Internal Energy, Specific Heat Capacity and Latent Heat
What is Internal Energy?
All matter is made up of particles that are constantly moving. The internal energy of a substance is the total energy stored by all the particles inside it. This energy comes from two sources:
- The kinetic energy of particles moving around (vibrating, rotating, or moving freely)
- The potential energy stored in the forces between particles
Internal energy increases when a substance is heated and decreases when it cools down. The internal energy determines both the temperature and the state of matter.
When you heat a substance, you transfer energy to it. This energy makes the particles move faster and can also change how they’re arranged. The amount of internal energy depends on the substance’s temperature, mass, and what material it’s made from.
Specific Heat Capacity
Different materials need different amounts of energy to heat up by the same amount. For example, water takes much more energy to heat up than copper. This property is called specific heat capacity.
The relationship between energy, mass, temperature change, and specific heat capacity is given by:
$$\Delta E = m \times c \times \Delta T$$
Where:
- \(\Delta E\) = change in thermal energy (J)
- \(m\) = mass (kg)
- \(c\) = specific heat capacity (J/kg°C)
- \(\Delta T\) = temperature change (°C)
Water has a very high specific heat capacity (4200 J/kg°C), which is why it’s good for heating systems and why coastal areas have milder temperatures than inland areas.
Materials with high specific heat capacity take more energy to heat up but also store more energy when hot. This makes them good thermal stores. Metals generally have lower specific heat capacities than water, which is why a metal spoon heats up quickly in hot soup.
Latent Heat and Changes of State
When you heat ice, something interesting happens. At first, the temperature rises as the ice warms up. But when it reaches 0°C, the temperature stops rising even though you’re still adding energy. Instead, the ice melts into water. This energy is called latent heat.
There are two main types of latent heat:
- Latent heat of fusion — energy needed to melt a solid or freeze a liquid
- Latent heat of vaporisation — energy needed to boil a liquid or condense a gas
The latent heat of vaporisation is always much larger than the latent heat of fusion for the same substance.
During a change of state, all the energy goes into breaking or forming bonds between particles rather than making them move faster. This is why the temperature stays constant during melting, boiling, condensing, or freezing.
The energy required for a change of state is calculated using: \(E = m \times L\), where \(E\) is energy (J), \(m\) is mass (kg), and \(L\) is the specific latent heat (J/kg).
Particle Model Explanation
The particle model helps explain these energy changes. In a solid, particles vibrate in fixed positions with strong forces holding them together. When heated, particles vibrate more vigorously, increasing the temperature.
Solid to liquid (melting): Energy breaks some bonds between particles. They can now slide past each other but stay close together.
Liquid to gas (boiling): Energy completely overcomes forces between particles. They move freely and far apart.
Gas to liquid (condensing): Particles lose energy and forces pull them back together.
Liquid to solid (freezing): Particles lose more energy and lock into fixed positions.
This model explains why gases take up much more space than liquids or solids, and why different substances have different melting and boiling points — it depends on how strong the forces between their particles are.