Answer to Question #129906 in Mechanics | Relativity for Nqaba Mkhize

Question

A metal rod of length 15 cm is heated to 38 °C. If the length of rod expands to 15.12 cm after some time, calculate the coefficient of linear expansion (Room temperature is 27 °C).

Answer 1

Thermal expansion of the rod is described with the equation: $l_1=l_0(1+α \cdot ΔT)$, where $l_0$ is initial length and $l_1$ is length after heating/cooling, ΔT is difference of temperatures, α is the coefficient of linear expansion. In our case:

$15.12 \cdot 10^{-2}=15 \cdot 10^{-2} \cdot (1+α\cdot (38-27)) \Rightarrow 15.12=15+α \cdot 11 \cdot15 \Rightarrow α=\frac {0,12}{11\cdot15}=7.3\cdot 10^{-4} \frac{1}{°C}$