At 11 degrees C, an aluminum ring has an inner diameter of 8 cm anda brass rod h

Question

At 11 degrees C, an aluminum ring has an inner diameter of 8 cm anda brass rod has a diameter of 8.06 cm. If the temperaturecoefficient of expansion for brass is b =1.9 X 10^-5 (degrees C ^-1) and the temperature coefficient ofexpansion for aluminum is a = 2.4 X 10^-5(degrees C^-1), to
(a.) what temperature must the ring be heated so that it willjust slip over the rod? Answer in units of degrees C.
(b.) to what temperature must both be heated so that the ringjust slips over the rod? Asnwer in units of degrees C.
(a.) what temperature must the ring be heated so that it willjust slip over the rod? Answer in units of degrees C.
(b.) to what temperature must both be heated so that the ringjust slips over the rod? Asnwer in units of degrees C.
(b.) to what temperature must both be heated so that the ringjust slips over the rod? Asnwer in units of degrees C.

Explanation / Answer

Lo = 8.00 cm = .0800 m Lf = 8.06 cm = .0806 m L = .06 cm = .0006 m =2.4e-5 L = LoT T = (L)/(Lo) =(.0006)/((2.4e-5)(.08)) = 312.5 C Tf = 11 + 312.5 = 323.5 C b) aluminum ring: a = 2.4e-5 Lalum=LoalumT =(2.4e-5)(.08)(T) brass rod: b = 1.9e-5 Lbrass=LobrassT =(1.9e-5)(.0806)(T) Set: Lalum = Lbrass + .0006 (2.4e-5)(.08)(T) = (1.9e-5)(.0806)(T) + .0006 T = 1544.0 C T= 11 + 1544 = 1555 C

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