A bar of aluminum (bar A ) is in thermal contact with a bar of iron (bar B ) of

Question

A bar of aluminum (bar A) is in thermal contact with a bar of iron (bar B) of the same length and area. One end of the compound bar is maintained at Th = 73.0°C while the opposite end is at 30.0°C. Find the temperature at the junction when the energy flow reaches a steady state.
58.25 C---this is incorrect
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.°C

Explanation / Answer

Since area and length are the same, they divide out of the equations for the energy transfer of the two bars when they are set equal. The equilibrium temperature falls somewhere between the two given temperatures, so:

k[T(h) - T(c)](Al) = k[T(h) - T(c)](Iron)
205J/s•m•K[73.0+273 - T] = 79.5J/s•m•K[T - 30.0+273K]
70930J/s•m - (205J/s•m•K)T = (79.5J/s•m•K)T - 24088.5J/s•m
(284.5J/s•m•K)T = 95018.5J/s•m
T = 333.984 K = 60.98 C

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