Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Jun 5 2006, 12:15 PM
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#1
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Junior Member Group: Members Posts: 57 Joined: 13-February 06 From: Brisbane, Australia Member No.: 679 |
Hi All
This might seem like a really dumb question, but what's the mass of the Cytherean atmosphere per unit area? At first pass I thought it was easy - same as for an isothermal atmosphere, Po/g, where Po is surface pressure and g is surface gravity. Simple. Except Venus doesn't come close to approximating an isothermal atmosphere. From a graph in Mark Bullock's PhD thesis (Hi Mark if you're visiting) I pulled the figures for Po and To as 92 bar and 735 K, while the left-side of the temperature curve was 250 K at 0.1 bar and 63 km. At about 210 K the temperature drop with altitude stops, then slowly rises into the Cytherean stratosphere. Ok. My atmospheric physics is pretty limited - I 'modelled' that lapse rate pressure curve as a power law: P/Po = (T/To)^n and likewise for density, d/do = (T/To)^n. Temperature, T, as a function of altitude, Z, I computed as T(Z) = To*(1-Z/(n.Zo)). Zo = (k.T/m.g), where k is Boltzmann's constant and m is the molecular mass of the atmosphere. These equations I then integrated between 210 K and 0.033 bar, 70 km, and 735 K and 92 bar, zero altitude. The resulting equation is m = (n/(n+1))*(do.Zo)*(1 - (T/To))^(n+1) - a bit of simple algebra and the Gas equation shows that do.Zo = Po/g. Thus the mass is lower than for a simple isothermal atmosphere by roughly (n/(n+1)). In this case n = 6.33, higher than the dry adiabat for CO2 which gives n = 4.45. Now an adiabatic or polytropic atmosphere is an idealisation, but it seems odd to me that whenever Venus' atmospheric mass is discussed people always use the higher isothermal value. Have I missed something important in the physics, or is Venus's atmospheric mass just 86.4% of the usually quoted value? |
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Jun 12 2006, 11:23 AM
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#2
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Senior Member Group: Members Posts: 3516 Joined: 4-November 05 From: North Wales Member No.: 542 |
Fine. I agree the adiabatic model is probably a better approximation for the real Venus atmosphere than the isothermal (or quasi-isothermal with a ballistic 'cap'). I would therefore prefer your lower estimate of the mass to one calculated on the quasi-isothermal model. The only thing I don't quite understand is this quote from your post #3:- 'I still get the non-intuitive answer that a polytropic (adiabatic?) atmosphere with the same surface pressure masses less than an isothermal atmosphere.' To me this result is exactly what one WOULD expect intuitively. The atmosphere is cooler at the top, therefore closer to the surface and experiencing higher g, therefore less mass is required to account for the observed surface pressure.
My extended ramble into the isothermal model was just because I was intrigued by the infinite integral and its implications, especially the fact that the particulate nature of gases can be 'deduced' in this way, which I had not realised before. |
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Jun 12 2006, 08:56 PM
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#3
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Member Group: Members Posts: 624 Joined: 10-August 05 Member No.: 460 |
Fine. I agree the adiabatic model is probably a better approximation for the real Venus atmosphere than the isothermal (or quasi-isothermal with a ballistic 'cap'). I would therefore prefer your lower estimate of the mass to one calculated on the quasi-isothermal model. The only thing I don't quite understand is this quote from your post #3:- 'I still get the non-intuitive answer that a polytropic (adiabatic?) atmosphere with the same surface pressure masses less than an isothermal atmosphere.' To me this result is exactly what one WOULD expect intuitively. The atmosphere is cooler at the top, therefore closer to the surface and experiencing higher g, therefore less mass is required to account for the observed surface pressure. Confusing, but I find myself agreeing with Gaal. The fact that the temperature is decreasing with altitude means the upper atmosphere is more dense at that altitude than it would be under isothermal conditions, and each inversion in temperature would lead to more compacting of the molecules relative to isothermal conditions. At the altitude after which there are no further inversions, the expansion is the same as under the isothermal condition, except that there is a denser layer under the inversion than in the isothermal case. The only exception would be if the last inversion is very close to the surface, and the temperature increase after this inversion is much much greater than the gradient between the surface and the inversion. It is worth noting that in the current model of the Titan atmosphere, they use many inversion layers in order to support the density distribution found by Huygens - (Titan's atmosphere is very thick in general, relative to the earth's, but also has a more exaggerated vertical scale due to the lower mass of the moon.) We will know more about Titan after the limb and bistatic radar measurements are evaluated...The Cassini altimeter data should help, too. |
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