Solve Heat Current Problem at Junction of Copper, Brass & Steel Rods

[sdoug041]

Homework Statement

Rods of copper, brass, and steel are welded together to form a Y-shaped figure. The cross-sectional area of each rod is 2.00 cm^2. The free end of the copper rod is maintained at 100.0 degrees C, and the free ends of the brass and steel rods at 0.0 degrees C. Assume there is no heat loss from the surfaces of the rods. The lengths of the rods are: copper, 13.0 cm; brass, 18.0 cm; steel, 24.0 cm

What is the temperature at the junction?

Homework Equations

H = kA(T[hot]-T[cold]) / L

Where H is the heat current, k is the materials thermal conductivity, A is the cross-sectional area,
T[hot]-T[cold] / L is the temperature gradient. (change in temp divided by length).

The Attempt at a Solution

I can solve these types of questions with only 2 bars. What I would do is plug in the values for each material into the heat current formula , make them equal each other, then solve for T at the junction. This method won't work for 3 materials coming together. Please help! Thanks.[Edit] I'm sorry for posting this in the advanced physics thread it was supposed to be in introductory. If any mod sees this they can move it, thank you!

 

[Mapes]

Can you show where you're getting stuck? It looks like you're going to have four equations and four unknowns.