The density of gold is 19.30 g / cm^3 at 20.0^∘ C, and the...

The density of gold is $19.30 \mathrm{~g} / \mathrm{cm}^{3}$ at $20.0^{\circ} \mathrm{C}$, and the coefficient of linear expansion is $14.3 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$. Compute the density of gold at $90.0^{\circ} \mathrm{C}$. [Hint: Take a look at Problem 15.9.]

Key Concepts

Density and Its Temperature Dependence

Density is defined as mass per unit volume, and when temperature changes cause thermal expansion, the volume of the material changes while the mass remains constant. This leads to an inverse relationship between density and volume. As the temperature increases and the volume expands, the density correspondingly decreases. Understanding this relationship is vital when evaluating how material properties such as density vary with temperature.

Volume Expansion

Volume expansion describes the change in volume of a material as a function of temperature change. For isotropic materials, the volumetric expansion coefficient is typically approximated as three times the coefficient of linear expansion. This relationship is crucial because, while the material expands in all directions, the overall effect on volume—and consequently on properties like density—is derived from this three-dimensional scaling.

Thermal Expansion

Thermal expansion is the phenomenon by which the dimensions of a material change with temperature. When materials are heated, their particles move more vigorously, leading to an increase in distance between them and thereby causing the material to expand. Understanding thermal expansion is essential for predicting how objects will behave under temperature variations, and it is closely related to other concepts such as linear and volumetric expansion.

Coefficient of Linear Expansion

The coefficient of linear expansion quantifies the fractional change in length per unit change in temperature. It is specific to the material and indicates how much a unit length of the material will expand or contract when the temperature changes by one degree. This coefficient is a key parameter in calculating the overall dimensional changes of solids subjected to thermal variations.

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