Answer
(a) The space that should be left between the slabs is $3.60~mm$
(b) The gap between the slabs is $10.8~mm$
Work Step by Step
(a) We can find the increase in length of each concrete slab when it is heated:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(20.0~K)(15~m)$
$\Delta L = 3600\times 10^{-6}~m$
$\Delta L = 3.60\times 10^{-3}~m$
$\Delta L = 3.60~mm$
Since we can assume that each slab expands by half of this distance in each direction, the space that should be left between the slabs is $3.60~mm$
(b) We can find the decrease in length of each concrete slab when it is cooled from $40.0^{\circ}C$ to $-20.0^{\circ}C$:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(-60.0~K)(15~m)$
$\Delta L = -10,800\times 10^{-6}~m$
$\Delta L = -10.8\times 10^{-3}~m$
$\Delta L = -10.8~mm$
Since we can assume that each slab decreases by half of this distance in each direction, the gap between the slabs is $10.8~mm$
