Proving a thermal conductivity/resistance formula.

[thatguythere]

Homework Statement

The figure below shows a block that consists of two materials with different thicknesses l 1 and l 2 and different thermal conductivities λ1 and λ2. The temperatures of the outer surfaces of the block are Thigh and Tlow, as shown in the figure. Each face of the block has a cross-sectional area A. Using the thermal resistance equation R = l/λ,show that the temperature Tx at the interface of the block is given by:
Tx = R1Thigh + R2Tlow/R1 + R2

Homework Equations

R=l/λ

The Attempt at a Solution

I'm not even sure where to begin. A nudge in the right direction would be greatly appreciated.

 

[haruspex]

You will need a separate equation for the heat flow through each block. (I assume you have an equation relating heat flow, temperature difference etc.) Invent unknowns as necessary. Some unknowns will be common to the two equations.

 

[Chestermiller]

Think about two electrical resistors in series between a voltage of Vhigh and Vlow. Get the voltage at the junction of the two resistors.