Particles, Heating and the Particle Model
The Particle Model and States of Matter
The particle model explains the properties of solids, liquids and gases in terms of the arrangement and movement of particles. In a solid, particles are closely packed in a regular arrangement, vibrating about fixed positions — this explains why solids have a definite shape and volume. In a liquid, particles are close together but can move past each other — liquids have a definite volume but no fixed shape. In a gas, particles are widely spaced and move rapidly and randomly in all directions — gases have neither a fixed shape nor a fixed volume.
As a substance is heated, its particles gain energy and move faster (or vibrate more vigorously). Temperature is a measure of the average kinetic energy of the particles. The higher the temperature, the faster the average particle speed. This is why gases exert pressure — the constant collisions of particles with container walls create an outward force.
Temperature measures the average kinetic energy of particles. Internal energy is the total energy (kinetic + potential) of all the particles in the substance — it depends on both temperature and the amount of material.
Internal Energy and Specific Heat Capacity
Internal energy is the sum of the kinetic energy and potential energy of all particles in the system. When a substance is heated, energy is transferred into its internal energy store. This can either:
• Raise the temperature — particles move faster, increasing their average kinetic energy. The substance stays in the same state.
• Cause a change of state — particles gain potential energy to overcome attractions, and temperature stays constant during the change.
Different materials require different amounts of energy to raise their temperature by the same amount. This is captured by specific heat capacity (c). The equation is:
$$\Delta E = m \times c \times \Delta\theta$$
Where \(\Delta E\) is the change in thermal energy (J), \(m\) is mass (kg), \(c\) is specific heat capacity in J/(kg °C), and \(\Delta\theta\) is the temperature change in °C. Water has a high specific heat capacity (approximately 4 200 J/(kg °C)), which is why it is used in central heating systems — it can carry a large amount of thermal energy for its mass.
Question: A 2 kg block of aluminium (specific heat capacity 900 J/(kg °C)) is heated from 20 °C to 80 °C. Calculate the energy transferred.
Step 1: Temperature change: \(\Delta\theta = 80 - 20 = 60 \text{ °C}\)
Step 2: \(\Delta E = m \times c \times \Delta\theta = 2 \times 900 \times 60 = 108\,000 \text{ J}\)
Interpretation: This energy has been transferred from the heater's electrical energy store into the internal energy store of the aluminium block.
Changes of State and Specific Latent Heat
When a substance changes state (e.g. melts or boils), energy is transferred but the temperature does not change. The particles are gaining potential energy — not kinetic energy — to overcome the attractive forces holding them together. The energy required for a change of state is described by specific latent heat (L):
$$E = m \times L$$
Where \(E\) is energy in joules, \(m\) is mass in kg and \(L\) is specific latent heat in J/kg. There are two types: specific latent heat of fusion (melting/freezing) and specific latent heat of vaporisation (boiling/condensing). These values are much larger than those needed to raise temperature — it takes far more energy to evaporate water than to heat it from 0 °C to 100 °C.
The key changes of state are: melting (solid → liquid), freezing (liquid → solid), evaporation/boiling (liquid → gas), condensation (gas → liquid), and sublimation (solid directly to gas, as with dry ice). All changes of state are physical changes — they are reversible and no new substances are formed. Mass is always conserved.
Evaporation occurs at the surface of a liquid at any temperature — the fastest-moving particles at the surface have enough energy to escape as gas. Boiling occurs throughout the entire liquid at the specific boiling point. Evaporation causes cooling because the most energetic particles leave the liquid, reducing the average kinetic energy of the remaining particles. This is why sweating cools the skin — evaporation of sweat removes thermal energy from the body surface.
Limits of the Particle Model
The particle model is a very useful tool for explaining the behaviour of matter, but like all scientific models, it has limitations. The model treats particles as identical, hard, spherical objects with no internal structure. In reality, atoms and molecules have complex internal structures and interact through a range of forces. The model cannot fully explain phenomena such as surface tension, viscosity or the precise behaviour of real gases at very high pressures or very low temperatures. Recognising these limitations is part of good scientific thinking — models are tools, not perfect pictures of reality.
During a change of state, energy is transferred but temperature does not change. Specific latent heat describes this energy per kilogram. Specific heat capacity describes energy needed to change temperature without changing state.