### Re: How is Jupiter's core 30,000 degrees Celsius.How do I calculate that myself

Date: Fri Dec 21 09:53:08 2007
Posted By: David and John Free, Post-doc/Fellow, MFA, MFA
Area of science: Earth Sciences
ID: 1192205229.Es
Message:
```
Hello Gabriel

The calculations published, see refs (1) to (7), give estimated
temperatures in the range 10,000 to 30,000 K. So you are well in line
with this!

Two perhaps useful approaches are these:

1.	When we compress a gas it gets hot
2.	Jupiter was made from “solar material” 4 billion years ago and
its current rate of cooling is known, ref (16). A similar estimate
for “age of the Earth” can be found in ref (13). They got it all wrong as
they did not allow for radioactive heating within the Earth.
A third approach is, as in ref (8), to think that SOME thermonuclear
fusion processes are taking place within Jupiter’s core, despite them
being rare “spontaneous” events unable to sustain continuous fusion
temperatures.

So maybe, if you want 30,000 degrees you should start with the compressed
gas idea 1. above. You will find no need to think of ways to maker it
hotter!

If we compress a perfect gas the temperature rise can be calculated from
T1/T2 = (Density1/Density2) raised to power alpha

This comes from the gas laws PV=RT and, for adiabatic compression
PV^gamma = constant. Henhce T2/T1 = Density ratio power (gamma - 1)

We know Jupiter’s gas is 95% H2 at the radius where its pressure is one
Earth’s atmosphere.   Here (see NASA data below) the temperature T1 is
165 K, (although ref (10) says 1360).
So you would be happy if  T1/T2 equalled 1/200, for 200 times 165 is
33,000.

For diatomic H2 (alpha = 3/2) this would require compression to a
density  of only 0.45 grams/ml and we know that densities higher than
that exist within Jupiter. For dividing Jupiter’s mass by its volume
(taken at one atmosphere pressure radius) we get a MEAN density of 1.3
grams/millilitre. According to ref (14) this density, 1.3 is that of
metallic hydrogen. That the mean density of Jupiter is that of metallic
hydrogen is no coincidence. It simply means that a major part of Jupiter
is metallic hydrogen. Its properties (as far as known) are well described
in David Ceperley’s page ref (15).

As the density increases (atoms closer together) the electron-states of
the atoms begin to overlap (coupled oscillators) and the allowed states
of hydrogen become continuous conduction bands. It becomes a metal.
Attempts to further compress it gives rise to “exclusion principle
repulsion forces” as the electrons (not allowed to share states) are
forced into higher energies.
The electrons are free to move as in a metal (metallic hydrogen) and this
is a very hot metal that readily conducts any heat generated deep within
it! The transition (gradual-with-depth change from 1.08 to 1.3 g/ml)
takes place at around 2.5 million atmospheres pressure, ref (14). Once
all is in the metallic state the material is extremely stiff but the
pressures very high! So the work done PdV is a huge number times a tiny
one, neither of which are known but can only make it hotter!

If you’d like the temperature profile with depth within Jupiter you could
build a model that solves the equation

-dP/dR = D(R)G(R)

This says the increase of pressure as we descend 1 meter into Jupiter is
Jupiter’s gravity at radius R times its gas density at radius R
G(R) is proportional to the mass within R and decreases as the square of
R, so we can calculate it from known conditions – see below -  at
Jupiter’s surface (taken as where the gas pressure is one Earth
atmosphere). All we need to do is guess several “reasonable” density
profiles D(R). (They MUST contain ALL Jupiter’s mass within a radius of
71,492  Km, and you will find all these reasonable profiles can (by means
of the compressed gas gets hot or other ideas) can be made to give 30,000
degrees.

Good luck with your continued researches

John

NASA Data on Jupiter from Dr. David R. Williams,
dave.williams@gsfc.nasa.gov
NSSDC, Mail Code 690.1 NASA Goddard Space Flight Center Greenbelt, MD
20771

Bulk parameters
Jupiter      Earth   Ratio
(Jupiter/Earth)
Mass (1024 kg)                      1,898.6     5.9736      317.83
Volume (1010 km3)                 143,128     108.321      1321.33
Equatorial                     71,492       6,378.1      11.209
Polar                          66,854       6,356.8      10.517
Volumetric mean radius (km)        69,911       6,371.0      10.973
Ellipticity                         0.06487     0.00335      19.36
Mean density (kg/m3)                1,326       5,515         0.240
Gravity (eq., 1 bar) (m/s2)        24.79        9.80          2.530
Acceleration (eq., 1 bar) (m/s2)   23.12        9.78          2.364
Escape velocity (km/s)             59.5        11.19          5.32
GM (x 106 km3/s2)                 126.686       0.3986      317.8
Solar irradiance (W/m2)            50.50     1367.6           0.037
Black-body temperature (K)        110.0       254.3           0.433
________________________________________
Jovian Atmosphere
Surface Pressure: >>1000 bars
Temperature at 1 bar: 165 K (-108 C)
Temperature at 0.1 bar: 112 K (-161 C)
Density at 1 bar: 0.16 kg/m3
Wind speeds
Up to 150 m/s (<30 degrees latitude)
Up to  40 m/s (>30 degrees latitude)
Scale height: 27 km
Mean molecular weight: 2.22 g/mole
Atmospheric composition (by volume, uncertainty in parentheses)
Major:       Molecular hydrogen (H2) - 89.8% (2.0%); Helium (He) -
10.2% (2.0%)
Minor (ppm): Methane (CH4) - 3000 (1000); Ammonia (NH3) - 260 (40);
Hydrogen Deuteride (HD) - 28 (10); Ethane (C2H6) - 5.8 (1.5);

References:

(1)     The Interior of Jupiter
Most of the interior of Jupiter is liquid (primarily hydrogen and about
10% helium). The central temperatures are thought to lie in the 13000-
35000 degree ...
csep10.phys.utk.edu/astr161/lect/jupiter/interior.html - 4k - Cached -
Similar pages

(2)      Jupiter
The Interior of Jupiter This picture illustrates the internal structure
of Jupiter. The outer layer is primarily composed of molecular
hydrogen. ...
www.solarviews.com/eng/jupiter.htm - 39k - Cached - Similar pages

(3)     Jupiter
Our knowledge of the interior of Jupiter (and the other gas planets) is
highly indirect and likely to remain so for some time. (The data from
Galileo's ...
www.nineplanets.org/jupiter.html - 29k - Cached - Similar pages

(4)     Jupiter Interior Overview
Jupiter's interior composition is primarily that of simple molecules such
as hydrogen and helium, which are liquids under the high pressure
environments ...
Cached - Similar pages

(5)     Chapter 3 - The Interior of Jupiter
Models of Jupiter's interior that are described in the chapter can be
going HERE.
lasp.colorado.edu/JUPITER/CH3/Ch3.html - 2k - Cached - Similar pages

(6)     Jupiter :: The interior -- Britannica Online Encyclopedia
Britannica online encyclopedia article on Jupiter, The interior: The
atmosphere of Jupiter constitutes only a very small fraction of the
planet, ...
www.britannica.com/eb/article-54264/Jupiter - 77k - Cached - Similar pages

(7)     Nov 13: Jupiter II
Jupiter's interior consists mostly of hydrogen and helium. These elements
are gaseous at the top of Jupiter's atmosphere down to several thousand
kilometers ...
zebu.uoregon.edu/disted/ph121/js19.html - 6k - Cached - Similar pages

(8)      D-D Fusion in the Interior of Jupiter?, Title Page
Recent measurements of sound velocities in Jupiter show substantial
disagreement with the existing models for the Jovian interior. ...
www.journals.uchicago.edu/cgi-bin/resolve?1998ApJ...501..367OCHK -
Similar pages

(9)      Jupiter
At the temperature and pressure of Jupiter's interior hydrogen is a
liquid, ... This interior heat probably causes convection deep within
Jupiter's liquid ...
seds.lpl.arizona.edu/nineplanets/nineplanets/jupiter.html - 28k - Cached -
Similar pages

(10)     Effective temperature - Wikipedia, the free encyclopedia
The effective temperature for Jupiter is 112 K and 51 Pegasi b
(Bellerophon) ... but the black body temperature is 1359 K. The internal
heat within Jupiter ...
en.wikipedia.org/wiki/Effective_temperature - 21k - Cached - Similar pages

(11)     Heat Sources within the Giant Planets
File Format: Microsoft Word - View as HTML
Smaller giants (0.15MJupiter) begin separation in less than a billion
years, and reach the equilibrium temperature within 7Gyrs. Conversely,
only after this ...
www.cs.berkeley.edu/~samw/projects/ay249/z_heat_sources/Paper_small.doc -
Similar pages

(12)     Space Exploring The Heavens: Encyclopedia: Jupiter
(Similar to the Sun but at a far lower temperature). At the temperature
and pressure of ... causes convection deep within Jupiter's liquid layers
and is probably ...
library.thinkquest.org/10701/encyclopedia-jupiter.html - 57k - Cached -
Similar pages

(13)     Carslaw and Jaeger        The Conduction of Heat      Oxford
University Press

(14)    Handbook Of Chemistry and Physics      CRC Press  59th edition
page B-28

(15)   Making A Metal Out Of Hydrogen
One of these other personalities, which is being investigated by NCSA
physicist and Alliance Executive Committee member David Ceperley, is
metallic hydrogen ...
access.ncsa.uiuc.edu/Stories/MetalHydrogen/Hydrogen.html - 16k - Cached -
Similar pages

(16)   Jupiter: Sun. Jupiter
In spite of this, Jupiter still radiates more heat than it receives from
the ... [24] This additional heat radiation is generated by the Kelvin-
Helmholtz ...
www.lycos.com/info/jupiter--sun-jupiter.html - 15k - Cached - Similar
pages

```

Current Queue | Current Queue for Earth Sciences | Earth Sciences archives