Discovering the Mass and Density of Mercury and Water: A Calculated Comparison

Understanding the Mass Density of Mercury and Its Applications

Mercury is a fascinating element, known for its unique physical properties such as its high density and its fluidity even at low temperatures. The mass density of mercury is a crucial characteristic that defines its physical behavior and its applications in various fields, including electronics, thermometers, and barometers. Mercury has a mass density of 13.6 grams per cubic centimeter (g/cm3). This property makes mercury particularly interesting, especially when comparing it with other substances like water.

Calculating the Volume and Mass of Mercury in a Cylinder

Consider a cylinder of mercury with a diameter of 1 cm and a height of 76 cm. To calculate its volume, we first note that the radius of the cylinder is half of the diameter, which is 0.5 cm. Using the formula for the volume of a cylinder, V πr2h, we can find the volume of the mercury cylinder.[ V_{mercury} π times (0.5 , text{cm})^2 times 76 , text{cm} ][ V_{mercury} π times 0.25 , text{cm}^2 times 76 , text{cm} ][ V_{mercury} ≈ 59.7 , text{cm}^3 ]Next, we can calculate the mass of this volume of mercury using its density:[ text{Mass of mercury} text{Volume} times text{Density} ][ text{Mass of mercury} 59.7 , text{cm}^3 times 13.6 , text{g/cm}^3 ][ text{Mass of mercury} 811.92 , text{g} ]

Comparing the Volume and Height of Water with the Same Mass

The question now is, what would the height of a cylinder of water with a diameter of 1 cm need to be, if it has the same mass as the mercury cylinder? Water has a much lower density compared to mercury, approximately 1 g/cm3.We already know the mass of the mercury cylinder is 811.92 grams. To find the volume of water with the same mass, we use the formula:[ text{Volume of water} frac{text{Mass}}{text{Density}} ][ text{Volume of water} frac{811.92 , text{g}}{1 , text{g/cm}^3} ][ text{Volume of water} 811.92 , text{cm}^3 ]Now, to find the height of this water cylinder, we use the volume formula for a cylinder, rearranged to solve for height:[ text{Height of water cylinder} frac{text{Volume}}{πr^2} ]The radius of the water cylinder is 0.5 cm, so we calculate:[ text{Height of water cylinder} frac{811.92 , text{cm}^3}{π times (0.5 , text{cm})^2} ][ text{Height of water cylinder} frac{811.92 , text{cm}^3}{π times 0.25 , text{cm}^2} ][ text{Height of water cylinder} ≈ frac{811.92 , text{cm}^3}{0.785 , text{cm}^2} ][ text{Height of water cylinder} ≈ 1020 , text{cm} ]Converting this height from centimeters to meters:[ text{Height of water cylinder} ≈ 10.20 , text{m} ]Interestingly, this is quite long and would indeed be taller than the average building.

Conclusion and Practical Applications

This exercise not only demonstrates the significant difference in the density of mercury and water but also highlights the practical implications of such differences. Mercury's high density is used in a variety of technical applications where high stability and precision are critical. In contrast, the low density of water makes it a more practical choice for many everyday uses, such as drinking, sanitation, and irrigation.Understanding these concepts can be crucial for students and professionals in various fields, including chemistry, physics, engineering, and environmental science. The ability to calculate and compare densities and volumes is essential for problem-solving and real-world applications.

Key Takeaways

- Mercury has a mass density of 13.6 g/cm3.- The volume of a 1 cm diameter 76 cm high mercury cylinder is approximately 59.7 cm3.- The height of a 1 cm diameter water cylinder with the same mass (811.92 g) is approximately 10.20 understanding these fundamental concepts, one can better grasp the unique properties of elements like mercury and their applications in practical scenarios.

For more detailed information on density, mass, volume, and their applications, refer to the following resources:

Density Density and Specific Gravity Density and Mass