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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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 23 2006, 12:42 PM
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Junior Member Group: Members Posts: 57 Joined: 13-February 06 From: Brisbane, Australia Member No.: 679 |
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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