Imagine a hypothetical material whose average temperature coefficient of linear expansion is 0.1 /°C. Find the fractional increase in the area of a thin square plate of above material when temperature increase by 10°C.

Engineering

Physics

Thermal Expansion

Question

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Changed side length ℓ = ℓ₀ (1 + αΔθ) = ℓ₀ (1 + 0.1 × 10) = 2ℓ₀
hence changed area = 4ℓ₀2 = 4A₀
(A₀ = original area)
Hence, fractional increase = $\frac{4 A_{0} - A_{0}}{A_{0}} = 3$ .

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