- #1
jhartc90
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Homework Statement
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.
Homework 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)
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