Question

A metal bar at 50cm long at 15°C is heated to 85°C. If it expands by 0.088cm ,determine it's linear expansitivity

Answer 1

By definition, the increase in length will be:

$$\Delta L = \beta L_0\Delta T$$

where $\beta$ is the linear expansivity, $L_0 = 50cm$ is the initial length, and $\Delta T = 85\degree C - 15\degree C = 70\degree C$ is the change in temperature. Since $\Delta L = 0.088cm$, the linear expansivity is:

$$\beta = \dfrac{\Delta L}{L_0\Delta T}\\ \beta = \dfrac{0.088}{50\cdot 70} \approx 2.51\times 10^{-5}\degree C^{-1}$$

Answer. $2.51\times 10^{-5}\degree C^{-1}$.