A bar of aluminum (bar A) is in thermal contact with a bar of copper (bar B) of the same length and area. One end of the compound bar is maintained at Th 82.0°C while the opposite end is at 30.0°C. Find the temperature at the junction when the energy flow reaches a steady state.I was pretty sure I did this right. i got 32.6 degrees celcius as my answer, but its wrong. Does anyone know how to do it?
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Don't feel too bad because the problem is so badly worded that it can't be solved. If the two bars are joined together side by side, then obviously there is no one junction temperature. The junction temperature would vary fro 30C at one end to 82C at the other. So, could the bars be meant to be joined in series? I mean, one end is one metal at 30C and the other end is the other metal at 82C? In that case it has to be specified which metal is at 30C and which at 82C. The problem is thus not defined. Whoever worded it need a course in exposition. That's not unusual with nerdy types who never bother to learn to write comprehensible English.All one can do here is calculate the drop in temperature across the two bars, assuming they're connected end-to-end. Since conductivity of Cu is 9.2e-2 (never mind the units; not important) and that of Al in the same units id 4.9e-2, the temperature drop will be inversely proportional to these conductivities. Thus, the drop across the Al bar will be 9.2/4.9 times the drop across the Cu bar, or 9.2/(9.2+4.9)*(82-30) 33.9 deg and the drop across the Cu bar will be the rest, i.e. 52-33.9 18.1 deg. Obviously, the junction temperature will be either 30 + 33.9 63.9C if the Al bar is at the 30C end, or 30 + 18.1 48.1C if the 30C end is the Cu end.
