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22 November, 20:47

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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  1. 22 November, 21:22
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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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