Physics Length Problem

Question

A steel beam being used in the construction of a skyscraper has a length of 33.000 m when delivered on a cold day at a temperature of 14.000°F. What is the length of the beam when it is being installed later on a warm day when the temperature is 93.000°F? (Give your answer to at least five significant figures.) 

_____m

Answer 1

l₁ = l₀(1 + λT₁); l₂ = l₀(1 + λT₂); l₂ = l₁(1 + λT₂)/(1 + λT₁).

l₁ = 33.000m; T₁ = (14 - 32)/1.8 = - 10°C; T₂ = (93 - 32)/1.8 = 33.889°C; λ = 1.3·10^-5C^-1

l₂ = 33.000·(1 + 1.3·10^-5 ·33.889)/(1 - 1.3·10^-5·10)m = 33.01883 m