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Kinetic Theory of Gases & Escape Speed

  1. Oct 4, 2008 #1
    1. The problem statement, all variables and given/known data
    In the first 2 parts of the problem, I calculated at what temperatures the rms speeds vrms of H2 molecules and O2 molecules would equal the escape speed of Earth (11200 m/s). The answers I calculated for this were 10000 K for H2 and 160000 K for O2. Those answers are correct according to the back of the textbook.

    The last part of the question states: Considering the answers to parts (a) and (b), should there be much hydrogen and oxygen high in the Earth's upper atmosphere, where the temperature is about 1000 K?


    Attempt at a solution
    According to the back of the textbook, the answer is no for H2 and yes for O2.

    My thought process was the answer is yes for both because the temperature of 1000 K high in the Earth's upper atmosphere is small relative to both the temperatures I calculated (10000 K for hydrogen and 160000 K for oxygen). Thus the temperatures of either gas molecules will not reach a high enough temperature to have a large fraction of the molecules of either gas reach the escape speed of Earth.

    How is the answer no for hydrogen? What am I missing here?
     
  2. jcsd
  3. Oct 4, 2008 #2
    I'm not sure how high up in the atmosphere 1000 K would correspond to, but the escape speed taken in respect to that elevation should be less than when taken at the surface of Earth.

    Just a side question...the atmosphere would be 1000 K for when it is facing the sun, right (that seems a bit high otherwise)?
     
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