Question

At `30^(@)`C, the hole in a steel plate has diameter of 0.99970 cm. A cylinder of diameter exactly 1 cm at `30^(@)`C is to be slide into the hole. To what temperature the plate must be heated?
(Given `alpha_(Steel)=1.1xx10^(-5^(@))C^(-1)`
A. `58^(@)`C
B. `55^(@)`C
C. `57.3^(@)`C
D. `60^(@)`C

Answer 1

c) `Deltal=1-0.99970=0.00030`cm
`Deltal= alphalDeltaT`
`Deltat= (Deltal)/(alphal) = (0.0003)/(1.1 xx 10^(-5) xx 0.9997)` = `27.3^(@)`C
So, plate temperature must be raised to `30^(@)` + 27.36 = `57.3^(@)`C