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Relationship between pressure and thermal conductivity

  1. Feb 21, 2016 #1
    1. The problem statement, all variables and given/known data
    I would like to derive an equation that relates the thermal conductivity to the pressure using the kinetic theory of gases. However, I assumed that thermal conductivity was independent of pressure.

    2. Relevant equations
    I know that P = 2N/3V (1/2mv^2)

    Also:

    I believe that thermal conductivity is dependent on the temperature gradient in a material.

    I know the flow of heat is proprotional to the temp. gradient.

    So:

    q = lambda * (grad T)


    3. The attempt at a solution
    I cannot attempt this until I understand how the two are related. I know that the thermal conductivity can be related to the temperature gradient. I guess temperature is dependent on pressure. But I am fairly lost in how to relate the two.

    Could I used the ideal gas law?

    PV=nRT

    grad(P)V = nR grad(T)

    so grad(T) = grad(P) V / nR

    q = lambda * grad(T)

    lambda = q / grad (t)

    Then

    lambda = q / grad(P) V / nR
     
  2. jcsd
  3. Feb 21, 2016 #2
    There is a derivation of this in Transport Phenomena by Bird, Stewart, and Lightfoot.
     
  4. Feb 21, 2016 #3
    what page in the book is the derivation of this on? All I see is a figure (Fig. 9.2-1)
     
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