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Specific heat capacity: formula and worked examples

Use the specific heat capacity equation to calculate the energy needed to heat a material, with worked examples and practice questions.

IntermediateUpdated 5 Nov 2026
GCSEHigh School

Curriculum fit: GCSE Physics and Combined Science (particle model of matter). US: high school physical science (energy and thermal properties).

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What is it?

Different materials need different amounts of energy to raise their temperature. The specific heat capacity of a substance is the energy needed to raise the temperature of 1 kg of it by 1 °C.

Water has a very high specific heat capacity, about 4200 J/kg°C. This means it takes a lot of energy to warm up, and it stores a lot of energy when hot.

Key formulas and ideas

  • Change in thermal energy ΔQ = mass × specific heat capacity × change in temperature.
  • ΔQ = m c Δθ (ΔQ in joules, m in kg, c in J/kg°C, Δθ in °C).
  • Rearranged: Δθ = ΔQ ÷ (m c) and c = ΔQ ÷ (m Δθ).

Worked examples

Example 1: Energy needed

Question: How much energy is needed to heat 2 kg of water by 10 °C? (c = 4200 J/kg°C)

  1. ΔQ = m c Δθ.
  2. = 2 × 4200 × 10 = 84 000.

Answer: 84 000 J

Example 2: Temperature rise

Question: 50 400 J is supplied to 3 kg of water. Find the temperature rise.

  1. Δθ = ΔQ ÷ (m c).
  2. = 50 400 ÷ (3 × 4200) = 50 400 ÷ 12 600 = 4.

Answer: 4 °C

Example 3: Aluminium

Question: How much energy heats 0.5 kg of aluminium from 20 °C to 60 °C? (c = 900 J/kg°C)

  1. Δθ = 60 − 20 = 40 °C.
  2. ΔQ = 0.5 × 900 × 40 = 18 000.

Answer: 18 000 J

Common mistakes

  • Using grams instead of kilograms.
  • Forgetting to subtract to find the temperature change.
  • Mixing up the symbols c (specific heat capacity) and C (Celsius).
  • Using the final temperature instead of the change.

Practice questions

1. Energy to heat 1 kg of water by 5 °C (c = 4200)?
2. Which unit is specific heat capacity measured in?
3. A 2 kg block gains 3600 J and its temperature rises by 2 °C. What is c?
4. A material with a high specific heat capacity will…
5. 0.5 kg of water, 8400 J added. Temperature rise?

Frequently asked questions

Why is water used in heating systems?

Its high specific heat capacity means it can carry a lot of thermal energy for a small temperature change.

How can you measure specific heat capacity?

Heat a known mass of material with an electric heater, record the energy supplied and the temperature rise, then use c = ΔQ ÷ (mΔθ).

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Sources and review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.