Question

Assuming equal volumes, the expansion of solids is usually:

a) Linear
b) Exponential
c) Constant
d) Inverse

Answer 1

The expansion of solids under equal volumes and normal conditions tends to be linear, with each dimension increasing in proportion to the change in temperature, according to the coefficient of linear expansion (option a).

Step-by-step explanation:

The question relates to the expansion behavior of solids when subjected to a change in temperature. Assuming equal volumes and isotropic materials (ones that have no preferred direction of expansion), the expansion of a solid is usually linear. That is to say, each dimension of the solid increases by a proportion that is directly related to the change in temperature.

The formula for linear thermal expansion is ΔL = αLΔT, where ΔL is the change in length L, ΔT is the change in temperature, and α is the coefficient of linear expansion, which can vary slightly with temperature. When we consider the three-dimensional expansion of the solid, we find that the volume expansion is also proportional to the temperature change for most solids, given that the proportions of the solid do not change; only its overall size changes.

Hence, the answer is option a.

Answer 2

According to this statement option a) Linear is correct answer.

Step-by-step explanation:

The expansion of solids is generally linear, meaning that the change in length (ΔL) is directly proportional to the original length (L₀) and the change in temperature (ΔT). This relationship is expressed by the formula:

`\[ \Delta L = \alpha \cdot L₀ \cdot \Delta T \]`

where ΔL is the change in length, α (alpha) is the linear coefficient of expansion, L₀ is the original length, and ΔT is the change in temperature. The linear expansion equation indicates that the change in length is proportional to the original length and the temperature change.

The linear expansion behavior is observed in many materials, such as metals and solids, under normal temperature ranges. It is important to note that this linear relationship holds as long as the material does not undergo phase transitions or experience extreme temperature conditions that could alter its thermal behavior. In practical terms, linear expansion allows for the accurate prediction of dimensional changes in solids when subjected to temperature variations, making it a crucial concept in fields like engineering and materials science.

In summary, the expansion of solids is typically linear, and the linear coefficient of expansion (α) characterizes this behavior by describing how much the material's length changes for each degree of temperature change. This linear relationship simplifies calculations and predictions related to thermal expansion in various applications.