2
$\begingroup$

We know that the density of water is 1000 $kg/m^3$ and that of air is 1.225 $kg/m^3$. If I were to calculate the pressure of air at a square at sea level of area 1 $m^2$ in newtons, I'd need the height of that column of air, which means that I'd need the height of the atmosphere in that square.

Taking the value we know as 101325 Pascals at the surface, we get the weight of the air column as 10332.27 kg, or an air column of height 8434.51 meters or 8.5 km.

I know from prior knowledge that the atmosphere is actually much thicker than that - almost 300 km thick. Am I doing something wrong?

$\endgroup$
4
  • 5
    $\begingroup$ The density of air in the atmosphere is not constant. $\endgroup$
    – ACuriousMind
    Jan 28, 2016 at 16:52
  • $\begingroup$ Density as a function of height $Y$, $\rho(Y)$, depends on weight of the column above $Y$ and the temperature at $Y$. The temperature is not constant but is generally a linear function of negative slope in the troposphere. The weight of the column depends on $\rho(Y)$ integrated. Have fun! $\endgroup$
    – Bill N
    Jan 28, 2016 at 17:01
  • 1
    $\begingroup$ For what it's worth, I think your question was fine. I don't understand why it was closed as off-topic. $\endgroup$
    – avl_sweden
    Jan 10, 2018 at 21:07
  • $\begingroup$ It seems to be a common trend of SE now, I find these questions because I'm going through the same doubts and many of them have been labeled as off-topic $\endgroup$
    – Jon
    Apr 16, 2021 at 6:27

1 Answer 1

3
$\begingroup$

Air density decreases as height increases. It is typically much lower than $1,225$kg.m$^{-3}$ at a height of a few tenths of km.

$\endgroup$
2
  • $\begingroup$ What is the height of the atmosphere then? $\endgroup$
    – cst1992
    Jan 28, 2016 at 17:12
  • $\begingroup$ There's no "height of the atmosphere" precisely defined, because air density slowly decreases with altitude, it does not brutally becomes zero. Check this graph for evolution of pressure with height : en.wikipedia.org/wiki/Atmospheric_pressure#/media/… $\endgroup$
    – Dimitri
    Jan 28, 2016 at 17:30

Not the answer you're looking for? Browse other questions tagged or ask your own question.