|MadSci Network: Earth Sciences|
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, email@example.com 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 Radius (1 bar level) (km) 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). 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