Thermodynamics Cubes of Metal Problem

[mneox]

Homework Statement

Three cubes of equal lengths, lead, iron, and copper are arranged between heat boxes at 100C and 0C. The heat current between boxes is 155W.

1) What is the side length of the cube?
2) What is the temperature between the lead and iron cubes?

Some k values are also given for the materials.

I know that we have to use H = [kA (T2-T1)] / L and the teacher partially explained it but moved along too fast for me to catch.

Homework Equations

H = [kA (T2-T1)] / L

The Attempt at a Solution

I realize that since it's a cube, A = L^2.

So therefore:

H = k L (100 - T1) = k L (T1 - T2) = k L (T2 - 0)

And then I get stuck because I want to find L, but my temperatures are still unknown. Isn't there some way to find the length without the temperature? Thank you for any help!

 

[rl.bhat]

$$H = \frac{kA(T_2 - T_1)}{L}$$

In the given problem, it becomes

$$H = \frac{k_{eff}.L^2(T_2 - T_1)}{3L}$$

$$H = \frac{k_{eff}.L(T_2 - T_1)}{3}$$...(1)

If A1 = A2 = A3 = A and L1 = L2 = L3 = L

$$\frac{3}{k_{eff}} = \frac{1}{k_1} + \frac{1}{k_2} + \frac{1}{k_3}$$

Find keff, and substitute in equation 1 and solve for L.

 

[mneox]

Thanks for your reply.. but what is keff??

(Not the value, but what does it stand for?)

 

[rl.bhat]

Thanks for your reply.. but what is keff??

(Not the value, but what does it stand for?)

It is the effective thermal conductivity. If you have a single block of same dimension instead of three different blocks, what would be its thermal conductivity to have the same rate of energy flow.