Changes of state and specific latent heat — AQA GCSE Combined Science

When a solid melts or a liquid boils, energy is transferred to the particles without raising the thermometer reading. This hidden energy is called latent heat. It increases the internal energy stored by the particles because their potential energy increases as bonds or intermolecular forces are overcome, while their average kinetic energy, and therefore temperature, stays constant. For example, ice at 0°C absorbs energy and becomes water at 0°C; the temperature does not rise until all the ice has melted. Similarly, steam at 100°C condenses to water at 100°C, releasing latent heat. The flat sections on a heating curve show these changes of state, where energy supplied changes internal energy but not temperature.

Specific latent heat is a property of a material that tells you how much energy is needed to change the state of one kilogram of it without changing its temperature. It is measured in joules per kilogram (J/kg). For example, the specific latent heat of fusion of ice is 334 000 J/kg, meaning 334 000 J are needed to melt 1 kg of ice at 0°C into water at 0°C. The specific latent heat of vaporisation of water is 2 260 000 J/kg. To calculate the energy required for a given mass, use E = m × L, where E is energy in joules, m is mass in kilograms and L is specific latent heat in J/kg. This applies to both melting/freezing and boiling/condensing, using the appropriate latent heat value.

When a substance melts, freezes, boils or condenses, its temperature stays constant even though energy is being transferred. That energy does not raise the average kinetic energy of the particles; instead it breaks or forms the intermolecular bonds that hold the particles in a particular arrangement. The energy needed per kilogram is the specific latent heat, L, and it differs for each material and for each change. Melting or boiling uses the specific latent heat of fusion or vaporisation respectively; freezing and condensing release the same amount per kilogram. To calculate, multiply the mass in kilograms by the specific latent heat in joules per kilogram. For example, melting 0.50 kg of ice (L = 3.34 × 10⁵ J/kg) needs 0.50 × 3.34 × 10⁵ = 1.67 × 10⁵ J.

This is the shorthand form of the energy equation for a change of state. E stands for the energy transferred in joules, m for the mass in kilograms and L for the specific latent heat in joules per kilogram. The equation applies only while the substance is changing state, so the temperature is constant and no temperature change term appears. Rearranged, L = E ÷ m gives the energy needed per kilogram, and m = E ÷ L gives the mass that a given energy can change. For example, if 6.0 × 10⁴ J vaporises 0.025 kg of a liquid, then L = 6.0 × 10⁴ ÷ 0.025 = 2.4 × 10⁶ J/kg. Always convert grams to kilograms and keep powers of ten consistent when substituting.

Energy is a measure of the capacity to do work or transfer heat, and in the context of changes of state it is the quantity transferred when a substance melts, boils, condenses or freezes without changing temperature. The symbol E stands for energy and the unit is the joule, J. One joule is the energy transferred when a force of one newton moves an object one metre, and it is also the energy needed to raise about 0.24 g of water by 1 °C. In specific latent heat calculations you use E = mL, where E is in joules, m is mass in kilograms and L is specific latent heat in J/kg. For example, melting 0.50 kg of ice with L = 3.34 × 10⁵ J/kg requires E = 0.50 × 3.34 × 10⁵ = 1.67 × 10⁵ J. Always convert kJ to J by multiplying by 1000 before substituting.

Mass is the amount of matter in an object and is measured in kilograms, kg. In specific latent heat calculations, m is the mass of the substance changing state, and it must be in kilograms so that the product mL gives energy in joules when L is in J/kg. One kilogram is 1000 grams, so 250 g is 0.25 kg. For example, to find the energy needed to boil 0.20 kg of water with L = 2.26 × 10⁶ J/kg, use E = mL = 0.20 × 2.26 × 10⁶ = 4.52 × 10⁵ J. Mass is not the same as weight; weight is a force in newtons, while mass in kg is constant anywhere. Always convert grams to kilograms before substituting into E = mL.

Specific latent heat, L, is the energy needed to change the state of one kilogram of a substance without changing its temperature. It is measured in joules per kilogram, J/kg. During a change of state, energy is transferred to or from the substance, but the temperature stays constant because the energy is used to overcome forces between particles rather than increase their kinetic energy. For example, melting 0.50 kg of ice requires energy E = mL. If L for ice is 334 000 J/kg, then E = 0.50 × 334 000 = 167 000 J. The same value of L applies when the substance changes back, so freezing releases energy. You must be able to use the equation E = mL, rearrange it, and interpret the unit J/kg as energy per kilogram.

The specific latent heat of fusion is the energy required to change 1 kg of a solid into a liquid at its melting point, without any change in temperature. It is a specific case of latent heat, measured in joules per kilogram, J/kg. For example, melting 2.0 kg of ice at 0 °C requires energy E = mL, where L is the specific latent heat of fusion of ice. If L = 334 000 J/kg, then E = 2.0 × 334 000 = 668 000 J. During melting, energy is transferred to the ice to break the forces holding the particles in a fixed lattice, allowing them to move more freely as a liquid. The temperature stays at 0 °C until all the ice has melted. The same amount of energy is released when the liquid freezes back to a solid.

Specific latent heat of vaporisation is the energy needed to change 1 kg of a substance from liquid to vapour at its boiling point, without any temperature change. During boiling, energy is transferred to the particles to overcome the forces holding them together in the liquid, so the particles separate into a gas. The energy supplied does not increase the average kinetic energy of the particles, so the thermometer reading stays constant. The specific latent heat of vaporisation, Lv, is calculated using E = m × Lv, where E is energy in joules, m is mass in kilograms and Lv is in J/kg. For example, vaporising 0.50 kg of water requires 0.50 × 2 260 000 = 1 130 000 J. This is much larger than the energy needed to melt the same mass of ice because vaporisation breaks all the intermolecular forces completely.

Heating and cooling graphs show how temperature changes with time as energy is transferred. A sloping section shows a temperature change in a single state, where the gradient depends on the mass, specific heat capacity and rate of energy transfer. A flat section, or plateau, shows a change of state at a constant temperature; here energy is used to break or form intermolecular forces rather than to change the average kinetic energy of the particles. On a heating graph, flat sections occur at the melting point and boiling point. On a cooling graph, flat sections occur at the condensing point and freezing point. The length of a plateau depends on the mass and the specific latent heat of the substance. For example, a pure ice sample heated steadily shows a plateau at 0 °C while melting and another at 100 °C while boiling.

Specific heat capacity and specific latent heat both describe energy transfer per unit mass, but they apply to different situations. Specific heat capacity, c, is the energy needed to raise the temperature of 1 kg of a substance by 1 °C without changing state, calculated using E = mcΔθ. Specific latent heat, L, is the energy needed to change the state of 1 kg of a substance without changing its temperature, calculated using E = mL. For example, heating 2 kg of water from 20 °C to 100 °C uses E = mcΔθ, while boiling that water at 100 °C uses E = mL. During a change of state, energy breaks or forms intermolecular bonds rather than increasing kinetic energy, so temperature stays constant.