Question

The height of the Washington Monument is measured to be 170 m on a day when its temperature is 35.0°C. What will the change in its height be on a day when its temperature falls to -15.0°C? Although the monument is made of limestone, take the thermal coefficient of expansion to be that of marble.

Answer 1

Since change in length due to temperature is given by,

dL = L0*alpha*dT

here, L0 = initial length = 170 m

alpha = thermal coefficient of expansion of marble = 4.4*10^-6 degC^-1 (Check this value in your reference book as it may varies in different books)

dT = Tf - Ti = -15 - 35 = -50 degC

So, dL = 170*(4.4*10^-6)*(-50)

dL = -0.0374 m = -3.74*10^-2

dL = -3.74 cm

SO, height of monument will be decreased by 3.74 cm at the temperature falls to -15.0 degC.

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