# What is this equation?

## Main Question or Discussion Point

p(h) = (p0e)-(mgh/kT)

where p0 is the atmosphere at sea level, m is the mass of an object at height h, g is the gravitational proportionality constant...

is there a specific name for this equation? is this derived from the Boltzmann’s distribution law? Also, I'm really confused about what e is... Thank you!

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e is Euler's number, about 2.7. Search wiki for it.

It's the pressure at a height, h at a temperature T. k is Boltzmann's constant.

Also g is not the same thing as G. G is the gravitational proportionality constant, g is the acceleration due to gravity.

Ken G
Gold Member
Also,the p_o should not be inside the parentheses. Only the e is being raised to that power. It is not a Boltzmann factor, that would be statistical physics. This is a solution to a force equation, the hydrostatic equilibrium that looks like dp/dh = -rho * g, where rho = mp/kT from the ideal gas law and p is gas pressure.

SteamKing
Staff Emeritus
Homework Helper
It's the Law of Atmospheres:
http://www.cmmp.ucl.ac.uk/~als/teaching/1B28/Lecture notes/Lecture_8.pdf

See p. 4 of the attachment.

It predicts the number of gas molecules at a given height h, and consequently the pressure at that height in terms of the surface pressure Po.

N.B.: k is indeed Boltzmann's constant.

D H
Staff Emeritus