# Urgent help on a physics problem (final exam preparation)

1. Jul 21, 2004

### Mathwizard6254

Two rods, one of aluminum and the other of copper, are joined end to end. The cross-sectional area of each is 4.0 x 10^-4 m^2, and the length of each is 0.040m. The free end of the aluminum rod is kept at 302 degrees Celsius, while the free end of the copper rod is kept at 25 degrees Celsius. The loss of heat through the sides of the rods may be ignored. How much heat is conducted through the unit in 2 seconds? Please show the work done in solving this problem. THank you very much!

2. Jul 21, 2004

### jamesrc

You should show what work you have done so that people can help you understand it better. To solve this problem, you'll need to look up the thermal conductivity of each material involved. The following equation defines the rate of conduction heat transfer through a barrier (aka Fourier law of heat conduction - I think my notation is standard or at least self-explanatory; I hope you can follow it):

$$q = \frac{Q}{t} = kA\frac{T_2 - T_1}{L}$$

When dealing with a series of barriers as in this case, it is useful to consider the concept of a thermal resistance (analagous to electrical resistance):

$$R_{th} = \frac{L}{kA}$$

Then you can sum the resistances that are in series to find:

$$\frac{Q}{t} = \frac{\Delta T}{\Sigma_i{R_{th, i}}}$$

(For this problem, you'll want to solve for Q.)