1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the mass of earths troposphere

  1. Jul 21, 2010 #1
    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 kg


    I know that can't be right, but what did I do wrong?
     
  2. jcsd
  3. Jul 21, 2010 #2

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    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
     
  4. Jul 21, 2010 #3

    K^2

    User Avatar
    Science Advisor

    There is one more error. [itex]A = 4\pi R^2 \neq (4 \pi R)^2[/itex]
     
  5. Jul 21, 2010 #4
    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 ????
     
    Last edited: Jul 21, 2010
  6. Jul 21, 2010 #5

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    You have force = pressure/area^2 instead of pressure/area, I think you are getting cofused because pressure is N/m^2
     
  7. Jul 21, 2010 #6

    K^2

    User Avatar
    Science Advisor

    @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.
     
  8. Jul 21, 2010 #7
    Okay thank you. I understand now. I just wasn't thinking.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the mass of earths troposphere
  1. The mass of Earth. (Replies: 29)

Loading...