Q12PE - College Physics (Urone)

Question

Question: How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0ºC greater than when they were laid? Their original length is 10.0 m.

Step-by-Step Solution

Answer

Answer

The expansion gap that should be left should be of between the steel railroad rails.

Step 1: Introduction

We calculate the change in length of the steel railroads rails by the formula for linear expansion in solids.

Step 2: Given parameters and formula for linear expansion

Coefficient of linear expansion of marble =$1.2\mathbf{\times }{\mathbf{10}}^{-5}{\mathbf{/}}^{\mathbf{0}}\mathit{C}$

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 is the temperature change. 

Step 3: Expansion

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

$$\begin{gathered} ∆L=\alpha L∆T \\ =(\text{1.2}\times {\text{10}}^{\text{ - 5}}\text{/°C)×10.0m×(35°C)} \\ =4.2\times {10}^{-3}m \end{gathered}$$

Therefore, the expansion gap that should be left should be of between the steel railroad rails.