Ideal Gas Law in Two Dimensions

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In creating a two-dimensional model of an ideal gas, determining initial velocity is crucial for achieving a velocity distribution that aligns with the Maxwell-Boltzmann curve. Assigning initial velocities randomly may not suffice, as elastic collisions could lead to particles merely swapping velocities, especially if they share the same speed. The conservation of momentum implies that while individual velocities change, the overall velocity distribution might not evolve toward the desired Maxwell-Boltzmann shape without appropriate initial conditions. Thus, careful consideration of how initial velocities are assigned is essential for simulating realistic gas behavior.
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Can a maxwell-boltzmann curve be recreated in a 2d model of an ideal gas?
I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity.
Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign initial velocities randomly?
I'm not sure it will, as the collisions are elastic and I kept the mass of the particle the same — wouldn't the velocities simply swap?
 
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Only if they are the same speed. The change in velocity of each particle will be the same, and the total velocity after the impact will be the same as the total velocity before the impact.
 

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