College Physics (4th Edition)

The brass ring should be heated to a temperature of $74.6^{\circ}C$
We can find the required change in temperature of the brass ring so that the increase in radius $\Delta R$ is 0.0010 cm: $\Delta R = \alpha~\Delta T~R$ $\Delta T = \frac{\Delta R}{\alpha~R}$ $\Delta T = \frac{0.0010~cm}{(19~\times 10^{-6}~K^{-1})(1.0000~m)}$ $\Delta T = 52.6~K$ $\Delta T = 52.6^{\circ}C$ The required increase in temperature is $52.6^{\circ}C$, so the brass ring should be heated to a temperature of $74.6^{\circ}C$