B1-1. Matter and Temperature

1. Solids, Liquids & Gases

The kinetic theory of matter attempts to explain the macroscopic properties of the three states of matter by considering the microscopic arrangement and motion of particles.

  • Solids: Particles are closely packed in a fixed, regular pattern (lattice structure). They have strong intermolecular forces and can only vibrate about their fixed positions. They have a fixed shape, fixed volume, and are difficult to compress.
  • Liquids: Particles are closely packed but arranged randomly. Intermolecular forces are weaker than in solids, allowing particles to flow past one another. Liquids take the shape of their container, have a fixed volume, and are difficult to compress.
  • Gases: Particles are far apart and randomly arranged. Intermolecular forces are negligible. Particles move rapidly in all directions at a variety of speeds. Gases have no fixed shape or volume, and are highly compressible.

2. Density

Density is a measure of how much mass is contained in a given volume of a substance.

Density Formula:

$$\rho = \dfrac{m}{V}$$
  • $\rho$: Density in kilograms per cubic metre (kg m⁻³)
  • $m$: Mass (kg)
  • $V$: Volume (m³)

Example 1: Understanding Density

If two objects occupy the exact same volume, the object with a lower density will have a lower mass. For example, a bucket completely filled with feathers will have a significantly lower mass than the exact same bucket filled with sand, because feathers have a much lower density ($\rho$) than sand.

3. Temperature Scales & Kinetic Energy

Temperature is a scalar quantity indicating how hot or cold an object is. Macroscopic temperature is directly linked to the microscopic motion of particles.

Conversion Formula:

$$T(\text{K}) = T(^\circ\text{C}) + 273.15$$

Note: A change in temperature ($\Delta T$) of $1^\circ\text{C}$ is exactly equal to a change of $1$ K.

The absolute temperature (in Kelvin) of a substance is directly proportional to the average random kinetic energy of its particles.

$$E_k = \dfrac{3}{2} k_B T$$
  • $E_k$: Average kinetic energy of a particle (J)
  • $k_B$: Boltzmann constant ($1.38 \times 10^{-23}$ J K⁻¹)
  • $T$: Absolute temperature (K)