Thermal properties: specific heat capacity and latent heat

What you'll learn

This topic explores how substances respond when thermal energy is transferred to or from them. You'll learn why different materials require different amounts of energy to change temperature, and why energy is needed during changes of state even when temperature remains constant. These concepts underpin everything from calculating energy requirements for heating water to understanding the cooling effects of evaporation.

Key terms and definitions

Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K), measured in J/(kg °C) or J/(kg K)

Latent heat — the energy absorbed or released when a substance changes state at constant temperature, without changing the kinetic energy of the particles

Specific latent heat of fusion — the energy required to change 1 kg of a substance from solid to liquid (or released when liquid changes to solid) at constant temperature, measured in J/kg

Specific latent heat of vaporisation — the energy required to change 1 kg of a substance from liquid to gas (or released when gas changes to liquid) at constant temperature, measured in J/kg

Thermal energy — the total kinetic and potential energy of all particles in a substance

State change — a physical change where a substance transforms between solid, liquid and gas phases

Melting point — the fixed temperature at which a pure substance changes from solid to liquid

Boiling point — the fixed temperature at which a pure substance changes from liquid to gas throughout the bulk of the liquid

Core concepts

Energy and temperature change

When a substance absorbs thermal energy without changing state, its temperature increases. The amount of energy required depends on three factors:

• The mass of the substance (m) — more mass requires more energy
• The temperature change (Δθ or ΔT) — larger temperature changes require more energy
• The specific heat capacity (c) — different materials require different amounts of energy per kilogram per degree

The relationship is given by:

Energy transferred = mass × specific heat capacity × temperature change

E = m × c × Δθ

Where:

• E = energy transferred (J)
• m = mass (kg)
• c = specific heat capacity (J/(kg °C))
• Δθ = temperature change (°C or K)

Different substances have different specific heat capacities. Water has a particularly high specific heat capacity of 4200 J/(kg °C), meaning it requires substantial energy to heat up and releases substantial energy when cooling. This property makes water ideal as a coolant and explains why coastal regions experience more moderate temperatures than inland areas.

Common specific heat capacity values you should recognise:

Metals generally have low specific heat capacities, which is why metal objects heat up and cool down quickly compared to water.

Changes of state and latent heat

During a change of state, a substance absorbs or releases energy while remaining at constant temperature. This may seem counterintuitive, but the energy is used to break or form bonds between particles rather than increase their kinetic energy.

When a substance changes state:

Melting (solid → liquid):

• Energy is absorbed to overcome forces holding particles in fixed positions
• Temperature remains constant at the melting point
• Particles gain potential energy but not kinetic energy

Boiling (liquid → gas):

• Energy is absorbed to completely separate particles
• Temperature remains constant at the boiling point
• Much more energy is required than for melting because particles must be completely separated

Freezing (liquid → solid):

• Energy is released as particles form fixed arrangements
• Temperature remains constant at the freezing point (same as melting point)

Condensing (gas → liquid):

• Energy is released as particles come closer together
• Temperature remains constant at the boiling point

The energy involved in changes of state is calculated using:

Energy transferred = mass × specific latent heat

E = m × L

Where:

• E = energy transferred (J)
• m = mass (kg)
• L = specific latent heat (J/kg)

For water:

• Specific latent heat of fusion = 334 000 J/kg (melting/freezing)
• Specific latent heat of vaporisation = 2 260 000 J/kg (boiling/condensing)

The specific latent heat of vaporisation is much larger than the specific latent heat of fusion because completely separating particles (liquid to gas) requires far more energy than simply allowing them to move past each other (solid to liquid).

Heating and cooling curves

A heating curve shows how temperature changes as a substance is heated continuously. Key features include:

Sloped sections:

• Temperature increases
• Energy increases kinetic energy of particles
• Gradient depends on specific heat capacity (steeper = lower specific heat capacity)

Horizontal sections (plateaus):

• Temperature stays constant
• Energy is used for changing state
• Length of plateau depends on specific latent heat (longer = higher specific latent heat)

A typical heating curve for water shows:

1. Ice heating from below 0 °C to 0 °C (slope)
2. Ice melting at 0 °C (horizontal)
3. Water heating from 0 °C to 100 °C (slope)
4. Water boiling at 100 °C (horizontal)
5. Steam heating above 100 °C (slope)

The plateau at 100 °C is much longer than at 0 °C because the specific latent heat of vaporisation is much greater than the specific latent heat of fusion.

Cooling curves show the reverse process, with temperature decreasing except during state changes where plateaus appear at the same temperatures.

Practical applications

Specific heat capacity applications:

The high specific heat capacity of water has numerous practical consequences:

• Central heating systems use water because it can store and transport large amounts of thermal energy
• Car cooling systems use water-based coolant to absorb engine heat effectively
• Coastal climates are moderated because oceans absorb heat in summer and release it in winter
• Storage heaters use materials with high specific heat capacity to store energy overnight

Latent heat applications:

Changes of state and latent heat effects are used in:

• Refrigeration — liquid refrigerant evaporates inside the fridge, absorbing latent heat from food and cooling it; the gas condenses outside, releasing heat
• Cooling by evaporation — perspiration evaporates from skin, absorbing latent heat and cooling the body; this is why sweating cools you down
• Steam burns — steam at 100 °C causes more severe burns than water at 100 °C because the steam releases large amounts of latent heat when it condenses on skin
• Freeze-drying — water sublimates directly from ice to vapour, removing water from foods while preserving structure

Energy conservation in thermal processes

In any thermal process, energy is conserved. The total energy input must equal the total energy transferred to substances and surroundings.

For example, when an electric kettle heats water:

Electrical energy input = energy increasing water temperature + energy lost to surroundings

If we assume no energy losses (ideal scenario):

Electrical energy = m × c × Δθ

In reality, some energy is transferred to the kettle itself, the surrounding air, and through the kettle walls.

When a substance cools and changes state:

Energy released by substance = energy transferred to surroundings

For ice melting in a warm room:

Energy absorbed by ice = m × L (for melting) + m × c × Δθ (for warming water formed)

Worked examples

Example 1: Calculating energy to heat water

Question: A kettle contains 1.5 kg of water at 20 °C. Calculate the energy required to heat the water to 100 °C. The specific heat capacity of water is 4200 J/(kg °C). [3 marks]

Solution:

Step 1: Identify the values

• m = 1.5 kg
• c = 4200 J/(kg °C)
• Δθ = 100 °C − 20 °C = 80 °C [1 mark]

Step 2: Use the equation E = m × c × Δθ [1 mark]

Step 3: Calculate E = 1.5 × 4200 × 80 E = 504 000 J (or 504 kJ) [1 mark]

Mark scheme notes: The mark for temperature change rewards showing the subtraction explicitly. Always include units in your final answer.

Example 2: Energy in state changes

Question: Calculate the total energy required to completely melt 0.5 kg of ice at 0 °C and then heat the resulting water to 20 °C. Specific heat capacity of water = 4200 J/(kg °C) Specific latent heat of fusion of ice = 334 000 J/kg [4 marks]

Solution:

Step 1: Calculate energy to melt ice E₁ = m × L E₁ = 0.5 × 334 000 E₁ = 167 000 J [1 mark]

Step 2: Calculate energy to heat water from 0 °C to 20 °C E₂ = m × c × Δθ E₂ = 0.5 × 4200 × 20 E₂ = 42 000 J [1 mark]

Step 3: Calculate total energy Total energy = E₁ + E₂ [1 mark] Total energy = 167 000 + 42 000 Total energy = 209 000 J (or 209 kJ) [1 mark]

Mark scheme notes: Questions involving multiple stages require clear separate calculations. Show that you understand the two distinct processes — changing state, then changing temperature.

Example 3: Comparing specific heat capacities

Question: Two blocks of metal, each with mass 2.0 kg, are heated using identical heaters for 5 minutes. Block A (aluminium) increases in temperature by 45 °C. Block B (copper) increases in temperature by 110 °C. Explain why the temperature changes are different even though the same energy is supplied to each block. [2 marks]

Solution:

The two metals have different specific heat capacities. [1 mark] Copper has a lower specific heat capacity than aluminium, so it requires less energy per kilogram per degree to change temperature, resulting in a larger temperature increase for the same energy input. [1 mark]

Mark scheme notes: "Explain" questions require reasoning, not just stating facts. You must link the difference in specific heat capacity to the effect observed.

Common mistakes and how to avoid them

• Confusing the two equations — Remember: E = m × c × Δθ is for temperature changes; E = m × L is for state changes. If temperature is changing, use specific heat capacity. If the substance is changing state at constant temperature, use latent heat.

• Using incorrect units — Always convert mass to kilograms and temperature to Celsius (or Kelvin). Energy will then be in joules. Check the units given in the question for specific heat capacity — they're usually J/(kg °C), not J/(g °C).

• Forgetting temperature stays constant during state changes — Students often write that temperature increases throughout heating. During melting and boiling, temperature remains constant while energy is absorbed. This is a key characteristic of changes of state.

• Mixing up fusion and vaporisation — Fusion relates to melting/freezing (solid ↔ liquid). Vaporisation relates to boiling/condensing (liquid ↔ gas). The specific latent heat of vaporisation is always much larger than fusion for the same substance.

• Not showing working clearly in multi-step calculations — When a question involves melting ice then heating water, or cooling steam then condensing it, calculate each stage separately and clearly label E₁, E₂, etc. This helps you gain method marks even if you make a calculation error.

• Ignoring the direction of energy transfer — When substances cool or condense, they release energy to surroundings. When substances warm or melt/boil, they absorb energy from surroundings. Use the context of the question to determine whether energy is gained or lost.

Exam technique for "Thermal properties: specific heat capacity and latent heat"

• Command word awareness — "Calculate" requires numerical working and a final answer with units (usually 3-4 marks). "Explain" requires reasoning that links cause and effect (usually 2-3 marks). "Describe" requires stating what happens without necessarily explaining why (usually 2 marks).

• Equation questions strategy — Write the equation in symbols first, then substitute values with units, then calculate. This structured approach gains method marks even if your final answer is incorrect. Always show Δθ = θ₂ − θ₁ explicitly when calculating temperature change.

• Multi-stage calculations — Questions combining heating and state changes are common. Break the problem into clear stages: (1) heating to melting/boiling point, (2) changing state, (3) further heating. Calculate energy for each stage separately before finding the total.

• Graph interpretation — Be prepared to identify melting and boiling points on heating curves, explain why plateaus occur, and relate gradient to specific heat capacity. Steeper gradients indicate lower specific heat capacity because temperature changes more rapidly for the same energy input.