Knowing that a $0\mathrm{.}02$ in gap exists when the temperature is $75F,$ determine $($a$)$ the temperature at which the normal stress in the aluminum bar will be equal to $-11$ ksi $,($b$)$ the corresponding exact length $(2$ decimal places in ${10}^{-3}$ inches$)$ of the aluminum bar.

Bronze

$A=2\mathrm{.}4i{n}^2$

$E=15{10}^6$

$=12\frac{{10}^{-6}}{}F$

Aluminum

$A=2\mathrm{.}8i{n}^2$

$E=10\mathrm{.}6{10}^6$

$=12\mathrm{.}9\frac{{10}^{-6}}{}F$