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I am currently creating a 2D ideal gas simulator whereby the user can determine three of the four variables (P, V, n, T) and the gas would adjust accordingly.

I was wondering how I could calculate the pressure within this simulation. I was struggling with how to approach this problem considering how I am attempting to model a 3d scenario in 2d.

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  • $\begingroup$ I think how you would approach this is a bit dependent on the problem you want to translate into 2D. Do you have a specific geometry and density/temperature structure in the third dimension in mind? Because usually 2D-pressure is a quantity that is proportional to column density instead of volume density, garnered with numerical prefactors that come from integrating the density/temperature profile in the third direction. $\endgroup$ – AtmosphericPrisonEscape Jul 31 at 15:34
  • $\begingroup$ Well, I'm trying to make this relatively simple. I'm going to make the all of the particles equal mass, and temperature equal to the square of the particle speed... I hope this answers your question. $\endgroup$ – nomnom123 Aug 1 at 0:02
  • $\begingroup$ So do you have particles or a continuum? I'm confused. Pressure and temperature are only evolvable in a continuum theory. $\endgroup$ – AtmosphericPrisonEscape Aug 1 at 19:24
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since the gas is a 2D one, you most start using pA=Nm*(mean square velocity)/2

A=area (which is the 2D-volume, indicated in your question as V) N= # of molecules enclosed in A ( 2D- volume) hence n=N/A

then, the temperature can be estimated using pA=NkT where k is Boltzmann constant

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