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16 June, 10:50

The height of the washington monument is measured to be 170 m on a day when the temperature is 30.0°c. what will its height be in meters on a day when the temperature falls to - 16.0°c? 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. 16 June, 11:07
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    This is a case of linear expansion. The general expression of linear expansion is given by:

    ΔL = αLΔT, ΔL = change in length or height, α = coefficient of linear thermal expansion, ΔT = Change in temperature.

    In the current case;

    α = 2.5*10^-6 / °C (for Marble)

    L = 170 m at 30.0°C

    ΔT = 30 - (-16) = 46°C

    Substituting;

    ΔL = 2.5*10^-6 * 170*46 = 0.01955 m

    Height at - 16°C = 170 - 0.01955 = 169.98 m
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