Chapter 13.4, Problem 39PP

To determine

Length of the aluminum house sided at $\text{39°C}$ .

Answer to Problem 39PP

The piece of aluminum will be $6.1mm$ longer on hot summer day of temperature $\text{39°C}$ .

Explanation of Solution

Given information:

A piece of aluminum house, ${\text{L}}_{\text{1}}\text{=3}\text{.66}\text{m}$

Initial temperature, ${\text{T}}_{\text{1}}\text{=-28°C}$

Secondary temperature, ${\text{T}}_{\text{2}}\text{=39°C}$

For aluminum, coefficient of linear expansion, ${\text{α = 25×10}}^{\text{-6}}{\text{°C}}^{\text{-1}}$

Formula used:

The length, L, of a solid at temperature T can be found with the following equation:

  $L_2=L_1+\alpha L_1(T_2-T_1)$

Where, $L_1$ is the length at temperature $T_1$ , $L_2$ is the length at temperature $T_2$ , $\alpha$ is the coefficient of linear expansion.

Calculation:

Apply the given formula, $L_2=L_1+\alpha L_1(T_2-T_1)$.

So, $\Delta L=\alpha L_1(T_2-T_1)$

  $\text{ΔL=}\left({\text{25×10}}^{\text{-6}}{\text{°C}}^{\text{-1}}\right)\left(\text{3}\text{.66}\text{m}\right)\left(\text{39°C-}\left(\text{-28°C}\right)\right)$

  $\text{ΔL}\text{=}\text{6}{\text{.1×10}}^{\text{-3}}\text{m = 6}\text{.1}\text{mm}$

Conclusion:A piece of aluminum is $6.1mm$ longer on a hot summer day.