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At 18.80 ∘C a brass sleeve has an inside diameter of 2.21983 cm and a steel...

At 18.80 ∘C a brass sleeve has an inside diameter of 2.21983 cm and a steel shaft has a diameter of 2.22253 cm. It is desired to shrink-fit the sleeve over the steel shaft.

To what temperature must the sleeve be heated in order for it to slip over the shaft?

Alternatively, to what temperature must the shaft be cooled before it is able to slip through the sleeve?

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