The Eiffel Tower in Paris is 984 ft tall and is made mostly of steel.
If this is its height in winter when its temperature is -8.00 ∘C, how much additional vertical distance must you cover if you decide to climb it during a summer heat wave when its temperature is 41.3 ∘C?
Express the coefficient of linear expansion of steel in terms of Fahrenheit degrees.
Part A) I'll use α = 12e-6/ºC
ΔL = α L ΔT = 12e-6/ºC 984ft (41.3 - -8.00)ºC = 0.582 ft ◄
or almost 7 inches.
Part B) 12e-6/ºC * 5ºC/9ºF = 6.67e-6/ºF ◄
assuming the value of α that I have.
Hope this helps!
h = ho(1+λsΔT) = 984(1+1210^-6*49.3) = 984.58 feet
Δh = h-ho = 984.58-984 = 0.58 feet
λs = (12*49.3/120.75)*10^-6 = 4.90*10^-6 °F^-1