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The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0ºC. What will its height be on a day when the temperature falls to –10.0ºC ? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s

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Answer:    169,98 m

Explanation:  The final height Lf will be calculated according to a formula that includes a change in length, that is height ΔL, while the initial length is L₀.

Lf = L₀ + ΔL

Change in length i.e. height ΔL, depend on the change in temperature. The α linear expansion coefficient is also used  incorporating material characteristics and their relationship to temperature change, while the change in temperature is ΔT.

α = 2,5 · 10 ⁻⁶ /°C  for marble

We will express the change in length ΔL as the product of the initial length L₀, the alpha coefficient and the temperature change ΔT.

ΔL = α · L₀ · ΔT =  2,5·10⁻⁶ · 170 · 45° =  - 0.019125 m

So that the final length Lf:

Lf = L₀ + ΔL = 170 - 0.019125 = 169,98 m

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