Density Notes

Density

Definition of Density

  • Density is defined as a physical quantity that measures the amount of matter per unit volume of a substance.
  • Represented by the Greek letter Rho (symbol: ρ).
  • Different pure substances have different densities, which can help identify or characterize them.

Properties of Density

  • Density is a characteristic property of a substance, which means it does not change regardless of the size or shape of the object.
  • Example: The density of lead remains constant, regardless of how much lead you have.

Formula for Density

  • The formula to calculate density is: ρ=mV\rho = \frac{m}{V} where:
    • ρ\rho is the density in kilograms per cubic meter (kg/m³)
    • mm is the mass in kilograms (kg)
    • VV is the volume in cubic meters (m³)

Units of Density

  • The SI unit for density is kilograms per cubic meters (kg/m³).
  • A commonly used unit for density, especially in chemistry and related fields, is grams per cubic centimeter (g/cm³).

Applications of Density Calculations

  1. Density of a Glass Piece:

    • Mass = 0.25 kg
    • Volume = 100 cm³ (convert to m³: 100 cm³ = 0.0001 m³)
    • Density:
      ρglass=0.25 kg0.0001 m3=2500 kg/m3\rho_{glass} = \frac{0.25 \text{ kg}}{0.0001 \text{ m}^3} = 2500 \text{ kg/m}^3

  2. Density of Water:

    • Mass = 1000 g (convert to kg: 1000 g = 1 kg)
    • Volume = 1 L (convert to cm³: 1 L = 1000 cm³)
    • Density:
      ρwater=1000 g1000 cm3=1 g/cm3\rho_{water} = \frac{1000 \text{ g}}{1000 \text{ cm}^3} = 1 \text{ g/cm}^3

Unit Conversions

  • To convert between kg/m³ and g/cm³:
    • Multiply by 1000:
    • from kg/m³ to g/cm³:  multiply by 11000\text{from kg/m³ to g/cm³: } \text{ multiply by } \frac{1}{1000}
    • Divide by 1000:
    • from g/cm³ to kg/m³:  multiply by 1000\text{from g/cm³ to kg/m³: } \text{ multiply by } 1000

Unit Conversion Examples

  1. Density of Iron:

    • Given: ρiron=7800 kg/m3\rho_{iron} = 7800 \text{ kg/m}^3
    • Convert to g/cm³:
      ρiron=7800 kg/m31000=7.8 g/cm3\rho_{iron} = \frac{7800 \text{ kg/m}^3}{1000} = 7.8 \text{ g/cm}^3

  2. Density of Glass:

    • Given: ρglass=2.6 g/cm3\rho_{glass} = 2.6 \text{ g/cm}^3
    • Convert to kg/m³:
      ρglass=2.6 g/cm3×1000=2600 kg/m3\rho_{glass} = 2.6 \text{ g/cm}^3 \times 1000 = 2600 \text{ kg/m}^3

  3. Density of Water:

    • Given: ρwater=1000 kg/m3\rho_{water} = 1000 \text{ kg/m}^3
    • Convert to g/cm³:
      ρwater=1000 kg/m31000=1 g/cm3\rho_{water} = \frac{1000 \text{ kg/m}^3}{1000} = 1 \text{ g/cm}^3

  4. Density of Mercury:

    • Given: ρmercury=13.6 g/cm3\rho_{mercury} = 13.6 \text{ g/cm}^3
    • Convert to kg/m³:
      ρmercury=13.6 g/cm3×1000=13600 kg/m3\rho_{mercury} = 13.6 \text{ g/cm}^3 \times 1000 = 13600 \text{ kg/m}^3