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Temperature of nitrogen

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data

    1.5 is a typical walking speed.
    At what temperature would nitrogen molecules have an rms speed of 1.5 ?


    2. Relevant equations

    V=(3*K_b*T/m)^.5
    V is the rms speed
    K_b is Boltzmann's constant
    T is temp in kelvin
    m is mass


    3. The attempt at a solution

    I am going to make the foolish assumption that when they mean mass, they mean the mass of one nitrogen molecule. So the mass of a proton and a neutron is 1.67E-27kg and the mass of an electron is 9.11E-31kg. One nitrogen atom has 7 protons, 7 neutrons and 7 electrons and multiply that by two because of the second nitrogen atom. So ((1.67E-27)(14)+(7)(9.11E-32))(2)=4.677E-26 kg.

    Now I rearrange my equation to solve for T and plug in.

    mV^2/(3*K_b)=T

    (4.677E-26)(1.5)^2/(3*K_b) = .0025 kelvin

    Am I close?

    Thanks!
     
  2. jcsd
  3. May 3, 2010 #2
    Never mind. My answer is correct.
     
  4. May 3, 2010 #3

    Redbelly98

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    Science Advisor
    Homework Helper

    Good job. For future reference, it may be easier and quicker to look up the mass of nitrogen or other elements in a periodic table.
     
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