The amount of increase in area of each surface will depend on the:

The relationship between temperature change and the expansion of materials is governed fundamentally by the coefficient of surface expansion. This property indicates how much a material will expand per unit length for each degree of temperature increase. When a material is heated, its particles gain energy and move apart, resulting in an increase in surface area.

Each material has a specific coefficient of surface expansion that quantifies how much it expands when subjected to a change in temperature. Therefore, the correct choice reflects the direct dependency of the increase in area on this coefficient, allowing engineers to predict how different materials will behave under thermal stresses.

While other factors may influence the overall thermal behavior of a material, like the rate of thermal conductivity, time allowed for heating, or changes in thickness, they do not directly define how much the area increases for a given temperature change as the coefficient of surface expansion does. This highlights the crucial role that the coefficient plays in understanding thermal expansion in engineering applications.