Answer:
The length at 0 °C is 300.05 cm
Coefficient of linear expansion of iron is 1.02×10¯⁵ C¯¹
Explanation:
From the question given above, the following data were obtained:
Length (L₁) at 100 °C = 300.36 cm
Temperature 1 (θ₁) = 100 °C
Length (L₂) at 159 °C = 300.54 cm
Temperature 2 (θ₂) = 159 °C
Length (L₀) at 0 °C =?
Coefficient of linear expansion (α) =?
L₁ = L₀ (1 + θ₁α)
300.36 = L₀ (1 + 100α) ....(1)
L₂ = L₀ (1 + θ₂α)
300.54 = L₀ (1 + 159α) ..... (2)
Divide equation (2) by (1)
300.54 / 300.36 = L₀ (1 + 159α) / L₀ (1 + 100α)
1.0006 = (1 + 159α) / (1 + 100α)
Cross multiply
1.0006 (1 + 100α) = (1 + 159α)
1.0006 + 100.06α = 1 + 159α
Collect like terms
1.0006 – 1 = 159α – 100.06α
0.0006 = 58.94α
Divide both side by 58.94
α = 0.0006 / 58.94
α = 1.02×10¯⁵ C¯¹
Substitute the value of α into anything of the equation to obtain L₀. Here we shall use equation (2).
300.54 = L₀ (1 + 159α)
α = 1.02×10¯⁵ C¯¹
300.54 = L₀ (1 + 159 ×1.02×10¯⁵)
300.54 = L₀ (1 + 0.0016218)
300.54 = L₀ (1.0016218)
Divide both side by 1.0016
L₀ = 300.54 / 1.0016
L₀ = 300.05 cm
Summary:
The length at 0 °C is 300.05 cm
Coefficient of linear expansion of iron is 1.02×10¯⁵ C¯¹
