A steel shaft of diameter 50.05mm at 20∘C is to be inserted into a brass sleeve whose inner diameter is 50.00mm at the same temperature. The shaft can be fitted only if the sleeve is first heated and then allowed to cool so that the two diameters become equal at some common temperature.
a. (i) Derive the condition on temperature T (in ∘C) at which the sleeve just fits the shaft, taking the initial temperature as the reference.
b. (ii) Using αsteel=1.2×10−5K−1 and αbrass=1.9×10−5K−1, determine the temperature to which the brass sleeve must be heated before insertion of the shaft.