There is an aluminum ring, .07 m in diameter at 5 deg. C. There is also an aluminum shaft whose diameter is .07003 m in diameter at 5 deg. C. What temp. should the shaft be cooled such that the ring will fit over the shaft.
/\L = Coefficient of Lin. Expansion (Original Length) /\T
The Attempt at a Solution
step 1) .07 - .07003 = 2.4 x 10^-5 (.07003) (5 - Tf)
* The original length is .07003 since is what is being cooled to eventually reach .07 m. Also, the Coefficient of Lin. Expansion for Aluminum is 2.4 x 10^ -5
step 2) -3.0 x 10^-5 = 1.681 x 10^-6 (5 - Tf)
step 3) -3.0 x 10^-5 = 8.405 x 10^-6 - 1.681 x 10^-6 Tf
now when i solve for Tf, it is not coming out to -12.85 deg. C, which the book states is the answer...so I'm assuming there is an error somewhere, or a few places...any help would be appreciated , thanks