Question

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.

Answer 1

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