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Perfect gasses temperature vs kinetic energy per molecule

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data
    I have been wondering about temperature and it's relation to kinetic energy I didn't study thermodynamics so I hope that replies could be simplified.I am trying to think about the perfect gas law to relate kinetic energy per molecule to temperature, and I want to know if I have a somewhat close understanding.


    2. Relevant equations
    PV=RnT


    3. The attempt at a solution
    PV=RnT
    I am thinking that P*V expresses the energy stored in the gas molecules since P =F/A and V=m^3 so P*V=F*m which is the unit of work so W=RnT
    and since the work expresses the change of kinetic energy
    deltaK= RnT
    (delta K)/n = RT
    so this gives me the intuition that since the change of kinetic energy per molecule is equal to a constant times the temperature so its proportional to it. I didn't study thermodynamics and only basics of physical chemistry so probably there are things I missed but is my intuition at least correct?
     
  2. jcsd
  3. Jul 15, 2010 #2

    lightgrav

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    Your intuition (or subconsciously-remembered info) is in the right direction
    ... but the PV is related to the Work that can be done on the Area (2-d),
    not the entire molecule KE , which comes from motion in all 3 dimensions.
    So, the KE per molecule (an average, of course) is actually 3/2 * PV/n .
    ... this is translational KE of the molecule's center-of-mass, not including
    rotational KE and vibrational KE of the atoms relative to that c.o.m.

    It is more traditional to write KE = 3/2 N kT , with N being the number of molecules,
    and k is Boltzmann's konstant = 1.38E-23 J/K , which is R/N_avagadro .
    The "3" signifies that there are 3 modes of motion which contribute to this KE ; every mode (including means rotations and vibrations also, if they occur) in a molecule holds E(average) = 1/2 kT .
     
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