The coefficient of volumetric expansion for solids is defined as:

The coefficient of volumetric expansion for solids is indeed defined as three times the coefficient of linear expansion. This relationship arises from the fact that when a solid object undergoes a temperature change, its dimensions expand in three dimensions—length, width, and height.

To elaborate, the coefficient of linear expansion quantifies how much a unit length of a solid material expands per degree change in temperature. When considering volumetric expansion, which involves changes in three dimensions, the total change in volume can be understood as the cumulative effect of the changes in length, width, and height. Therefore, the volumetric expansion can be expressed mathematically as three times the coefficient of linear expansion. This is illustrated with the formula for volumetric expansion, where the volume change (ΔV) is directly proportional to the product of the linear changes in the three dimensions, leading to the coefficient of volumetric expansion being three times that of linear expansion.

Understanding this concept is fundamental when dealing with thermal effects in materials and is crucial in various engineering applications, as it affects material behavior under temperature variations.