Answer
(a) $76^{\circ}C$
(b) $-89^{\circ}C$
Work Step by Step
(a) We know that
$\Delta L=\alpha L (T-T_{\circ})$
This can be rearranged as:
$T=T_{\circ}+\frac{\Delta L}{\alpha L}$
We plug in the known values to obtain:
$T=12.25+\frac{2.19893-2.19625}{1.9\times 10^{-5}(2.19625)}$
$T=76^{\circ}C$
(b) We know that
$\Delta L=\alpha L (T-T_{\circ})$
This can be rearranged as:
$T=T_{\circ}+\frac{\Delta L}{\alpha L}$
We plug in the known values to obtain:
$T=12.25+\frac{2.19625-2.19893}{12\times 10^{-6}(2.19893)}$
$T=-89^{\circ}C$
