Answer to Question #87844 in Molecular Physics | Thermodynamics for kara sylva

Question

an iron rod is length 50m when the temperature is 20 degree celcuis by how much will it expand when the temperature rises to 30 degree celcuis

Answer 1

By the definition of the linear thermal expansion we have:

$$\Delta L = \alpha L_0 \Delta T,$$

here, $\Delta L$ is the difference in the length of the iron rod after the change in the temperature (or the expansion of the rod) , $L_0 = 50 m$ is the original length of the iron rod, $\alpha = 11.8 \cdot 10^{-6} \dfrac{1}{^{\circ}C}$ is the coefficient of linear expansion for the iron rod and $\Delta T = T_{final} - T_{initial} = 30^{\circ}C - 20^{\circ}C = 10^{\circ}C$ is the change in temperature.

Then, from this formula we can calculate the linear expansion of the iron rod:

$$\Delta L = 11.8 \cdot 10^{-6} \dfrac{1}{^{\circ}C} \cdot 50 m \cdot 10^{\circ}C = 5.9 \cdot 10^{-3} m.$$

Answer:

$\Delta L = 5.9 \cdot 10^{-3} m.$