# What is the variation of atmospheric pressure at large heights?

In an approximation (though not a very accurate one), temperature can be assumed constant throughout the atmosphere. The Earth's gravitational field can also be assumed constant (a better assumption).

For these approximations, what is the calculated pressure at the top of Mt. Everest ($8848\ \mathrm m$), given that the pressure at the top of Mont Blanc ($4807\ \mathrm m$) is $4.32\times10^4\ \mathrm{Pa}$?

$T = 0.0\ \mathrm{^\circ C}$

$\rm g = 9.81\ \mathrm{m\ s^{-2}}$

$\ce{O2}$: $M = 32\ \mathrm{g/mol}$, percentage composition of atmosphere = $21\ \%$

$\ce{N2}$: $M = 28\ \mathrm{g/mol}$, percentage composition of atmosphere = $79\ \%$

I thought about using $pV=n\mathbb{R}T$ for this question – perhaps using the difference in the volume of air above the different heights, but I couldn't come to an answer.

• Over that small change in altitude just assume that pressure is linear with altitude, use the gas law, then look up the answer on line to see how close you were ;) Jan 13 '17 at 22:27
• @airhuff We use MathJax to format mathematical expressions and equations. I have looked through your suggested edits and noticed that you use HTML for this. While your effort is much appreciated, most of it won't last long since it will be changed by other users. If you want to know more, please have a look here and here. We prefer to not use MathJax in the title field, see here for details. Jan 14 '17 at 12:13
• @Martin-マーチン, very helpful. Since it worked, I thought the markup must be the same. Big wrong there! My apologies for all those edits and appreciation for the guidance. Jan 15 '17 at 10:19

From the given composition of the atmosphere you can calculate the mean molecular mass $M$ of air.
$$p(h_1) = p(h_0)~\mathrm{e}^{- \frac{M g}{R T} \Delta h}$$