Temperature at a junction between two rods?

[scarlson1193]

Homework Statement

A girl needs a rod that will carry heat from a pan of boiling water to a mixture of ice and water so that the ice will melt more quickly. She has a copper rod of diameter D_Cu and an aluminum rod of diameter D_Al, neither of which is long enough to reach from the pan to the ice-water mixture.

The longest rod is the copper rod of length L_Cu. She cuts a length L_Al from the aluminum rod and welds it to the copper rod so that the total L will reach between the pan and ice-water mixture. After steady-state heat flow is achieved, she measures the temperature at the junction between two rods. What is that temperature?

Homework Equations

First Law of Thermodynamics, where the change in internal energy is equal to the heat added to the system plus the work done by the system.

As well as conduction,

The Attempt at a Solution

Well, we know that we are dealing with solid metals to transfer the heat, so we use conduction. We are looking for the temperature at the junction, and so far, my group could only figure out how to get the heat of the entire system, instead of the junction.

 

[rock.freak667]

At steady-state heat flow, the heat transfer in the Cu rod = heat transfer in Al rod. And the cold junction in one rod is the hot junction in another. So equate the two.