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Luke Carlson edited introduction.tex
about 11 years ago
Commit id: ea94b7a3bd07600b3da0d43e901d70b3871e22da
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To experimentally obtain a pressure through a simulation, it is necessary to determine exactly how particles affect the pressure of a system. Pressure is the amount of force over a specific area, also written as $Pressure=F/A$. Force can also be described as change in momentum over change in time: $F = \frac{\Delta p}{\Delta t}$. The change momentum of a single particle equals its mass multiplied by its change in velocity: ${\Delta p} = m\Delta v$.
Since there is more than one particle in a system, the entire change in momentum is the combined change in velocities of each particle that hits the specified area. Thus, the following formula can be used to determine total force:
\verb|$F {\bf $F = \frac{2m * \displaystyle\sum\limits_{0}^n v}{\Delta
t}$| t}$}
Where $n$ is the number of collisions and $v$ is the velocity of the particle hitting the wall. Since the change in velocity is double the initial velocity, the 2 can be placed outside the summation along with the mass.