
average kinetic energy is -1/2 times the average gravitational
potential energy), the average kinetic temperature of a gas mass
corresponding to the sun is about 10^7 K, and for Jupiter still 10^5
K.

I'm glad you recognize that fact. Can you recognize that the
gravitational potential energy is not the same throughout the mass?
Do you realize that as individual molecules of the fluid fall or climb
in the gravity well, their kinetic energy (and therefore temperature)
will change?

As indicated above, in a state of a quasi-static equilibrium there are
no net energy changes anywhere in the volume, and hence the latter is
isothermal in the absence of any heat sources or sinks (particle
collisions will level out any initial temperature differences). And
the only heat sink here is the 'surface' of the mass as defined by the
point where the density gets small enough so that individual atoms can
exist, which enables inelastic collisions and thus a 'radiative
cooling'. This is why the 'surface' is cooler than the interior of the
gas ball (I have explained this in more detail on my page
http://www.plasmaphysics.org.uk/research/sun.htm for the case of the
sun).

When thermal energies exceed ionization energies, a plasma is
present, regardless of the density.

Yes, I agree, and this is exactly why an increase of pressure can only
turn a gas/plasma into a fluid below a certain temperature.

In the *real* world, sufficient pressure will compress even a plasma
into a metallic(!) state, describable as hydrogen ions embedded in a
Fermi "sea" of free electrons.

I would grant you that point if you could show me some experimental
data proving that hydrogen can be turned into a fluid at 10^5 K or
above. Otherwise, I would consider this claim just part of an
*imaginary* world.


The only circumstance that could change something about the 1/r^2
behaviour in my view is when the density becomes so high that the
atomic nuclei would be pushed into each other. But this would require
densities about 10^15 times higher than near the surface, i.e.
assuming a 1/r^2 density behaviour, this should occur at a fraction
3*10^-8 of the radius (about 20 m for the sun and 2 m for Jupiter),
and I would not want to speculate what the physical state of matter so
close to the center is.

Thomas
.

Relevant Pages

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