What is the length of the aluminum rod?

Question

A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100°C, and that of the far end of the aluminum rod is held at 0°C. If the copper rod is 0.88 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50°C?

Answer 1

Thermal conductivity:
Copper:
9.2*10-2 (kcal/sec)/((m^2)(Cdegree/meter))
Aluminum:
4.9*10-2 (kcal/sec)/((m^2)(Cdegree/meter))

We need to assume the rods don't loose any heat to the surroundings. Therefore the kcals conducted through both rods is equal. To calculate the heat conducted per second by the copper, multiply its conductivity,

9.2*10-2 (kcal/sec)/((m^2)(Cdegree/meter)),
times (A*50Cdegree/.88 m).

Set that expression equal to aluminum's conductivity times A*50Cdegree/L. Simplify and solve for L.

Edit: I don't know why the conductivity lines are truncated. Maybe Yahoo is making sure it is compatible with any screen resolution. Anyway, the truncated lines, that I see, should end with
")(Cdegree/meter))".

Answer 2

This is a good example of a heat transfer problem.