What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 x 10^6 m, and 10^5 N/m^2 = 1 ATM

I know the answer is 5*10^18 kg but how do I get that?

Question

What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 x 10^6 m, and 10^5 N/m^2 = 1 ATM

I know the answer is 5*10^18 kg but how do I get that?

anonymous · Answer

$$\frac{ 4\pi(6.4*10^6)^2*??? }{ 9.81 }$$

I got this far but what is the exact number that goes in the question marks?

mrnood · Answer

The pressure of the atmosphere at surface level is a result of the weight of the air above a given area.

The pressure "1 ATM" is the 'normal' surface pressure on th eearth (although it is an antiquated and almost obsolete unit). You are told that the pressure is 10^5 N/m^2

Your formula is correct - the 4pi r^2 gives oyu the area of the earth in m^2

So to calculate the total force you multiply area by the pressure  (So the ??? in your formula is the pressure in N/m^2)

That gives you the force in N - so oyu need to divide by g to give you the mass (as you have done (g=9.81 m/s^2))