A concrete slab has a length of $10 m$ on a winter night when the temperature is $0^{\circ} C$ . Find the length of the slab on a summer day when the temperature is $35^{\circ} C$ . The coefficient of linear expansion of concrete is ${1.0 \times 10^{- 5}}^{\circ} C^{- 1}$

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Solution

The length of the concrete slab $L_{0} = 10 m$
The coefficient of linear expansion $α = 1 \times 10^{- 5} /^{o} C$
The change in temperature of the slab is $t = 35$

New length of the slab is $L_{1} = ?,$

The change in the length o the slab due to change in temperature is given by:
$L_{1} = L_{0} (1 + α t)$

Substitute the values:
$L_{1} = 10 (1 + 10^{- 5} \times 35)$
$= 10 + 35 \times 10^{- 4}$
$= 10.0035 m$

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