What is the relationship between the change in length of an object and temperature increase?

The relationship between the change in length of an object and temperature increase is best described by the initial length of the object in relation to the temperature increase. When a material is heated, it tends to expand; this expansion is proportional to its initial length. The relationship is typically quantified by the coefficient of linear expansion, which indicates how much an object will expand per degree of temperature increase.

As the temperature rises, the particles within the object gain kinetic energy and move apart, leading to an increase in length. Hence, knowing the initial length of the object helps in predicting how much it will expand upon heating; a longer initial length will generally experience a more significant increase in length for the same temperature change compared to a shorter initial length.

The other choices involve different relationships that do not directly apply to length changes with respect to temperature. For example, cross-sectional area and volume changes may play a role in overall volume expansion, but they do not specifically address the direct relationship between initial length and temperature, which is the core focus of the question.