Expanding metals!

  • Thread starter squib
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A 38.0 g copper ring has a diameter of 2.54000 cm at its temperature of 0°C. An aluminum sphere has a diameter of 2.54508 cm at its temperature of 108°C. The sphere is placed on top of the ring as in the figure, and the two are allowed to come to thermal equilibrium, with no heat lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. What is the final temperature in kelvins? For copper, α = 1.7×10-5/°C. For aluminum, α = 2.3×10-5/°C.

tried pi(Dc)+(pi(Dc*a*deltaT)) = pi(Da) - (pi(Da*a*deltaT))

this came up with ~49 for change in temp, but this does not seem to be the right answer... any suggestions?
 

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  • #2
Doc Al
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Your equation assumes that both materials undergo the same temperature change. Not likely! Instead, write the delta T for each substance in terms of Tf and its initial temperature.

Also, why is everything multiplied by pi? (Since they cancel, it doesn't effect your answer. But why?)
 

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