Chapter 13, Problem 80A

To determine

Length of the aluminum bar after expansion.

Answer to Problem 80A

At $1.0K$ , the length of the aluminum bar becomes $1.3\times {10}^{-5}m$ .

Explanation of Solution

Given:

Length of aluminum bar: $L_1=0.500m$ at $T_1=273K$

  $\Delta T=1.0K=1.0°C$

Formula used: The length of the bar can be obtained by:

  $\Delta L=\alpha L_1\Delta T$

Where $\alpha =25\times {10}^{-6}°C^{-1}$ is the coefficient of linear expansion for aluminum.

Calculation: The length of aluminum bar is:

  $\begin{array}{l}\Delta L=(25\times {10}^{-6}°C^{-1})(0.500m)(1.0°C)\\ \Delta L=1.3\times {10}^{-5}m\end{array}$

Conclusion: Hence,inventor should measure $1.3\times {10}^{-5}m$ length of the bar.