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

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