Bariometric formula in Statistical Physics (particle density per unit volume)

[xowlinx]

Hi there.

In my homework, I had to calculate the variation of the pressure with the altitude for a classical gas. I know that I should calculate the density of particles per volume element.

I found this pdf on the net (http://cannoli.mps.ohio-state.edu/phy847/phy847-p2.pdf) .
If you see the third page of the pdf, the author calculates the density by introducing a delta function of the form \delta(r_1-r).

My question is: Why the delta is written in this way?, I mean, why the delta chooses the particle number 1 while not choosing another one?.

I hope my english didn't stop me from explaining what I mean.


Camilo Jimenez

 

[physics girl phd]

Camilo -- Your link doesn't have a third page and doesn't seem to have this problem...

 

[OlderDan]

Camilo -- Your link doesn't have a third page and doesn't seem to have this problem...

Try this

http://cannoli.mps.ohio-state.edu/phy847/phy847-p2.pdf

 

[OlderDan]

Hi there.

In my homework, I had to calculate the variation of the pressure with the altitude for a classical gas. I know that I should calculate the density of particles per volume element.

I found this pdf on the net (http://cannoli.mps.ohio-state.edu/phy847/phy847-p2.pdf) .
If you see the third page of the pdf, the author calculates the density by introducing a delta function of the form \delta(r_1-r).

My question is: Why the delta is written in this way?, I mean, why the delta chooses the particle number 1 while not choosing another one?.

I hope my english didn't stop me from explaining what I mean.


Camilo Jimenez

Consider a cylinder of infinite height filled with an ideal gas at constant temperature. Assume constant gravity. The pressure at any height is equal to the weight of the gas above that height divided by the area A of the cylinder. The density of the gas varies with pressure. Look at the difference in pressure between the bottom an top of a small cylinder of volume A*dy.

 

[dextercioby]

You need to find the Boltzmann distribution in the classical canonical ensemble and from there on it's elementary to find the density & pressure wrt altitude.

Daniel.