To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.870 cm in diameter is to be placed in a hole 1.868 cm in diameter in a metal at 25°C. To what temperature must the rivet be cooled if it is to fit in the hole? Express your answer using two significant figures.

-63.98° C

Explanation:

Initial diameter of rivet d = 1.873 cm

Hole diameter d ' = 1.871 cm

Coefficient of linear expansion of steel α = 12*10 - 6 / ° C

Initial temperature t = 25° C

We know α = (d' - d) / [ d (t ' - t) ]

t ' - t = (d ' - d) / [ d x α ]

putting values we get

t ' - t = - 88.98° C

t ' = - 88.98° C + t

= - 63.98° C

The temperature must the rivet be cooled if it is to fit in the hole (at 25°C) is - 63.98° C