Internal Energy, SHC and Latent Heat
Changes of State
Matter can change between three states — solid, liquid and gas. These are physical changes: they are reversible and no new substance is formed. Crucially, mass is conserved during any change of state — the same particles are present before and after; only their arrangement and spacing change.
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). Evaporation occurs at the surface of a liquid at any temperature — the fastest-moving particles at the surface escape as gas. Boiling occurs throughout the entire liquid at a specific temperature when enough energy is supplied. Evaporation causes cooling because the most energetic particles leave, reducing the average kinetic energy of those remaining.
Changes of state are physical, reversible changes that conserve mass. Evaporation occurs at the surface at any temperature; boiling occurs throughout the liquid at a fixed temperature. Both transfer particles from liquid to gas state.
Internal Energy
When you heat a substance, you increase its internal energy. Internal energy is the sum of the kinetic energy and potential energy of all the particles in the substance. 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 contributions from every particle.
Heating a substance can do one of two things. If the substance remains in the same state, the energy increases the kinetic energy of the particles — they move faster and the temperature rises. If a change of state is occurring, the energy instead increases the potential energy of the particles by breaking the forces between them (or forming them during cooling), and the temperature stays constant during this process.
A heating curve shows temperature on the y-axis against time (or energy supplied) on the x-axis. The graph has sloping sections, where temperature rises (kinetic energy of particles increases), and flat sections (plateaus), where the temperature stays constant while a change of state occurs (potential energy changes as bonds between particles are broken or formed).
The first plateau is at the melting point (solid changing to liquid). The second plateau is at the boiling point (liquid changing to gas). During each plateau, the substance exists as a mixture of two states. The length of each plateau depends on the specific latent heat of the substance for that change of state — a longer plateau means more energy is needed to complete the transition. The gradient of the sloping sections depends on the specific heat capacity — a shallower slope indicates a higher specific heat capacity (more energy per degree).
Specific Heat Capacity
Specific heat capacity (SHC) quantifies how much energy is needed to heat a given mass of 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 large amount of energy to heat it — which is why it is used in central heating systems and why coastal regions have more moderate climates than inland areas.
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 temperature change (°C). You must be able to rearrange this equation — for example, \(c = \frac{\Delta E}{m \times \Delta \theta}\) or \(\Delta \theta = \frac{\Delta E}{m \times c}\). Always check units before substituting.
Question: How much energy is needed to heat 2.0 kg of water from 20 °C to 80 °C? (SHC of water = 4200 J/(kg °C))
Answer: \(\Delta \theta = 80 - 20 = 60\) °C. \(\Delta E = m \times c \times \Delta \theta = 2.0 \times 4200 \times 60 = 504{,}000\) J = 504 kJ.
To investigate the SHC of a metal block: drill two holes in the block — one for a thermometer and one for an electrical immersion heater. Measure the block’s mass using a balance. Record the starting temperature, switch on the heater, and record the energy supplied using a joulemeter and the final temperature when heating is stopped. Rearrange to find \(c = \frac{\Delta E}{m \times \Delta \theta}\). The main source of error is heat lost to the surroundings; wrapping the block in insulating material (lagging) reduces this. This PAG also involves comparing the SHC of water and aluminium.
Specific heat capacity equation: \(\Delta E = mc\Delta\theta\). SHC is measured in J/(kg °C). Water has a high SHC (4200 J/(kg °C)), requiring a large energy input for a small temperature rise — making it ideal for central heating and thermal energy storage.
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 is no temperature change during the process — all the energy goes into breaking or forming the intermolecular forces between particles. There are two types:
• Specific latent heat of fusion (\(L_f\)) — the energy needed to change 1 kg of a substance from solid to liquid at its melting point (or released when it freezes). For water, \(L_f = 334{,}000 \text{ J/kg}\).
• Specific latent heat of vaporisation (\(L_v\)) — the energy needed to change 1 kg from liquid to gas at its boiling point. For water, \(L_v = 2{,}260{,}000 \text{ J/kg}\).
The latent heat of vaporisation is always much greater than the latent heat of fusion for the same substance, because particles must fully overcome the intermolecular forces to become a gas (much more energy is needed than just separating them partially as in melting). The equation relating thermal energy to a change of state is:
$$E = m \times L$$
Where \(E\) is the thermal energy for the change of state (J), \(m\) is mass (kg), and \(L\) is the specific latent heat (J/kg).
Question: How much energy is needed to completely melt 0.5 kg of ice at 0 °C? (\(L_f\) for water = 334 000 J/kg)
Answer: \(E = m \times L_f = 0.5 \times 334{,}000 = 167{,}000 \text{ J}\) (or 167 kJ). Note: the temperature stays at 0 °C throughout the melting process.
Specific heat capacity (SHC) — involves a temperature change, no state change: \(\Delta E = mc\Delta\theta\). Specific latent heat (SLH) — involves a change of state at constant temperature: \(E = mL\). The latent heat of vaporisation is always much larger than the latent heat of fusion.