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Calculating maximum amount of water vapor per unit volume

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Compute the maximum amount of water vapor per unit volume that air can hold at the surface, where Ts = 288 K, and at a height of 10 km where T = 220 K. Express your answers in kg m-3.

    2. Relevant equations

    [itex]e_{s}=Ae^{\beta T}[/itex]

    [itex]e=\rho _{v}R_{v}T[/itex]

    3. The attempt at a solution

    Since saturation occurs when e=[itex]e_{s}[/itex], I figured I would set the two equations equal to each other. However, solving for [itex]\rho _{v}[/itex] doesn't work... The units don't work out, and I get a really large number... I feel like I have to somehow relate this to the total pressure of the air, but I'm unsure how to go about this.
     
  2. jcsd
  3. Sep 19, 2011 #2
    I was incorrect in my previous post saying that the units didn't work out... Solving for [itex]{\rho _{v}}[/itex] when e=[itex]e_{s}[/itex] does produce an answer in [itex]\frac{kg}{m^{3}}[/itex].... However I'm getting 1,103,248.397 [itex]\frac{kg}{m^{3}}[/itex], for the first case where T=288 K, which is way off from what I should be getting (0.0126 [itex]\frac{kg}{m^{3}}[/itex]).

    I believe I then have to use the ideal gas equation, pV=nRT, plugging in p for e... But this is where the confusion comes in. Hopefully someone can help me with this tonight, since this HW is due tomorrow morning...
     
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