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Relation between energy annd pressure

  1. Jan 22, 2015 #1
    Me and and my friend were having discussion about the motion of molecules of gas.We talked about their velocity ,kinetic energy and much more. He asked me to derive a relation between pressure and energy. I was unable to explain him that... Can anyone explain the relation?
     
  2. jcsd
  3. Jan 22, 2015 #2

    Bystander

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    How would you begin? What information do you have?
     
  4. Jan 22, 2015 #3
    P=density*Vx*2

    T= 2/3k 1/2mv*2
     
  5. Jan 22, 2015 #4

    BvU

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    You could read up on the gas law, e.g. here
    Your equations feature in there, but one appears molecular to me and the other macroscopic:

    ##{1\over 2} mv^2 = {3\over 2} kT## average kinetic energy for a molecule.

    ##P = \rho v_x^2 = {mass\over V} v_x^2 ## may be ok if in the right context.

    I can wrangle a bit with formulas: $$ {1\over 2} mv^2 = {3\over 2} kT\ \Rightarrow\ {1\over 2} mv_x^2 = {1\over 2} kT$$ (the energy is equally distributed over the three degrees of freedom),

    ##\displaystyle \ \Rightarrow\ v_x^2 = {kT\over m} ##

    mass = number of molecules * mass of a molecule = number of moles * ##N_A## * mass of a molecule (Avogadro number); write mass = ##n\; N_A\; m##

    Leaves

    ##pV = n\;N_A\;m \ {kT\over m} = n\; N_A \;kT##;

    then use

    ##R_G = N_A \; k## (gas constant) to get the ideal gas law

    ##pV = nR_GT##.

    pressure times volume has the dimension of energy.

    It's not the whole story, but quite a big part of it.
     
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