Changes of State and Internal Energy
Changes of State
Matter can change between three states — solid, liquid and gas. These are physical changes: they can be reversed, and the original properties of the substance are recovered. Crucially, mass is conserved during any change of state — no atoms are created or destroyed, they simply rearrange.
The key changes of state are: melting (solid to liquid), freezing (liquid to solid), evaporation/boiling (liquid to gas), condensation (gas to liquid), and sublimation (solid directly to gas, such as dry ice turning to carbon dioxide gas).
There is an important difference between evaporation and boiling. 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 a specific, fixed temperature (the boiling point) when enough energy is supplied. Evaporation causes cooling because the most energetic particles leave, reducing the average kinetic energy of those left behind.
Mass is conserved during all changes of state. Physical changes differ from chemical changes because the material recovers its original properties if the change is reversed.
Internal Energy and Heating
When you heat a substance, you increase the internal energy of the system. Internal energy is the total kinetic energy and potential energy stored by all the particles. It is important to distinguish between temperature and internal energy: temperature is a measure of the average kinetic energy of the particles, while internal energy includes both kinetic and potential energy contributions.
Heating can do one of two things:
• Raise the temperature — particles move faster (or vibrate more vigorously), increasing their kinetic energy. The substance stays in the same state.
• Cause a change of state — particles gain potential energy to overcome the forces of attraction between them, but the temperature stays constant during the change. All the energy goes into breaking (or forming) intermolecular bonds.
A heating curve shows temperature on the y-axis against time (or energy supplied) on the x-axis. The curve has sloping sections (temperature rising, kinetic energy of particles increasing) and flat sections (temperature constant, change of state occurring as potential energy increases).
The first flat section is at the melting point (solid to liquid). The second flat section is at the boiling point (liquid to gas). During these plateaus, the substance is a mixture of two states. The length of each flat section depends on the specific latent heat of the substance — a longer flat section means more energy is needed for that change of state.
The gradient of the sloping sections depends on the specific heat capacity: a material with a high SHC will have a gentler slope because it takes more energy per degree of temperature rise.
Specific Heat Capacity
Specific heat capacity (SHC) tells you how much energy is needed to heat up a material. Different materials require different amounts of energy for the same temperature rise. Water has a high SHC of 4200 J/kg °C, meaning it takes a lot of energy to heat — this is why water is used in central heating systems and why coastal areas have milder climates.
The equation linking energy change to temperature change 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 the specific heat capacity (J/kg °C), and \(\Delta \theta\) is the change in temperature (°C). You must be able to rearrange this equation — for example, to find the temperature change: \(\Delta \theta = \frac{\Delta E}{m \times c}\).
Question: How much energy is needed to heat 2 kg of water from 20 °C to 100 °C? (SHC of water = 4200 J/kg °C)
Answer: \(\Delta E = m \times c \times \Delta \theta = 2 \times 4200 \times (100 - 20) = 2 \times 4200 \times 80 = 672{,}000 \text{ J} = 672 \text{ kJ}\)
To investigate the SHC of a metal block: drill two holes in the block — one for a thermometer and one for an electrical heater. Measure the block's mass on a balance. Record the starting temperature, turn on the heater, and record the energy supplied (using a joulemeter) and the final temperature. Calculate \(c = \frac{\Delta E}{m \times \Delta \theta}\). The main source of error is heat loss to the surroundings — insulating the block with a lagging jacket reduces this.
Specific Latent Heat
Specific latent heat (SLH) is the energy needed to change the state of 1 kg of a substance at constant temperature. There are two types:
• Specific latent heat of fusion (\(L_f\)) — energy to change 1 kg from solid to liquid at the melting point. For water, \(L_f = 334{,}000 \text{ J/kg}\).
• Specific latent heat of vaporisation (\(L_v\)) — energy to change 1 kg from liquid to gas at the boiling point. For water, \(L_v = 2{,}260{,}000 \text{ J/kg}\).
The latent heat of vaporisation is always much larger than the latent heat of fusion for the same substance, because the particles must completely overcome the intermolecular forces to become a gas. The equation is:
$$E = m \times L$$
Where \(E\) is the thermal energy for a change of state (J), \(m\) is mass (kg), and \(L\) is the specific latent heat (J/kg).
During a change of state, energy is transferred but the temperature does not change. This energy goes into breaking or forming bonds between particles (changing potential energy), not increasing kinetic energy.
Gas Pressure and Temperature
In a gas, particles are constantly moving and colliding with the walls of their container, creating pressure. Each collision exerts a tiny force on the wall. The total of all these collisions across the entire wall produces the overall gas pressure.
If you heat a gas at constant volume, the particles gain kinetic energy and move faster. This has two effects: collisions with the walls become more frequent and each collision is more forceful. Both factors increase the gas pressure. This is a qualitative relationship only at GCSE — you need to explain the trend, not calculate pressure values.
This has real-world safety implications. Sealed containers (such as aerosol cans or gas cylinders) can be dangerous if heated, because the increasing pressure may exceed the strength of the container, causing it to explode. This is why aerosol cans carry warnings not to expose them to temperatures above 50 °C.