What is the difference between coefficient of linear expansion (α) and coefficient of volume expansion (β)?

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Question restatement: What is the difference between coefficient of linear expansion (α) and coefficient of volume expansion (β)?

Option a: α is used for solids and liquids, β is for gases. This is inaccurate because α is typically defined for solids (and sometimes for liquids in a limited sense), but β is commonly associated with liquids and gases, not solids. The statement incorrectly assigns β to gases only and broadens α beyond its standard scope.

Option b: α is used for gases, β is for liquids and solids. This reverses the typical usage; α is not used for gases in standard contexts, and β is not defined for solids in the usual sense. The option contradicts the conventional definitions where α is linked to solids (and sometimes liquids) and β to liquids and gases.

Option c: α is used for solids, β is for liquids and gases. This aligns with standard practice: linear expansion coefficient α is defined for solids, describing how solid dimensions change with temperature. Volume expansion coefficient β (often denoted as γ or β in some texts) describes how volume changes and is especially relevant for liquids and gases where volumetric changes are more pronounced. This option matches the conventional distinctions between linear and volumetric expansion coefficients.

Option d: α is used for liquids, β is for solids and gases. This is inconsistent with the established definitions: α is not typically used for liquids, and β is not primarily described for solids. It misattributes the scope of both coefficients and would lead to incorrect application in calculations.

In summary, the core idea is that the linear expansion coefficient α characterizes dimensional changes in solids with temperature, while the volume (or volumetric) expansion coefficient β addresses volume changes in liquids and gases. The other options misassign the typical domains of α and β or reverse their conventional usage, leading to incorrect interpretations in practical problems.

UCIC 202503 PHYS101 Quiz 6

What is the difference between coefficient of linear expansion (α) and coefficient of volume expansion (β)?

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