1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

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).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook