A circular aluminum $a=23\mathrm{.}0\frac{{10}^{-6}}{}C$ ring is to be mounted on a circular steel tube. The ring will be heated so that it expands

enough to slip onto the steel tube. After the ring cools, there will be a tight fit between the aluminum ring and the steel tube. $($This

process is called shrink fit.$)$

The outside diameter of the steel tube is $540$ mm $,$ and the inside diameter of the aluminum ring is $538$ mm $.$ Assume that the

temperature of the steel tube remains constant and that an extra $0\mathrm{.}5$ mm in diameter is required for the ring to clear the steel tube.

Compute the temperature increase required to expand the ring sufficiently so that it can be slipped onto the steel tube.

Answer:

Temperature increase $=$

:

$C$