Chapter 13, Problem 82A

To determine

Change in length of $\text{2}\text{.00 }\text{m}$ cooper pipe if its temperature is raised from $\text{23}°\text{C}$ to $\text{978}°\text{C}$ .

Answer to Problem 82A

Change in length will be $0.032\text{m}$ .

Explanation of Solution

Given:

Length of cooper pipe, $L\text{= 2}\text{.00}\text{m}$

Higher temperature, $T_1\text{= 978}°\text{C}$

Lower Temperature, $T_2\text{= 23}°\text{C}$

Linear coefficient of expansion, $\alpha \text{ = 16}\times {\text{10}}^{-6}\text{per}°\text{C}$

Formula used:

Formula of Linear thermal expansion is $\Delta L=a{L}_1\Delta T$ .

Where, $\Delta L$ is the change in length  $L_1$ , $\alpha$ is a coefficient of linear expansion, $\Delta T$ is the change in temperature and $L_1$ is the length at temperature $T$

Calculation:

Substituting the given values in the formula, $\Delta L=a{L}_1\Delta T$

  $\Delta L=17\times {10}^{-6}\text{per}°\text{C}\times 2\text{m}\times \left(978-23\right)°\text{C}$

  $\Delta L=17\times {10}^{-6}\times 2\text{m}\times 955$

  $\Delta L=0.032\text{m}$

Conclusion:

Change in length of cooper pipe will be $0.032\text{m}$ .