Question

By how much would you need to heat a 3 meters bar of zinc to make it expand by 5 cm?

Answer 1

Since we know that the thermal law of linear expansion can be written as $\Delta L=L_0\alpha \Delta T$ , we rearrange it and calculate $\Delta T$ with the thermal linear expansion coefficient of this metal ($\alpha =$ 3 X 10⁻⁵ °C⁻¹), the length of the zinc bar (300 cm) and the desired expansion (5 cm):

$\Delta T = \frac{\Delta L}{L_0\alpha }= \frac{5\,\cancel{cm}}{(300\,\cancel{cm})(3\times10^{-5}\,°C^{-1})}=555.55\, °C$

In conclusion, the zinc bar has to be heated until $\Delta T =555.55\, °C$.

Reference:

• Young, H. D., Freedman, R. A., & Ford, A. L. (2006). Sears and Zemansky's university physics (Vol. 1). Pearson education.
• Carvill, J. (1994). Mechanical engineer's data handbook. Butterworth-Heinemann.