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 $25.0^{\circ} \mathrm{C}^{2}$ The density of mercury at these temperatures is 13.596 $\mathrm{g} / \mathrm{cm}^{3}$ and 13.534 $\mathrm{g} / \mathrm{cm}^{3}$ , respectively.

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 $25.0^{\circ} \mathrm{C}^{2}$ The density of mercury at these temperatures is
13.596 $\mathrm{g} / \mathrm{cm}^{3}$ and 13.534 $\mathrm{g} / \mathrm{cm}^{3}$ , respectively.

Key Concepts

Thermal Expansion

Thermal expansion is the phenomenon in which a substance increases in volume as its temperature rises. In the context of the thermometer, the mercury expands when heated due to its increasing kinetic energy, with the expansion being reflected in a slight decrease in density. This change in volume is what leads to the mercury rising in the capillary tube.

Density

Density is defined as the mass of a substance per unit volume. In the given problem, the density of mercury changes with temperature, which implies that while the mass remains constant, the volume occupied by the mercury increases as the temperature rises. Understanding the relationship between density, mass, and volume is crucial for calculating the change in mercury's volume and, consequently, the height it rises in the capillary.

Capillary Geometry

Capillary geometry refers to the characteristics, specifically the cross-sectional area, of the narrow tube in which the mercury rises. The cross-sectional area, determined by the tube’s diameter, is used to relate a change in volume to a corresponding change in height. This geometric relationship allows one to convert the expanded volume of mercury into a measurable shift in its level within the capillary tube.

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