Mercury is often used in thermometers. The mercury sits in a...

Mercury is often used in thermometers. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains $3.380 \mathrm{~g}$ of mercury and has a capillary that is $0.200 \mathrm{~mm}$ in diameter. How far does the mercury rise in the capillary when the temperature changes from $0.0^{\circ} \mathrm{C}$ to $25.0^{\circ} \mathrm{C}$ ? The density of mercury respectively.

Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. In fluids, this expansion is governed by the coefficient of volumetric expansion, which relates the temperature change to the change in volume. This concept is essential for understanding how a change in temperature affects the volume of a liquid, such as mercury in a thermometer.

Density

Density is a measure of mass per unit volume and is used to determine the initial volume of a substance given its mass. In problems involving thermal expansion, knowing the density allows one to calculate the original volume of a liquid before any temperature-induced changes occur.

Geometric Volume Relationships

Geometric volume relationships involve using the dimensions of a container to determine how a change in volume translates to a change in another dimension, such as height. In the context of a capillary tube, the cross-sectional area is used to convert the expanded volume of the liquid into a rise in height.

Coefficient of Volumetric Thermal Expansion

The coefficient of volumetric thermal expansion quantifies the fractional change in volume per degree change in temperature. It is a key property used to calculate the expected volume change of a liquid when its temperature is altered, which then can be related to changes in observable dimensions in devices like thermometers.

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