When the temperature of an object is increased, its change in length is proportional to what?

The change in length of an object as its temperature increases is indeed proportional to its initial length and the temperature increase. This principle is rooted in the concept of thermal expansion, which states that materials expand when heated. Specifically, the linear expansion of a solid material can be expressed mathematically through the formula:

ΔL = αL₀ΔT

Here, ΔL represents the change in length, α is the coefficient of linear expansion (a material property), L₀ is the initial length, and ΔT is the change in temperature.

What this means is that if the initial length of the object is greater, the resulting change in length from a specific temperature increase will also be greater. Thus, it is the initial length of the material that plays a significant role in determining how much it will expand or contract with temperature changes.