The two cylindrical rod segments shown in the figure below $($Figure $1)$ are fixed to the rigid walls such that there is a gap of $0\mathrm{.}01$ in

$.$between them when T$1=50$F

$.$ Each rod has a diameter of $1\mathrm{.}7$ in

$.$ Take $\backslash$alpha al$=13(106)/$F

$,$ Eal$=10(103)$ksi

$,(\backslash$sigma Y$)$al$=40$ksi

$,\backslash$alpha cu$=9\mathrm{.}4(106)/$F

$,(\backslash$sigma Y$)$cu$=50$ksi

$,$ and Ecu$=15(103)$ksi

$.$

Figure$1$ of $1$

A $12-$inch copper rod extends right from a wall. A $6-$inch aluminum rod extends left from a wall. There is a $0\mathrm{.}01-$inch gap between them.

Part A

What larger temperature T$2$

is required in order to just close the gap?

Express your answer to three significant figures. Determine the magnitude of the average normal stress in each rod if T$2=320$F

$.$