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I have a programme built in python and rust, procedurally generating stars, planets, etc.

I have come to a point where I have to work on atmospheric characteristics, hopefully managing to get a pseudo-realistic outcome in terms of:

  • composition/constituents in terms of substance
  • surface pressure
  • equilibrium temperature
  • surface temperature
  • total mass of atmosphere
  • etc

Where pressure and temperature determine the states of the atmosphere constituents.

For example, I have just generated an atmosphere composed on the following approximate percentages:

  • Methane 51%
  • Ammonia 38%
  • Nitrogen (N2) 4%
  • Water 4%
  • and negligible traces of other gases

And with the following characteristics outcome:

  • equilibrium temperature: 152 K
  • surface temperature: 200 K
  • surface pressure: 21497.75 Pa, 0.21 atm

For a terrestrial planet ~0.55 the radius of earth and ~0.23 the mass of earth. Bond albedo is assumed to be 0.3.

Now to try and determine the state of the constituents, (solid/liquid/gas) I try and use Clausius-Clapeyron equation, shuffled around a bit so I can find the fusion and vaporisation points of each constituent under the given pressure and temperature:

Tf2 = 1 / (1/T1 - R . ln(P2/P1) / ΔHfus)

and

T2v = 1 / (1/T1 - R . ln(P2/P1) / ΔHvap)

where:

  • T1 is the fusion/vaporisation temperature at pressure P1 = 101325 Pa for the given substance
  • P2 is the "simulated" surface pressure for the planet
  • T2f: is the fusion point for the substance given the "environment"
  • T2v: is the vaporisation point for the substance given the "environment"

In the example above, this results (for water) as the following:

  • T2f = 172.18K
  • T2v = 333.55K

which means water will be liquid at the surface of this planet.

And while I am not looking for absolutely correct numbers (speed is more important than absolute correctness), I once in a while get the numbers for the following other example planet:

  • planet radius: 1.82 earth
  • planet mass: 4.14 earth (so some kind of super earth)
  • T2 = 350 K
  • P2 = 12538738.28 Pa, 123.75 atm
  • T1 = 273.0 K / 373 K
  • P1 = 101325 Pa
  • Water heat of fusion: 6010.0 J/mol (at 273 K)
  • Water heat of vaporisation: 40657.0 J/mol (at 373 K)

and then these values

  • water melts at -333.02 K (yes! negative Kelvin)
  • water boils at 589.75 K (probably more realistic given the huge pressure!)

Obviously, getting negative K is far beyond the level of "pseudo" in "pseudorealistic".

So my question is; what am I forgetting and handling badly? Critical temperature? Critical pressure? Both? Variable heat of fusion and heat of vaporisation?

I have read that

Note that the enthalpies of fusion and vaporization change with temperature.

I am thinking to take that into account, assuming it would be the right thing to do? But is it?

Edit: I am not a physicist/chemist by trade or training... just a coder with a side project :-)

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Feb 23 at 13:45
  • $\begingroup$ Your planet is not a super earth, it's a gas giant. A rough estimate is that surface gravity given your size and mass is 12G. Surface gravity of Jupiter is 2.528 G $\endgroup$
    – HSharp
    Commented Feb 23 at 14:19
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    $\begingroup$ If you haven't already, keep in mind that atmospheric composition is not really a free variable. It depends heavily on the mass/gravity of the planet and the temperature and proximity of its sun. See worldbuilding.stackexchange.com/questions/201667/… $\endgroup$
    – Qami
    Commented Feb 23 at 14:57
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    $\begingroup$ @HSharp: en.wikipedia.org/wiki/Super-Earth $\endgroup$
    – Hal
    Commented Feb 23 at 14:57
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    $\begingroup$ @Qami: yes the ppms take escape velocity and RMS into account although again, not perfectly, as a ratio of 6.0 is assumed to hold on to considered substance "forever". $\endgroup$
    – Hal
    Commented Feb 23 at 14:58

1 Answer 1

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I think you balanced your equation wrong, try this:

Tf₂ = 1 / ((1/T₁) - (ln(P₁/P₂) / (-ΔHfus / R)))

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  • $\begingroup$ Thanks, will try this. the negative on ΔH is (I think!) when we start from the "P2 over P1" version of the equation. I started from the "P1 over P2" version, which switches the ΔH to positive: ln(P1/P2) = ΔH/R * (1/T2 - 1/T1) unless that version is wrong? $\endgroup$
    – Hal
    Commented Feb 23 at 21:28

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