Re: Density of hydrogen on Jupiter

On 5 Feb, 21:58, tadchem <tadc...@xxxxxxxxxxx> wrote:
On Feb 5, 1:24 pm, Thomas <thomas.s...@xxxxxxxxx> wrote:

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.

YOU are "assuming" a state of equilibrium; a condition never mentioned
in the OP.
Unless you want to consider some kind of doomsday scenario, the
assumption of an equilibrium is a reasonable one to make for the Sun
or Jupiter.


YOU are "assuming" an ideal gas; a composition never mentioned in the
OP.
As mentioned already, at a temperatures of 10^5 K or above, the
assumption of an ideal gas should be reasonable.

One must use an equation of state for a real gas. The amount of
hydrogen involved IS sufficient to generate pressures that will
compress hydrogen to a liquid and then to a metal, so it is an error
to assume it is all gas.

Again, at temperatures of 10^5 K and above I can't see hydrogen
becoming a fluid (whatever the density). So it should be OK to just
use the fundamental equations of classical mechanics here (rather than
thermodynamics).

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).
"No net energy changes within the volume" is a specification for an
adiabatic system. As pressure P varies (with depth) the available
energy (called enthalpy) H of a volume V of the hydrogen will vary

dH = V*dP

Requiring the energy to be in equilibrium is NOT the same as requiring
a uniform temperature.
'Temperature' represents the energy of one particle, not that of a
volume. And in the absence of any localized heat sources and sinks
that must be the same throughout a gas volume in equilibrium (two sub-
volumes with an initial different temperature would eventually acquire
the same temperature by means of heat transfer).

The data for the mass and radius of the Sun and Jupiter are in fact
consistent with an isothermal interior and the associated 1/^r^2
density decrease for an ideal gas (see further below).


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.

Done:
"Electrical resistivities were measured for liquid H2 and D2 shock
compressed to pressures of 93-180 GPa (0.93-1.8 Mbar). Calculated
densities and temperatures were in the range 0.28-0.36 mol/cm3 and
2200-4400 K. Resistivity decreases almost 4 orders of magnitude from
93 to 140 GPa and is essentially constant at a value typical of a
liquid metal from 140 to 180 GPa. The data are interpreted in terms of
a continuous transition from a semiconducting to metallic diatomic
fluid at 140 GPa and 3000 K."http://prola.aps.org/abstract/PRL/v76/i11/p1860_1

But this was only at 2200-4400 K, not at 10^5 K.

But this would require
densities about 10^15 times higher than near the surface,

Check your math. What density are you assigning for the "surface"?

The surface density is the maximum density that allows individual
atoms (and thus inelastic collisions) to exist, so it is the density
where the average distance between the particles is equal to twice the
atomic radius, which works out to about n=2.4*10^23 cm^-3. As shown on
my page http://www.plasmaphysics.org.uk/research/sun.htm (Eqs.(5)-
(9)), this is consistent with the radius and mass of the sun (for a
homogeneous density distribution at the same surface density, the
sun's mass would only be 1/3 of what it is). And the same can be said
for Jupiter as well. So essentially, the figures for the mass and
radius of the Sun and Jupiter confirm the 1/r^2 density distribution
(or something close to it).

The experimental data shows that
under lesser pressures hydrogen becomes a metallic liquid.
Not at a temperatute of 10^5K or above.

This also
accounts for the giant (earth's x 20,000) magnetic field ofJupiter.

This figure is actually for the magnetic dipole moment (the magnetic
field itself is just a factor 10-20 larger at the surface).
But you would indeed expect a big difference, because Jupiter has a
much larger mass than earth (318x), a much larger radius (11x) and
it rotates much faster (2.4x). The exact mechanism that produces the
magnetic field is not well known yet, but if you assume that for some
reason the dipole moment is proportional to the overall centrifugal
force, then you arrive indeed at a figure 318*2.4^2*11 =20000. So
there could be ways to explain this without involving metallic
hydrogen. Also, note that sun spots have magnetic field strengths of
up to 1000 times the earth's, and you hardly want to explain these
through metallic hydrogen. What is simply needed for a magnetic field
in general is a current, and you should always get a current if you
have a rotating plasma, as the electrons and protons have different
masses and thus will respond differently to the centrifugal force, and
there will thus be a very slight differential rotation of the positive
and negative charges, i.e. a current and thus a magnetic field.


Thomas



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