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I'm looking for a better relationship between the Kinetic energy of a gas and it's Temperature, and also how they vary with gravity (not altitude, just gravity!). So is there a model better than the Kinetic theory of gases that I can apply?

Thanks in advance!

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    $\begingroup$ I'm not sure that you are wanting when you say 'better relationship'; better than what? The Maxwell and Boltzmann distributions of velocities have been well verified by experiment. The effect of gravity between molecules is utterly minute and the effect of the earth's gravity is present as a constant force. You could re-derive the Maxwell/Boltzmann equations using, say, the van-der -Waals equation instead of using the ideal gas but I would expect the distributions to have the same shape but shifted in value this way or that depending on how the calculation pans out. $\endgroup$ – porphyrin Jun 20 '18 at 11:48
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The theory is for ideal gases, And accounts for macroscopic properties. The first assumptions that you have to eliminate to get a better result are

  1. Spherical assumption.
  2. Ideality assumption.

I suggest first you read through the concepts of Equations of state. Have a look at:

1.Van der Waals 2.Virial Equation of state 3.Tao Mason equation of state

Without you providing more information I can not see what do are you exactly looking for.

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