Chapter 13.4, Problem 47SSC

To determine

Whether the piece of copper could be heated enough to double its length.

Answer to Problem 47SSC

Copper could not be heated at $63,000°C$ , because it will get vaporized at that temperature.

Explanation of Solution

Formula used:

Length expansion:

  $L_2=L_1+\alpha L_1(T_2-T_1)$

Here, $L_2$ is the expanded length, $L_1$ is the original length, $\alpha$ is the coefficient of thermal expansion and $\Delta T=\left(T_2-T_1\right)$ is the change in temperature.

Calculation:

Let the original length be L. Then, $\Delta L=2L-L=L$

  $\Delta L=L=\alpha L\Delta T$

  $\alpha \Delta T=1$

Where, $\alpha =16\times {10}^{-6}°C^{-1}$ is the thermal coefficient for copper.

Therefore, $\Delta T=\frac{1}{\alpha }$

  $\Delta T=\frac{1}{16\times {10}^{-6}°C^{-1}}$

  $\Delta T=63,000°C$

Conclusion: No, piece of copper could not be heated at $63,000°C$ to double its length, as at such high temperature, copper gets vaporized.