What Volume Of Silver Metal Will Have A Mass Of Exactly 2.5 Kg, Given That The Density Of Silver Is $10.5 , \text{g/cm}^3$?(Hint: Note The Units Of Mass Given And The Units Of Density.)

by ADMIN 188 views

What Volume of Silver Metal Will Have a Mass of Exactly 2.5 kg?

Understanding the Problem

To find the volume of silver metal with a mass of exactly 2.5 kg, we need to use the formula for density, which is given by:

Density = Mass / Volume

We are given the density of silver as $10.5 , \text{g/cm}^3$ and the mass as 2.5 kg. However, the units of mass given are in kilograms, while the units of density are in grams per cubic centimeter (g/cm^3). We need to convert the mass from kilograms to grams to match the units of density.

Converting Mass from Kilograms to Grams

Since 1 kilogram is equal to 1000 grams, we can convert the mass of 2.5 kg to grams as follows:

Mass (in grams) = 2.5 kg x 1000 g/kg = 2500 g

Using the Formula for Density

Now that we have the mass in grams, we can use the formula for density to find the volume of silver metal:

Density = Mass / Volume

Rearranging the formula to solve for volume, we get:

Volume = Mass / Density

Substituting the values, we get:

Volume = 2500 g / 10.5 g/cm^3

Calculating the Volume

To calculate the volume, we can divide the mass by the density:

Volume = 2500 g / 10.5 g/cm^3 = 238.1 cm^3

Conclusion

Therefore, the volume of silver metal with a mass of exactly 2.5 kg is approximately 238.1 cubic centimeters.

Understanding the Significance of Density

Density is a measure of how much mass is packed into a given volume of a substance. In this case, the density of silver is 10.5 g/cm^3, which means that for every cubic centimeter of silver, there are 10.5 grams of mass. This is a relatively high density, which is why silver is a dense metal.

Real-World Applications of Density

Density is an important property in many real-world applications, including:

  • Materials Science: Density is used to determine the properties of materials, such as their strength, durability, and thermal conductivity.
  • Engineering: Density is used to design and optimize systems, such as bridges, buildings, and machines.
  • Geology: Density is used to determine the composition and structure of rocks and minerals.
  • Biology: Density is used to study the properties of living organisms, such as their buoyancy and movement.

Conclusion

In conclusion, the volume of silver metal with a mass of exactly 2.5 kg is approximately 238.1 cubic centimeters. This calculation demonstrates the importance of density in determining the properties of materials and its applications in various fields.

Additional Resources

For more information on density and its applications, please refer to the following resources:

  • National Institute of Standards and Technology (NIST): Provides information on density and its applications in various fields.
  • American Society for Testing and Materials (ASTM): Provides standards and guidelines for measuring density and its applications.
  • International Union of Pure and Applied Chemistry (IUPAC): Provides information on density and its applications in chemistry.

References

  • CRC Handbook of Chemistry and Physics: Provides information on density and its applications in various fields.
  • Kittel, C. (2005). Introduction to Solid State Physics. Wiley.: Provides a comprehensive introduction to solid-state physics, including density and its applications.
  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. Wiley.: Provides a comprehensive introduction to physics, including density and its applications.
    Frequently Asked Questions (FAQs) About Density and Its Applications

Q: What is density, and why is it important?

A: Density is a measure of how much mass is packed into a given volume of a substance. It is an important property because it determines the behavior of a substance in various situations, such as its buoyancy, thermal conductivity, and strength.

Q: How is density measured?

A: Density is typically measured by dividing the mass of a substance by its volume. This can be done using a variety of methods, including displacement, buoyancy, and direct measurement.

Q: What are some common applications of density?

A: Density has many applications in various fields, including:

  • Materials Science: Density is used to determine the properties of materials, such as their strength, durability, and thermal conductivity.
  • Engineering: Density is used to design and optimize systems, such as bridges, buildings, and machines.
  • Geology: Density is used to determine the composition and structure of rocks and minerals.
  • Biology: Density is used to study the properties of living organisms, such as their buoyancy and movement.

Q: How does density affect the behavior of a substance?

A: Density affects the behavior of a substance in various ways, including:

  • Buoyancy: A substance with a density less than that of water will float, while a substance with a density greater than that of water will sink.
  • Thermal Conductivity: A substance with a high density will typically have a high thermal conductivity, meaning it can conduct heat well.
  • Strength: A substance with a high density will typically be stronger than a substance with a low density.

Q: Can density be changed?

A: Yes, density can be changed by altering the mass or volume of a substance. For example, a substance can be compressed to increase its density, or it can be expanded to decrease its density.

Q: How does temperature affect density?

A: Temperature can affect density by causing a substance to expand or contract. In general, a substance will expand when heated and contract when cooled, which can change its density.

Q: What are some common mistakes to avoid when working with density?

A: Some common mistakes to avoid when working with density include:

  • Not accounting for temperature changes: Temperature changes can affect the density of a substance, so it's essential to account for these changes when working with density.
  • Not using the correct units: Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm^3).
  • Not considering the effects of pressure: Pressure can affect the density of a substance, so it's essential to consider these effects when working with density.

Q: What are some real-world examples of density in action?

A: Some real-world examples of density in action include:

  • Buoyancy: A ship will float if it has a density less than that of water, while a submarine will sink if it has a density greater than that of water.
  • Thermal Conductivity: A metal with a high density will typically have a high thermal conductivity, meaning it can conduct heat well.
  • Strength: A metal with a high density will typically be stronger than a metal with a low density.

Q: How can I learn more about density and its applications?

A: There are many resources available to learn more about density and its applications, including:

  • Online tutorials and videos: Websites such as Khan Academy and 3Blue1Brown offer interactive tutorials and videos on density and its applications.
  • Books and textbooks: There are many books and textbooks available on density and its applications, including "Introduction to Solid State Physics" by Charles Kittel and "Fundamentals of Physics" by David Halliday, Robert Resnick, and John Walker.
  • Professional organizations: Professional organizations such as the American Society for Testing and Materials (ASTM) and the International Union of Pure and Applied Chemistry (IUPAC) offer resources and information on density and its applications.

Conclusion

Density is a fundamental property of matter that has many important applications in various fields. By understanding density and its effects, we can better design and optimize systems, predict the behavior of substances, and solve real-world problems.