Question

at 20 degrees celsius, a steel rod and an aluminum rod are both 1.25 m long. (a) if both rods are heated to 100 degrees, which will be longer and by how much?

Answer 1

The elongation of a metal rod under heating is given as follows:

$$\Delta L = \alpha L\Delta T$$

where $\alpha$ is the coefficient of thermal expansion of metal, $L$ is the initial length, and $\Delta T$ is the change in temperature. In our case: $L = 1.25m$, $\Delta T = 100\degree C - 20\degree C = 80\degree C = 80K$, the expansivities are:

$$\alpha_{Al} = 23.1\times 10^{-6} K^{-1}\\ \alpha_{Cu} = 17\times 10^{-6} K^{-1}$$

Thus, the elongation of aluminium is:

$$\Delta L_{Al} = 23.1\times 10^{-6}\cdot 1.25\cdot 80 = 2.31mm$$

The elongation of cooper is:

$$\Delta L_{Cu} = 17\times 10^{-6}\cdot 1.25\cdot 80 =1.70mm$$

Thus, the aluminum rod will be longer by

$$\Delta L_{Al} - \Delta L_{Cu} = 2.31mm-1.70mm = 0.61mm$$

Answer. The aluminum rod will be longer by 0.61 mm.