A typical conduction problem involves creating a sandwich of two (or more layers) and determining the temperature at the interface(s) between the layers. Consider a two-layer problem where one layer has twice the thickness and six times the thermal conductivity as the other layer, but the layers have the same area. To find the temperature at the interface between the layers (after thermal equilibrium has been reached) you should:

1. find that the unknown temperature is halfway between the temperature on one side and the temperature on the other side (T = 12° C in this case) (0/107) (0%)
2. set up a ratio where the change in temperature across a layer is proportional to the thickness of the layer (T = 8° C in this case) (30/107) (28%)
3. set up a ratio where the change in temperature across a layer is inversely proportional to the thickness of the layer (T = 16° C in this case) (22/107) (21%)
4. set the rate of heat flow through one layer equal to the rate of heat flow through the other layer (T = 18° C in this case) (55/107) (51%)

Answer 4 is correct. If the layers had different rates of heat flow the temperature would be changing, and that is inconsistent with the fact that we're at equilibrium. Setting the heat flow rates equal:

6 k A

T1 - T 2 L

= k A

T - T2 L

Cancelling all the common factors, and plugging in T₁ = 24° C and T₂ = 0° C gives:

3 * (24 - T) = T

72° C = 4T

T = 18° C