Question

perature is 0◦F. How much taller is the building when the temperature is 107◦F? The linear expansion coefficient of steel is 1.1 × 10−5 ( ◦C)−1 .

Answer 1

1.000458 m taller.

Step-by-step explanation:

coefficient of Linear Expansion (∝) = (L₂ - L₁)/L₁ΔT

Where ∝ = coefficient of Linear Expansion, L₂ = Final length (m), L₁ = initial length (m), ΔT = Change in temperature ( ◦C⁻¹) = T₂ - T₁

∴ ∝ = L₂ - L₁/L₁ΔT

Making L₂ the subject of the formula in the equation above,

L₂ = L₁ + (1 + ∝ ΔT)

L₂ - L₁ (ΔL) = (1 + ∝ ΔT) .................... equation 1

Where L₁ = 222 m, ∝ of steel = 1.1 × 10−5 ◦C⁻¹, and ΔT = 107 - 0 = 107◦F

Coversion: (°F − 32) x 5/9 = °C

°C = (107 - 32) × 5/9 = (75 ×5)/9 = 41.66◦C

Substituting this values into equation 1

ΔL = 1 + (1.1×10⁻⁶ × 41.66) =1 + 0.000458

ΔL =1.000458 m.

Therefore The building is 1.000458 m taller.