A glass flask whose volume is 1000.00 cm^3 at 0.0^∘ C is completely filled with mercury at this

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A glass flask whose volume is 1000.00 cm^3 at 0.0^∘ C is...

A glass flask whose volume is $1000.00 \mathrm{~cm}^{3}$ at $0.0^{\circ} \mathrm{C}$ is completely filled with mercury at this temperature. When flask and mercury are warmed to $55.0^{\circ} \mathrm{C}, 8.95 \mathrm{~cm}^{3}$ of mercury overflow. Compute the coefficient of volume expansion of the glass. (Consult Tables $14.2 .)$

Key Concepts

Temperature Change

Temperature change is a fundamental driving force behind thermal expansion. The magnitude of the expansion of any material is directly proportional to the difference between the initial and final temperatures, making accurate temperature measurements essential in calculations involving expansion coefficients and volume changes.

Differential Expansion Between Container and Contents

In many practical scenarios, such as a fluid in a solid container, both the container and its contents expand when heated, but typically at different rates. Analyzing the overflow or deficit that occurs when the liquid and container expand differently enables the determination of one material's expansion coefficient when the other's behavior is known.

Thermal Expansion

Thermal expansion refers to the tendency of materials (solids, liquids, and gases) to change in volume in response to changes in temperature. When heated, most materials expand due to the increased kinetic energy of their molecules, and when cooled, they contract. This basic concept underpins many practical calculations in physics and engineering, such as determining the changes in dimensions of containers and the substances within them.

Coefficient of Volume Expansion

The coefficient of volume expansion is a material-specific constant that quantifies the fractional change in volume of a material per unit change in temperature. In solids, like glass, it describes how much the volume increases for each degree of temperature increase and is crucial for predicting how a container's capacity might change under different thermal conditions.

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