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What is the pressure?

  1. Jan 5, 2016 #1
    1. The problem statement, all variables and given/known data

    At an altitude of 11,000 m, the air temperature is -56.5 °C and the air desity is 0.364 kg / m3. What is the pressure of the atmosphere at that altitude?

    2. Relevant equations

    no equations found

    3. The attempt at a solution

    Ok. The problem gives the air density and using the expression ρ = p M / R T we can easily find the pressure. But suppose I want to find it by using the expression dp / dy = -ρ g, with ρ = p M / R T. In this case I would need to integrate both dy and dT. Am I right? And how could I do this? I've tried working on one attempt but it did'nt work. Maybe the reason is that I did'nt know the molar mass of the air in that altitude? (sorry my bad english). My work is shown below.

    dp / dy = -ρ g
    ρ = p M / R dT

    dp = - (dy p M g / R dT)

    - ∫dy M g = R ∫dT (∫dp / P)

    Ln P1 / P0 = - (Δy M g) / ΔT

    Finally,

    P1 = P0 e - (Δy M g / R ΔT)
     
  2. jcsd
  3. Jan 5, 2016 #2

    SteamKing

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    Homework Helper

    You might want to compare your model of the earth's atmosphere with this one:

    https://en.wikipedia.org/wiki/Barometric_formula
     
  4. Jan 5, 2016 #3
    Oh thanks. It was useful to me.
     
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