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Question
A concrete slab has a length of 10 m on a winter night when the temperature is 0°C. Find the length of the slab on a summer day when the temperature is 35°C. The coefficient of linear expansion of concrete is 1.0 × 10–5 °C–1.
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Solution
Given:
Length of the slab when the temperature is 0°C, L0 = 10 m
Temperature on the summer day, t = 35 °C
Let L1 be the length of the slab on a summer day when the temperature is 35°C.
The coefficient of linear expansion of concrete, α = 1 ×10–5 °C-1
\[L_1 = L_0 \left( 1 +∝t\right)\]
\[\Rightarrow L_1\] = 10 (1 + 10–5 × 35)
\[\Rightarrow L_1\] = 10 + 35 × 10–4
\[\Rightarrow L_1\] = 10.0035 m
So, the length of the slab on summer day when the temperature is 35oC is 10.0035 m.
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