CHEM

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One piece of copper jewelry at 101°C has exactly twice the mass of another piece, which is at 36.0°C. Both pieces are placed inside a calorimeter whose heat capacity is negligible. What is the final temperature inside the calorimeter (c of copper = 0.387 J/gK)?

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heat lost by piece 1 + heat gained by piece 2 = 0
[mass jewl 1 x specific heat x (Tfinal-Tinitial)]+[mass jew2 x specific heat x (Tfinial-Tinitial)] = 0

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I don't understand it still.

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heat lost by one object + heat gained by another object ALWAYS will reach equilibrium at some intermediate temperature. For example, if you have a 2g piece of iron at 20C and another 2 g piece of iron at 30C, you put them together so they can exchange heat, the final temperature will be 25C. Ergo, the 30 C piece of iron lost 5C and the 20 C piece of iron gained 5C.
Your jewelry problem isn't QUITE that simple because they don't weigh the same AND they are at uneven temperatures (not a simple 20 and 30C).
So heat lost or gained is
mass x specific heat metal x (Tfinal-Tinitial).
The mass isn't given, so make up a mass for the first one that is convenient, say 20 g; that makes the second piece of jewelry 10 g. What is the specific heat Cu. That's 0.387 in the problem.
[20 x 0.387 x (Tfinal-101)] + [10 g x 0.387 x (Tfinal-36)]= 0
The ONLY unknown is Tfinal. Solve for that.

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Thanks Bob, this helped!