Ideal Gas Law in Two Dimensions

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SUMMARY

The discussion focuses on modeling a two-dimensional ideal gas and determining the initial velocity of particles to achieve a Maxwell-Boltzmann velocity distribution. It is established that assigning initial velocities randomly may not suffice, as elastic collisions between particles with the same mass will lead to velocity swapping. The participants conclude that the total velocity before and after collisions remains constant, emphasizing the need for a more nuanced approach to initial velocity assignment to accurately simulate the desired distribution.

PREREQUISITES
  • Understanding of the Ideal Gas Law and its implications in two dimensions.
  • Familiarity with the Maxwell-Boltzmann distribution and its significance in statistical mechanics.
  • Knowledge of elastic collisions and their effects on particle velocity in physics simulations.
  • Basic skills in programming simulations, particularly in a physics engine or computational modeling environment.
NEXT STEPS
  • Research methods for generating random velocity distributions that conform to the Maxwell-Boltzmann curve.
  • Explore the principles of elastic collisions in two-dimensional systems and their mathematical representations.
  • Investigate simulation tools or libraries that facilitate modeling of gas dynamics, such as Python's Pygame or MATLAB.
  • Study advanced statistical mechanics concepts to enhance understanding of particle interactions in gas simulations.
USEFUL FOR

Physics students, computational modelers, and researchers interested in simulating gas dynamics and understanding statistical mechanics principles.

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TL;DR
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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