how much would the machinist have to lower the temperature (in °C) of the rod to make it fit the hole?

Question

A machinist wishes to insert a steel rod with a diameter of 9 mm into a hole with a diameter of 8.998 mm. By how much would the machinist have to lower the temperature (in °C) of the rod to make it fit the hole?

Answer 1

The coefficient of linear expansion of steel is 10.8 x 10^-3 = 0.0108 per degree celsius (looked this up online)

So if we lower the temperature by y degrees celsius the diameter of the rod will decrease by

0.0108y x 9 mm

This needs to be 9 - 8.998

So 0.0108 x 9 y = 9 - 8.998

0.0972 y = 0.002

y = 0.002 / 0.0972 = 0.02 celsius