Density

Definition of Density

Density is a measure of how much mass is contained in a given volume of a substance. It tells us how tightly packed the particles are.

Density is defined as:

$$\text{density} = \frac{\text{mass}}{\text{volume}}$$

The units of density are usually kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³). To convert between these units:

• 1 g/cm³ = 1000 kg/m³

For example, water has a density of about 1000 kg/m³ or 1 g/cm³.

Calculating Density

To calculate density, you need to measure the mass and volume of an object or substance.

• Mass is measured using a balance, usually in kilograms (kg) or grams (g).
• Volume can be measured in different ways depending on the object:
  • For regular-shaped objects (like cubes or spheres), calculate volume using measurements and geometric formulas. For example, volume of a cube = side³, volume of a cylinder = $\pi r^2 h$.
  • For irregular-shaped objects, use water displacement in a measuring cylinder to find volume.

Once you have mass and volume, use the formula:

$$\text{density} = \frac{\text{mass}}{\text{volume}}$$

For instance, if a block has a mass of 500 g and a volume of 200 cm³, its density is:

$$\text{density} = \frac{500 \text{ g}}{200 \text{ cm}^3} = 2.5 \text{ g/cm}^3$$

As a quick learning example, consider a block with mass 100 g and volume 50 cm³. Its density is $\frac{100}{50} = 2 \text{ g/cm}^3$.

Density and States of Matter

Density varies with the state of matter because the arrangement and spacing of particles change:

• Solids usually have the highest density because their particles are tightly packed in a fixed, orderly structure.
• Liquids have particles that are close together but can move around, so they are generally less dense than solids.
• Gases have particles that are far apart and move freely, making gases the least dense state of matter.

For example, ice (solid water) is less dense than liquid water, which is why ice floats. This is an exception to the general trend and is due to the structure of ice crystals.

Practical Determination of Density

Determining density is a required practical in AQA GCSE Physics. There are two common methods to find the density of an object depending on its shape:

Regular Objects

For objects with regular shapes (like cubes, spheres, cylinders):

• Measure the object's dimensions using a ruler or vernier caliper.
• Calculate the volume using the appropriate geometric formula (e.g., volume of a cube = side³, volume of a cylinder = $\pi r^2 h$).
• Measure the mass using a balance.
• Calculate density using the formula $\text{density} = \frac{\text{mass}}{\text{volume}}$.

Irregular Objects

For irregularly shaped objects:

• Measure the mass using a balance.
• Use a measuring cylinder filled with water to find the volume by water displacement:
  • Record the initial volume of water.
  • Submerge the object completely in the water.
  • Record the new volume of water.
  • The volume of the object = new volume − initial volume.
• Calculate density using the formula $\text{density} = \frac{\text{mass}}{\text{volume}}$.

This method works because the object displaces a volume of water equal to its own volume.