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Homework Help: Density of high altitude air

  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Treat the atmosphere as an ideal gas with a uniform temperature of 200 K. Find the density at 20 km.

    R= 260 N*m/(kg*k)
    g= 3.92 m/s^2
    rho(0)= 0.015 kg/m^3

    2. Relevant equations
    dp/dz= -rho*g

    3. The attempt at a solution
    I found the pressure at ground level using P=rho*R*T

    P=(0.015 kg/m^3) (260 N*m/(Kg K)) (200 K) = 780 N/m^2

    I'm not sure how to proceed from here.
    Last edited by a moderator: Feb 10, 2015
  2. jcsd
  3. Feb 10, 2015 #2
    That equation for the density looks like it's off by a factor of 100.

    As far as what to do next, take the equation for p and substitute it into the equation for dp/dz.

  4. Feb 10, 2015 #3

    Quantum Defect

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    Use the equations under 2 to write dp/dz in terms of P and T. Integrate to get a solution for P as a function of height.
  5. Feb 10, 2015 #4


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    Although the acceleration due to gravity g varies with altitude, it is not clear where you obtained a value of g = 3.92 m/s2 for an altitude of 20 km.

    You should check this figure before proceeding with your calculations.
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