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Kinetic Energy of atoms

  1. Jul 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Write an expression E for the average kinetic energy of Helium atoms using the Boltzmann constant.

    2. Relevant equations
    PV = nRT

    PV = [itex]\frac{1}{3}[/itex]mN[itex]\overline{c^2}[/itex]

    k = [itex]\frac{R}{N_A}[/itex]

    [P - Pressure ; V - Volume ; m - Mass of an atom ; N - Number of atoms ; others have their general meanings.]

    3. The attempt at a solution
    My problem is they're asking for an expression for the average kinetic energy of Helium atoms. It's plural. I can build an expression for the kinetic energy of a single atom.

    nRT = [itex]\frac{1}{3}[/itex]mN[itex]\bar{c^2}[/itex]

    [itex]\frac{3}{2}[/itex]nRT = [itex]\frac{1}{2}[/itex]mnNA[itex]\overline{c^2}[/itex]

    [itex]\frac{3}{2}[/itex]RT = [itex]\frac{1}{2}[/itex]mNA[itex]\overline{c^2}[/itex]

    [itex]\frac{3}{2}[/itex]kT = [itex]\frac{1}{2}[/itex]m[itex]\overline{c^2}[/itex] = E (Kinetic Energy of an atom)

    Rest of the question is easy if this is the expression they're asking.
    Do I have to take mN as the total mass of the gas and calculate it from there taking R as kNA? That way it's making the sum a bit difficult because they haven't defined the constant NA in the question, giving out a hint that it's not involving in this, may be.
     
  2. jcsd
  3. Jul 27, 2013 #2

    ehild

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    Homework Helper
    Gold Member

    The average kinetic energy of an atom is the sum of the KE of the individual atoms divided by the number of the atoms KEav=ƩKEi/N

    You certainly know the Equipartition Principle. The average energy of a particle in an ideal gas is (f/2)kT where f is the degrees of freedom. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html. A He atom can only translate, its kinetic energy is translational energy with three degrees of freedom. Your final formula is the answer to the problem: The average kinetic energy of the He atoms (of a He atom in the He gas) is 3/2 kT, expressed with the Boltzmann constant k.

    ehild
     
  4. Jul 27, 2013 #3
    Thanks for the help and the link! :D
     
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