The coefficient of linear expansion of glass is 9.0 ×10^-6...

The coefficient of linear expansion of glass is $9.0 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1} .$ If a specific gravity bottle holds $50.000 \mathrm{~mL}$ at $15^{\circ} \mathrm{C}$, find its capacity at $25^{\circ} \mathrm{C}$.

Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change in size or volume in response to a change in temperature. When substances are heated, their constituent particles move more vigorously, typically resulting in an increase in dimensions. This concept is essential in understanding how objects like glass containers will expand or contract with changes in temperature.

Coefficient of Linear Expansion

The coefficient of linear expansion quantifies how much a material’s length changes per unit temperature change. It is given in units of inverse temperature (e.g., °C?¹) and allows prediction of how dimensions such as length or width will vary with temperature. This coefficient is particularly useful for describing expansion in solids along one dimension.

Volumetric Thermal Expansion

Volumetric thermal expansion refers to the change in volume of an object as its dimensions expand with temperature. For isotropic materials, where expansion is uniform in all directions, the volumetric expansion coefficient is approximately three times the linear expansion coefficient. This relationship helps in determining how the total capacity of a container changes with temperature.

Temperature Differential

The temperature differential is the difference between the initial and final temperatures of a system. It is a critical factor in calculating thermal expansion, as the extent of expansion is directly proportional to this temperature change. Understanding the temperature differential is necessary to accurately estimate the resulting dimensional or volumetric changes.

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