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Venus Atmosphere Puzzle, one man's struggle with atmospheric physics
qraal
post Jun 5 2006, 12:15 PM
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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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qraal
post Jun 23 2006, 12:42 PM
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Hi All

Well I decided to do a numerical experiment on a model Venus atmosphere and sum up 100 metre high blocks of atmosphere, computing Cp, p, rho, T, m, and energy with each step. I looked up the behaviour of CO2's heat capacity, Cp, over the temperature range I was interested in and discovered it varied dramatically - from 0.735 KJ/kg.K at 200 K to 1.148 KJ/kg.K at 750 K. Quite unlike the behaviour of air for which Cp is constant over the terrestrial temperature range. I could fit the behaviour of Cp with temperature well enough with a quadratic over the range 275 K - 750 K, and a linear fit between 275-200 K.

I baulked at an analytical solution, so I chucked the equations of state into an Excel spread-sheet and summed it up, from 735 K and 92 bar to 0.17 bar at 198 K. What I found was the mass is exactly Po/g, which was quite a "surprise" considering my first doubts. The total atmospheric heat energy is 0.706 teraJoules, which would radiate away to space in about 138 years at a constant 231 K effective temperature - if you could shade Venus. Of course at 304 K the lower reaches would start condensing as liquid, adding extra latent heat.

My final task is to work out the average temperature.

Adam
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The Messenger
post Jun 23 2006, 04:44 PM
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[quote name='qraal' date='Jun 23 2006, 06:42 AM' post='59569']
Hi All

Well I decided to do a numerical experiment on a model Venus atmosphere and sum up 100 metre high blocks of atmosphere, computing Cp, p, rho, T, m, and energy with each step. I looked up the behaviour of CO2's heat capacity, Cp, over the temperature range I was interested in and discovered it varied dramatically - from 0.735 KJ/kg.K at 200 K to 1.148 KJ/kg.K at 750 K.
[/quote]
That is good news - now we know that as the average Earth temperature increases, the additional CO2 will act as a heat sink and the glaciers will come back unsure.gif

Seriously, this was good analytical work, eliminating a gross inconsistency and demonstrating that there is almost order in the universe...

[/quote]
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Posts in this topic
- qraal   Venus Atmosphere Puzzle   Jun 5 2006, 12:15 PM
- - remcook   QUOTE do.Zo = Po/g This is the equation for hydro...   Jun 5 2006, 02:15 PM
|- - qraal   Hi rem That's exactly what I did and I still ...   Jun 5 2006, 11:45 PM
|- - The Messenger   QUOTE (qraal @ Jun 5 2006, 05:45 PM) That...   Jun 9 2006, 01:57 PM
- - ngunn   In an atmosphere in which temperature decreases ra...   Jun 6 2006, 11:37 AM
|- - qraal   Hi ngunn Thanks for the reply. You know I wondere...   Jun 7 2006, 12:14 PM
- - ngunn   Well you've done the detailed calculations, no...   Jun 7 2006, 12:46 PM
|- - qraal   Hi ngunn I've read it before, but replicated ...   Jun 9 2006, 12:43 PM
- - Phil Stooke   There's some great Venus atmosphere stuff (and...   Jun 7 2006, 01:50 PM
|- - DonPMitchell   QUOTE (Phil Stooke @ Jun 7 2006, 06:50 AM...   Jun 7 2006, 08:33 PM
- - ngunn   Very interesting, and I follow the reasoning you g...   Jun 9 2006, 12:57 PM
- - ngunn   Hi graal. I think that the messenger's messag...   Jun 10 2006, 10:39 AM
|- - qraal   Hi Nigel Ok. Let's try again. Everything you...   Jun 10 2006, 12:34 PM
- - ngunn   Fine. I agree the adiabatic model is probably a b...   Jun 12 2006, 11:23 AM
|- - The Messenger   QUOTE (ngunn @ Jun 12 2006, 05:23 AM) Fin...   Jun 12 2006, 08:56 PM
- - ngunn   Hi Messenger. You found my post confusing??!...   Jun 14 2006, 09:04 AM
- - remcook   just a note: Titan's temperature does vary sig...   Jun 14 2006, 11:36 AM
- - qraal   Hi All Well I decided to do a numerical experimen...   Jun 23 2006, 12:42 PM
|- - The Messenger   [quote name='qraal' date='Jun 23 2006,...   Jun 23 2006, 04:44 PM
- - qraal   Hi again And the average temperature is 630 K. H...   Jun 23 2006, 01:11 PM
|- - ngunn   QUOTE (qraal @ Jun 23 2006, 02:11 PM) Hmm...   Jun 23 2006, 01:51 PM
- - qraal   Hi Messenger & ngunn Hey thanks for the nice ...   Jun 25 2006, 12:50 AM
- - RNeuhaus   Venus' Double Vortex Confirmed in New Animatio...   Jun 27 2006, 10:21 PM
|- - DonPMitchell   At last, some pictures from VEX. These are fascin...   Jun 28 2006, 01:33 AM
||- - qraal   Thanks Don Man that's so bizarre. Venus is a...   Jun 28 2006, 10:21 AM
||- - qraal   Hi All Updated the gravity - now it's a linea...   Jun 30 2006, 02:11 PM
|- - JRehling   QUOTE (RNeuhaus @ Jun 27 2006, 03:21 PM) ...   Jul 3 2006, 10:02 PM
- - edstrick   The soviet venus descent probes measured light lev...   Jul 1 2006, 07:43 AM
- - qraal   Hi ed Thanks for the heads up on that reference, ...   Jul 1 2006, 12:38 PM
- - edstrick   The Univ of Arizona has had a method of producing ...   Jul 2 2006, 08:41 AM
- - DonPMitchell   The U of Arizona books are essential. There are a...   Jul 2 2006, 05:56 PM
|- - qraal   Hi Don Hey thanks for the insights - Venus is tru...   Jul 2 2006, 11:47 PM
|- - rlorenz   QUOTE (DonPMitchell @ Jul 2 2006, 01:56 P...   Jul 13 2007, 12:08 PM
- - DonPMitchell   That is a mystery. Many believe there are no crys...   Jul 3 2006, 01:01 AM
|- - qraal   Hi Don The exobiological theory is the most excit...   Jul 3 2006, 08:52 AM
- - edstrick   The Pioneer Large Probe Cloud Particle Size Spectr...   Jul 3 2006, 09:18 AM
- - DonPMitchell   Vega-1 and Vega-2 performed similar experiments. ...   Jul 3 2006, 04:16 PM
|- - qraal   Thanks Don & Ed More data to cram into my bra...   Jul 4 2006, 01:16 AM
- - DonPMitchell   Planetary circulation is fascinating. Rotating pa...   Jul 4 2006, 01:26 AM
|- - Bob Shaw   QUOTE (DonPMitchell @ Jul 4 2006, 02:26 A...   Jul 4 2006, 02:31 PM
- - MichaelT   QUOTE (qraal @ Jun 5 2006, 12:15 PM) Hi A...   Jul 4 2006, 09:25 AM
|- - ngunn   QUOTE (MichaelT @ Jul 4 2006, 10:25 AM) I...   Jul 4 2006, 03:51 PM
|- - MichaelT   QUOTE (ngunn @ Jul 4 2006, 03:51 PM) meas...   Jul 4 2006, 04:40 PM
|- - The Messenger   QUOTE (MichaelT @ Jul 4 2006, 10:40 AM) O...   Jul 4 2006, 07:22 PM
- - edstrick   I'd forgotten the instruments on the Vega prob...   Jul 4 2006, 10:17 AM
- - ngunn   Which is what I still don't understand (or bel...   Jul 5 2006, 09:19 AM
|- - qraal   Hi ngunn For the first 200 km of altitude Venus...   Jul 5 2006, 11:18 AM
- - ngunn   Ah! qraal with a Q - my apologies. It's th...   Jul 5 2006, 01:08 PM
- - qraal   Hi ngunn & MichaelT As you might've guess...   Jul 5 2006, 10:32 PM
|- - MichaelT   QUOTE (qraal @ Jul 5 2006, 10:32 PM) If s...   Jul 6 2006, 06:27 PM
|- - qraal   Hi Michael There's quite a lot of literature,...   Jul 10 2006, 07:56 AM
- - DonPMitchell   You're looking at Mark Bullock's thesis I ...   Jul 5 2006, 10:49 PM
- - ljk4-1   Venus Atmosphere Profile from a Maximum Entropy Pr...   Sep 26 2006, 02:36 PM
|- - rlorenz   QUOTE (ljk4-1 @ Sep 26 2006, 10:36 A...   Jul 13 2007, 12:16 PM
- - qraal   Hi All I haven't bothered with this for some ...   Jul 12 2007, 11:05 PM
- - edstrick   "....Sadly, it isnt cheap..." I'd sa...   Jul 14 2007, 06:03 AM


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