A steel beam being used in the construction of a skyscraper has a length of 38.000 m when delivered on a cold day at a temperature of 11.000°F. What is the length of the beam when it is being installed later on a warm day when the temperature is 87.000°F? (Give your answer to at least five significant figures.)

length of the Steel beam = 39.00327 m

Explanation:

Linear expansivity (∝) of a metal : Is defined as an increase in length per unit length for one degree rise in temperature.

It is express mathematically as

∝ = (L₁-L₂) / (L₁ΔT) ... Equation 1

∴ L₂ = L₁ + (1 + ∝ΔT) ... Equation 2

Where ∝ = linear expansivity of the metal (K⁻¹), L₁ = Initial length (m), L₂ = Final length (m)

L₁ - L₂ = ΔL = Change in length of the metal (m)

ΔT = T₂ - T₁ (K)

∴ L₂ = L₁ + (1 + ∝ΔT) ... Equation 2

The linear expansivity of steel = 11 * 10⁻⁶ (K⁻¹),

L₁ = 38.00 m, ΔT = 87 - 11 = 76 °F

Conversion

°F to Kelvin = K = 5/9 (° F - 32) + 273

T (K) = 5/9 (76-32) + 273

T (K) = 5/9 (44) + 273

T (K) = 297.44 K

substituting these values into equation 2

L₂ = 38 + (1 + {11*10⁻⁶ * 297.44})

L₂ = 38 + (1 + 0.00327)

L₂ = 38 + (1.00327)

L₂ = 39.00327 m.

Therefore, length of the Steel beam = 39.00327 m