Consult Multiple$-$Concept Example $4$ for insight into solving this problem. A copper rod is fastened securely at both ends to immovable supports. When this rod is stretched, it will rupture when a tensile stress of $3\mathrm{.}18$ x $107$ N$/$m$^2$ is applied at each end. The rod just fits between the supports, so initially there is no stress applied to the rod. The rod is then cooled. What is the magnitude $($AT$)$ of the change in temperature of the rod when it ruptures?