Question

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.

Answer 1

169.98 m

Step-by-step explanation:

`\alpha` = Thermal coefficient of marble =
`2.5* 10^(-6)/^(\circ)C`

`L_0` = Initial length = 170 m

`\Delta T` = Change in temperature = (-10-35)°C

Change in length is given by

`\Delta L=\alpha L_0\Delta T\\\Rightarrow \Delta L=2.5* 10^(-6)* 170* (-10-35)\\\Rightarrow \Delta L=-0.019125\ m`

The height on the given day will be
`170-0.019125=169.98\ m`