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Homework Help: In terms of Einstein's theory of heat capacity

  1. Oct 26, 2004 #1
    A) What temperature will the energy per mole of a solid achieve one third its classical value of 3RT. Express in terms of einstein temperature
    Einstein Temperature [tex] T_{e} = \frac {h \nu}{k} [/tex]

    where h is plancks constant
    k = boltzmann's constant

    Not really sure on how to do this?

    Do i use this formula

    [tex] C_{v} = \frac{3 N_{a} h^2 \nu^2}{k T^2} \frac{e^\frac{h\nu}{kT}}{(e^\frac{h\nu}{kT} - 1)^2} [/tex]

    i know that the term hv / kT must be the exponent of e but i cant get it to work. but that is beside the point
    but how do i manipulate it to get what i need?

    Now onto the Blackbody radiation topic
    IIfyou have the wavelength and the temperature then which function would you use for finding the Total Radiancy?

    R = Sigma T^4 or the big formula 2pi h c^2 / lambda ^5 ( 1 / e^ hc / lambda k T)

    Which is the the Total radiancy function?
    Last edited: Oct 27, 2004
  2. jcsd
  3. Oct 27, 2004 #2


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    How about integrating C_v from 0 to T and setting it equal to 3RT? Then solve the resulting equation for T.

    To help with the integration use the transformation T = 1/u!
  4. Oct 27, 2004 #3

    James R

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    The total radiated intensity (power per unit area) of a black body is given by the Stefan-Boltzmann law:

    [tex]R = \sigma T^4[/tex].
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