# Given atmospheric composition, density and scale height, planetary radius, and escape velocity, what is the lapse rate?

My planet

Mass = 0.602 MEarth

Density = 5.04 g/cm3

vesc = 9.3 km/s

Temperature = 272 K

My atmosphere

74.84% N2

22.04% O2

1.38% CH4

1.25% Ar

0.27% H2O

0.11% CO2

Molecular mass = 28.88

Rspecific = 287.90

Density at sea level = 1.18 kg/m3

Pressure at sea level = 0.91 atm

Scale height = 10013.78 m

Trying to find cp values, will edit them in if I find them.

This is all to determine if my atmosphere is realistically gonna be retained, and eventually to find the altitude of my tropopause.

• 12.04% O2 and 1.38% CH4 is not stable over geological scale. You would need some active processes to keep these numbers that way, otherwise it'll bee CO2 and H2O relatively soon. – Mołot Feb 22 '18 at 15:15
• What processes might you suggest? I'm very new to this and I don't know where to start! – Rúnatál Davino Feb 22 '18 at 15:27
• Most of the time such things are kept stable by biology, volcanic activity etc. Anything that can use energy to "under burn". – Mołot Feb 22 '18 at 15:35
• Perhaps I’ve misunderstood, but that much water & pressure at 5C 278K) is a liquid. Liquids don’t have a lapse rate as such. – Bob Jacobsen Feb 22 '18 at 16:30
• Aa! thought I edited this. – Rúnatál Davino Feb 23 '18 at 13:29

There are two lapse rates: dry and moist.

Dry is pretty simple. If we also assume equilibrium, then the lapse rate is just g/c_p in metric units.

If there’s a gas with high enough concentration that it condenses at some point, I.e. water forms clouds, then it’s much more complicated. The latent heat release results in several different possible outcomes, and you’ll have to work it through.

Sticking with “dry”, now you need to know Cp for your mix. Getting that exactly right is complicated, but we can approximate by looking at how far your mix of monatomic, diatomic and complex gases you have. Monatomic and complex gas additions move Cp in opposite directions, so will mostly cancel, and you’ve mostly got diatomic N2 and O2 just like air. So I suspect you’ll come out near air’s value of about 1.

Combine that with g and you’re done.