# A 0.4 m rod of metal elongates to 0.48 mm on heating from 20 degrees to 90 degrees. Determine the...

## Question:

A 0.4 m rod of metal elongates to 0.48 mm on heating from 20 degrees to 90 degrees. Determine the value of the coefficient of thermal expansion for the material and the type of metal used in this situation.

## Thermal Expansion

Thermal expansion happens when a material undergoes a change in its temperature. The rate of expansion varies on each material and is usually more evident for metals than other materials.

To get the thermal expansion coefficient of the metal, we will use the formula for the deformation caused by the temperature change

{eq}\Delta L = L\alpha \Delta T {/eq}

{eq}\alpha = \Delta L/(L\Delta T) {/eq}

{eq}\alpha = (0.48\ \rm mm)/((400\ \rm mm)(90\ \rm ^{\circ}C - 20\ \rm ^{\circ}C)) {/eq}

{eq}\alpha = 17x10^{-6}\ \rm /K {/eq}

The metal that has the closest thermal expansion to the one solved in the problem is copper.