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The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0°C. What will its height be on a day when the temperature falls to −10.0°C ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

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Answer:

169.98 m

Explanation:

[tex]\alpha[/tex] = Thermal coefficient of marble = [tex]2.5\times 10^{-6}/^{\circ}C[/tex]

[tex]L_0[/tex] = Initial length = 170 m

[tex]\Delta T[/tex] = Change in temperature = (-10-35)°C

Change in length is given by

[tex]\Delta L=\alpha L_0\Delta T\\\Rightarrow \Delta L=2.5\times 10^{-6}\times 170\times (-10-35)\\\Rightarrow \Delta L=-0.019125\ m[/tex]

The height on the given day will be [tex]170-0.019125=169.98\ m[/tex]

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