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Ideal gas law problem : part 3

  1. Jan 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Assuming that the temperature of the atmosphere is independent of height, solve the barometric equation to obtain the pressure as a function of height: P(z)=P(0)exp(-mgz/kT)
    Show that the density obeys a similar equation.
    2. Relevant equations

    3. The attempt at a solution

    First part it is

    dP/P=-mgdz/kT ==>P=P(0)exp(-mgz/kT)

    rho=m/V, V=nkT/P => rho= m*P/nkT

    From the first part of this problem , rho=m*(P(0)exp(-mgz/kT))/nkT. now I can diffentiate rho with respect to z?
  2. jcsd
  3. Jan 16, 2009 #2
    The ideal gas law says:


    Where M is the molar mass. Hence p and rho are proportional.

    Now try to express rho with p ;)
  4. Jan 18, 2009 #3
    I thought the ideal gas law says that :

    nkT=PV or PV=nRT==> PV/n=RT

    It just makes sense to me now to differentiate P with respect to z. rho=m*(P(0)exp(-mgz/kT))/nkT, P being P(0)exp(-mgz/kT).
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