When the temperature of an object is raised, its increase in length is proportional to its:

When the temperature of an object is raised, its increase in length is indeed proportional to both its initial length and the temperature rise. This principle is largely described by the concept of linear thermal expansion, which states that most materials expand when heated. The formula governing this phenomenon can be expressed as:

ΔL = αL₀ΔT

In this equation, ΔL represents the change in length, α is the coefficient of linear expansion (a material-specific constant), L₀ is the initial length of the object, and ΔT is the change in temperature (the temperature rise).

From this relationship, it's clear that the amount an object expands (in terms of length) is directly proportional to its initial length; a longer object will expand more than a shorter object when subjected to the same temperature increase. Similarly, the expansion also depends on how much the temperature has changed. Thus, both the initial length of the object and the temperature rise contribute directly to the increase in length, making this answer the most accurate reflection of the fundamental principles of thermal expansion.