Final answer:
The relation between linear, superficial, and cubical expansion is that as temperature increases, objects expand in length, area, and volume. The degree of expansion can be described by different coefficients, with the volumetric expansion coefficient being roughly three times the linear expansion coefficient.
Step-by-step explanation:
The relation between linear, superficial, and cubical expansion involves understanding how different dimensions of an object change with temperature. Linear expansion refers to the change in length, superficial expansion refers to the change in area, and cubical expansion refers to the change in volume. As temperature increases, objects generally expand in all three dimensions. This is explained by the increase in atomic or molecular vibrations, causing materials to take up more space. The equation ΔV = βVΔT describes the cubical expansion, where ΔV is the change in volume, β is the volumetric expansion coefficient, V is the original volume, and ΔT is the change in temperature. Superficial and linear expansion can often be related to cubical expansion. In general, for isotropic materials which expand uniformly in all directions, the volumetric expansion coefficient (β) is approximately three times the linear expansion coefficient (α). Thus, superficial expansion will be influenced by these properties as well.