Answer
We can rank the slabs in order of how much their lengths increase, from greatest to smallest:
$b = d = e \gt a \gt c$
Work Step by Step
We can find the increase in length in each case:
(a) $\Delta L = \alpha~\Delta T~L$
$\Delta L = (8\times 10^{-6}~K^{-1})(20~K)(0.90~m)$
$\Delta L = 144\times 10^{-6}~m$
(b) $\Delta L = \alpha~\Delta T~L$
$\Delta L = (8\times 10^{-6}~K^{-1})(30~K)(0.90~m)$
$\Delta L = 216\times 10^{-6}~m$
(c) $\Delta L = \alpha~\Delta T~L$
$\Delta L = (8\times 10^{-6}~K^{-1})(20~K)(0.60~m)$
$\Delta L = 96\times 10^{-6}~m$
(d) $\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(20~K)(0.90~m)$
$\Delta L = 216\times 10^{-6}~m$
(e) $\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(30~K)(0.60~m)$
$\Delta L = 216\times 10^{-6}~m$
We can rank the slabs in order of how much their lengths increase, from greatest to smallest:
$b = d = e \gt a \gt c$
