Question

The height of the Washington Monument is measured to be 170 meters on a day when the temperature is 35 degrees Celsius. Assume it’s thermal coefficient of linear expansion is .0000025/degrees Celsius. What will its height be in meters on a day when the temperature falls to -10 degrees Celsius?

Answer 1

By the definition of the linear thermal expansion we have:
∆L/L_0 =α∆T,
here, ∆L is the change in the height of the monument after the change in temperature, L_0 is the height of the monument before the change in temperature, α is the thermal coefficient of linear expansion of the monument and ∆T is the change in temperature.
Then, from this formula we can find ∆L:
∆L=αL_0 ∆T=2.5∙〖10〗^(-6) (℃)^(-1)∙170 m∙(-10℃-35℃)=-0.0191 m.
Finally, we can find the new height of the monument:
L=L_0+∆L=170 m+(-0.0191 m)=169.98 m.