Two metal rods -- one lead, the other copper -- are connected in series (with the same length, cross-sectional

Two metal rods -- one lead, the other copper -- are connected in series (with the same length, cross-sectional area). Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a side. The temperature at the copper end is 106 C.





(a) The average temperature of the two rods is 54.0 C. Is this temperature in the middle, at the lead-copper interface, greater than, less than, or equal to 54.0 C? Explain.





(b) Given that the heat flow through each of these rods in 1.00 s is 1.41 J, find the temperature at the lead-copper interface.





I think the temperature should be greater than for (a), but can't really give an explanation. (I check the answer and it is indeed greater than, but the answer key does not given the explanation, either.)





From the answer key, the answer for (b) should be 98 C.

Two metal rods -- one lead, the other copper -- are connected in series (with the same length, cross-sectional
For (a) the temperature at the interface is greater than 54C because Copper's thermal conductivity is great than Lead's (401 W/(m*K) vs. 35.3 W/m*K).





Think of each element as a resistor. The higher the thermal conductivity, the lower the resistance to heat flow.





Since copper has a higher thermal conductivity it has a lower resistance. So, the temperature drop across the copper element will be less than the drop across the lead element.





You can find the temperature at the interface by calculating the temp drop across the copper element.





Copper has a thermal conductivity k = 401 W/(m*K)





k = (Heat transfer rate in Watts)*(distance between P1 and P2) / (area of heat transfer in m^2)*( difference in temperature between P1 and P2)





Setting up the equation from the given info:





401 = (1.41 (note J/s = W))*(0.525) / ((0.000225)*(dT))





Solving for dT = 8.20 degrees K





106 - 8.20 = 97.8 C after rounding = 98 C
Reply:i guess they are connected end to end with the other end of the copper rod at 106C and the other end of the lead rod at some lower temperature. then the temperature at the interface would be higher since the thermal conductivity k of cu is higher. the heat flow along a rod is J=k*A/l*dT like ohms law for electric flow