# Relationship between pressure and thermal conductivity

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1. Feb 21, 2016

### jhartc90

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

lambda = q / grad (t)

Then

lambda = q / grad(P) V / nR

2. Feb 21, 2016

### Staff: Mentor

There is a derivation of this in Transport Phenomena by Bird, Stewart, and Lightfoot.

3. Feb 21, 2016

### jhartc90

what page in the book is the derivation of this on? All I see is a figure (Fig. 9.2-1)