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An aluminum rod with cross-sectional area 0.0400 cm^2 and length 80.00 cm at a temperature of 140.0 Celcius is laid alongside a copper rod of cross-sectional area 0.0200 cm^2 and length 79.92 cm at temperature T. The two rods are laid alongside each other so that they are in thermal contact. No heat is lost to the surroundings, and after they have come to thermal equilibrium, they are observed to be the same length. Calculate the original temperature T of the copper rod and the final temperature of the rods after they come to equilibrium.

I tried using the MCAT equation (Q = mc X Delta T) but I can't seem to derive a formula that works for the lengths of TWO objects in thermal equilbrium. In my textbook there is a formula that says that

The Change in the Length = Alpha X Initial Length X The Change in Temperature

I'm not sure if this helps, but I have worked hard on this problem, and asked several people for advice, ultimately gaining no progress. My book has the answers, but I need to know how to solve this one, not just the answer. But if it helps, the answer is:

89.7 Degrees Celcius for the Original Temperature of Copper.

119.2 Degrees Celcius for the final temperature of the two rods after they come to equilbrium.

Thanks to all that help me.

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# A Problem on Thermal Equilibrium

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