Q9PE - College Physics (Urone)

Question

Question: The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0ºC. What will its height be on a day when the temperature falls to –10.0ºC? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

Step-by-Step Solution

Answer

Answer

The new height of the Washington monument is 169.98 meters. 

Step 1: Introduction

We calculate the change in height of the monument and hence, by subtracting it from the original height we find the new height.

Step 2: Given parameters and formula for linear expansion

Coefficient of linear expansion of marble =$2.5\times {10}^{-6}/°C$

The formula for length expansion of solids is,

$∆L=\alpha L∆T$……………..(1)

Here, is the coefficient of linear expansion, L is the original length, and $∆T$is the temperature change. 

Step 3: decrease in height

Substitute the given values in equation (1), and we get,

Step 4: Calculate the new height

 $$\begin{gathered} L\text{'}=L-\Delta L \\ =\text{170} m-\text{1.92}\times {\text{10}}^{-\text{2}} m \\ =\text{169.98} m \end{gathered}$$

Therefore, the new height is  169.98m