A wire is 24.5 m long at 4.00°C and is 1.40 cm longer at 34.0°C. Find the wire's coefficient of linear expansion (in (°C)−1)

1.9×10⁻⁵ °C⁻¹

Explanation:

Coefficient of linear expansion: This can be defined as as increase in length of a material, per unit length per degree rise in temperature, The S.I unit is (K⁻¹).

From the question above,

α = ΔL/L(T₂-T₁) Equation 1

Where α = coefficient of linear expansion, ΔL = Change in length, L = original length, T₁ = Initial Temperature, T₂ = Final temperature.

Given: ΔL = 1.4 cm = 0.014 m, L = 24.5 m, T₁ = 4.00°C, T₂ = 34°C

Substitute these values into equation 1

α = 0.014/[24.5(34-4)]

α = 0.014/735

α = 1.9×10⁻⁵ °C⁻¹