# Conduction, 2 metal rods

hey, can anyone help me with this question? im really having trouble with it.

1. Two metal rods, one lead the other copper, are connected in series (end-to-end). Note that each rod is 0.525m in length and has a square cross section 1.5cm on a side. The temperature at the lead end of the rods is 2 degrees C; the temperature at the copper end is 106 degrees C.

a) The temperature of the two ends is 54 degrees C. Is the temperature in the middle, at the lead-copper interface greater than, less than or equal to 54 degrees C?
b) Given that the heat flow through each of these rods in 1 sec. is 1.41J, find the temperature at the lead-copper interface.

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OlderDan
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Lalasushi said:
hey, can anyone help me with this question? im really having trouble with it.

1. Two metal rods, one lead the other copper, are connected in series (end-to-end). Note that each rod is 0.525m in length and has a square cross section 1.5cm on a side. The temperature at the lead end of the rods is 2 degrees C; the temperature at the copper end is 106 degrees C.

a) The temperature of the two ends is 54 degrees C. Is the temperature in the middle, at the lead-copper interface greater than, less than or equal to 54 degrees C?
b) Given that the heat flow through each of these rods in 1 sec. is 1.41J, find the temperature at the lead-copper interface.
The problem statement is a bit confusing. I assume part a) is asking about the temperature at the junction if the temperatures at the far ends were both changed to 54C. I also assume that the temperature at the junction is to be determined after the rods have achieved thermal equilibrium with no heat input or output anywhere other than at the far ends.

Part b) is just a conduction problem. Heat will flow from the hot end to the cold end. Given time to reach thermal equlibrium, the rods will achieve a temperature gradient that will support a uniform heat flow. The question is to find the temperature at the junction such that the rate of heat flow is the same in both rods. You will need the thermal conductivities of the two materials to answer the question.