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

• xowlinx
In summary, the conversation discusses the calculation of pressure variation with altitude for a classical gas and the use of a delta function to determine density. The question arises as to why the delta function chooses a specific particle. The conversation also mentions finding the Boltzmann distribution in the classical canonical ensemble to determine pressure and density with altitude.
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

Last edited by a moderator:
Camilo -- Your link doesn't have a third page and doesn't seem to have this problem...

xowlinx said:
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.

Last edited by a moderator:
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.

## 1. What is the barometric formula in Statistical Physics?

The barometric formula in Statistical Physics is a mathematical equation that describes the relationship between the particle density per unit volume and the pressure of a gas. It is often used to model the behavior of gases in various physical systems.

## 2. How is the barometric formula derived?

The barometric formula is derived using statistical mechanics, which uses statistical methods to describe the behavior of a large number of particles. It takes into account the interactions between particles and the effects of temperature and pressure on the system.

## 3. What factors does the barometric formula take into account?

The barometric formula takes into account the number of particles in a given volume, the temperature of the system, and the pressure exerted by the particles on the walls of the container. It also considers the intermolecular forces between particles.

## 4. What is the significance of the barometric formula in physics?

The barometric formula is important in understanding the behavior of gases in various physical systems, such as in the Earth's atmosphere. It also has applications in other fields, such as meteorology, where it is used to predict changes in atmospheric pressure.

## 5. Can the barometric formula be applied to all gases?

The barometric formula is based on certain assumptions, such as the particles being in thermal equilibrium and the gas behaving ideally. Therefore, it is most accurate for gases that follow these assumptions, such as low-pressure gases. However, it can still provide useful approximations for other gases.

Replies
7
Views
6K
Replies
1
Views
1K
Replies
1
Views
1K
• Atomic and Condensed Matter
Replies
3
Views
2K
Replies
4
Views
2K
Replies
1
Views
1K
• Classical Physics
Replies
16
Views
1K
Replies
1
Views
1K
• Thermodynamics
Replies
15
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
1K