Question

Imagine a square column of the atmosphere, 1 m1 \mathrm{~m} on a side, that extends all the way to the top of the atmosphere. How much does this column of air weigh in newtons?

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If we take height of the troposphere to be h=15000h =15 000 m, and the air density ρ=1.225\rho = 1.225 kg/m3^3, then its weight is equal to:

G=mg,m=ρVG=ρVg=1.22515000119.81=180259NG=180kN.\begin{align*} G &= mg, \qquad m = \rho V \\ G &= \rho V g \\ &= 1.225 \cdot 15000 \cdot 1 \cdot 1 \cdot 9.81 \\ &= 180259 \, \text{N} \\ G&= 180 \, \text{kN.} \end{align*}

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