Venus Atmosphere Puzzle, one man's struggle with atmospheric physics Options

[qraal]

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?

[ngunn]

Very interesting, and I follow the reasoning you give but I still find the result surprising.

Consider the following thought experiment:
1/ Take one large solid globe, in vacuo.
2/ Release in it's vicinity finite amount of gas.
3/ Wait for the gas to form an atmosphere around the globe.
4/ Arrange for the atmosphere to be at a uniform temperature throughout.

Question: At what point does the mass of this finite amount of gas jump to infinity?