Finding the mass of earths troposphere

[zeromodz]

I was wondering if I could find the mass of all the air in the local 9.8 g range. This is what I came up with.

P = F / A^2
Ma = PA^2
M = PA^2 / a
M = P(4πR^2)^2 / a
M = P(16π^2R^4) / a
M = (101325)(16π^2(6400000^4)) / (9.8)
M = 2.74e37 kgI know that can't be right, but what did I do wrong?

 

[mgb_phys]

Surface area of Earth = 500 Million km^2 = 500E12m^2
Air pressure, 101kPa = 10tons/m^2
Total mass = 10E3kg/m^2 * 500E12m^2 = 500E15 kg

hint, you have A^2, but area is already m^2

 

[K^2]

There is one more error. $A = 4\pi R^2 \neq (4 \pi R)^2$

 

[zeromodz]

Surface area of Earth = 500 Million km^2 = 500E12m^2
Air pressure, 101kPa = 10tons/m^2
Total mass = 10E3kg/m^2 * 500E12m^2 = 500E15 kg

hint, you have A^2, but area is already m^2

Wait, I thought that the units were irrelevant from the formula.

Then why don't we say that?

P = F / L^2, instead of A^2 or LWH = V^3 ?

 

[mgb_phys]

Wait, I thought that the units were irrelevant from the formula.

You have force = pressure/area^2 instead of pressure/area, I think you are getting cofused because pressure is N/m^2

 

[K^2]

@aeromodz
He did. When he converted from Pa to tons, he effectively divided by g. It is no technically correct to have the equal sign in that step.

And F = P*A, not P*A^2. That's what mgb_phys means by A already being m^2.

Finally, you never, ever ignore units. Do computations WITH the units, to make sure your answer is correct.

For example, if I follow your computations keeping units in place, I end up with final answer being in units of kg*m^2 instead of just kg, and that tells me there was a mistake.

 

[zeromodz]

@aeromodz
He did. When he converted from Pa to tons, he effectively divided by g. It is no technically correct to have the equal sign in that step.

And F = P*A, not P*A^2. That's what mgb_phys means by A already being m^2.

Finally, you never, ever ignore units. Do computations WITH the units, to make sure your answer is correct.

For example, if I follow your computations keeping units in place, I end up with final answer being in units of kg*m^2 instead of just kg, and that tells me there was a mistake.

Okay thank you. I understand now. I just wasn't thinking.