# Deriving equations for pressure & number density for centrif

issacweirdo

## Homework Statement

Consider particles in a gas centrifuge. This device is used to separate gases of different molar mass by rotating a cylinder at high rates. Derive two equations: one for the pressure (P) and one for the particle number density (nv) as functions of M, r, w and T, where r is the radial distance from the center point and w is the angular frequency of the rotation. M and T are molar mass and temperature. Do this by applying Newton's 2^nd law to the circular motion of a segment of gas of mass delta(m) and width delta(r). Recall that centripetal acceleration is given by w^2 r and that the positive direction for r is radially outward from the center of the circle.

## Homework Equations

nv = n0 * e\^(m * r^2 * w^2 / (2 * k * T))
Net Fr = (m * v^2)/r

## The Attempt at a Solution

I have no clue what I'm supposed to do. I don't even know how I'm going to draw a FBD for this. I don't know what the pressure equation is supposed to look like, but I know the number density equation is supposed to look like this: nv = n0 * e\^(m * r^2 * w^2 / (2 * k * T)), where k is the boltzmann constant. I only know this because I was able to look online for this answer (though it did not explain how they derived this).

## Answers and Replies

issacweirdo
Er, I mean nv = n0 * e^(m * r^2 * w^2 / (2 * k * T)). This part may also be wrong, since I think it should be nv = n0 * e^(-m * r^2 * w^2 / (2 * k * T)) since it reminds me of the boltzmann factor.