You are an engineer designing an experiment to study how the temperature of a metal rod affects its rate of thermal expansion. Use the following information on the thermal expansion of a rod and the PERIOD method to discuss key considerations in you experiment design.

Thermal Expansion of a Rod

When a rod undergoes thermal expansion, it changes its dimensions $($primarily length$)$ as a response to an increase in temperature. For most solid materials, the expansion due to heat is primarily in length. This phenomenon is described by the linear expansion formula:

$L=L_{0}T$

where:

$L$ is the change in length,

$,$ is the coefficient of linear expansion $($specific to the material$),$

$,L_0$ is the original length, and

$,T$ is the change in temperature.

This formula shows that the increase in length is directly proportional to both the temperature change and the original length of the rod.

Effect on Shape and Structure

For slender rods, thermal expansion mainly affects the length.

If the rod is constrained $($e$.$g$.,$ fixed at both ends$),$ the increase in temperature can create thermal stress, potentially leading to bending or even breaking if the material cannot withstand the induced forces.

Real$-$World Applications and Considerations

Engineering Structures: Bridges, railways, and buildings often incorporate expansion joints to accommodate thermal expansion without damage.

Material Choice: In precise machinery or devices, materials with low thermal expansion coefficients are often chosen to maintain dimensional stability over a range of temperatures.