The big idea: To make something hotter you have to give it energy.
The specific heat capacity (c) of a substance tells you how much energy it takes to warm 1 kg of it by 1 degree.
Unit: J kg⁻¹ K⁻¹ (joules per kilogram per kelvin: the energy to raise 1 kg by 1 K, i.e. 1 °C).
Big c vs small c: A big c means the substance is hard to heat up — it soaks up lots of energy per degree.
Water has a very big c (about 4200 J kg⁻¹ K⁻¹), so it warms and cools slowly. A metal has a small c, so it heats up fast.
The energy you need depends on three things: how much stuff there is (mass m), how hard it is to heat (c), and how big a temperature rise you want (ΔT).
Multiply them together:
- thermal energy added or removed (J)
- mass of the substance (kg)
- specific heat capacity (J kg⁻¹ K⁻¹)
- temperature change (K, or °C — same size)
ΔT is a temperature CHANGE: ΔT means final temperature − start temperature (the Greek letter Δ, 'delta', means 'change in').
A change of 1 K is the same size as a change of 1 degree C, so you can use either — never convert to kelvin for ΔT.
| Symbol | Quantity | Unit |
|---|---|---|
| Q | thermal energy added/removed | J (joules) |
| m | mass | kg |
| c | specific heat capacity | J kg⁻¹ K⁻¹ |
| ΔT | temperature change (final − start) | K or degrees C |
Worked example — energy to heat water
How much energy is needed to heat 0.50 kg of water from 20 degrees C to 80 degrees C? Water has c = 4200 J kg⁻¹ K⁻¹.
Solution
- Start with the given formula:
- Work out the temperature change first (ΔT = 80 − 20):
- Put in the numbers (m = 0.50, c = 4200, ΔT = 60):
- Work it out — keep the unit:
Final answer
Q = 1.26 × 10⁵ J (126 kJ).
Practice with real exam questions
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How this is tested: Q = mcΔT is one of the most-used equations in Theme B.
- Paper 1A: quick MCQs — e.g. compare the energy two substances need, or spot that ΔT in K equals ΔT in degrees C. - Paper 2: rearrange the formula to find an unknown — most often the specific heat capacity c from a heating experiment, sometimes the mass or the energy.
Classic trap: putting the actual temperature into ΔT instead of the change, or forgetting that cooling means Q comes out (negative).
Rearranging for c: To find a substance's specific heat capacity from an experiment, rearrange the given formula:
c = Q ÷ (m × ΔT) — energy supplied, divided by mass and by the temperature rise.
IB-style question — find the specific heat capacity
In an experiment, 9.0 × 10³ J of energy is supplied to a 0.40 kg block of aluminium. Its temperature rises by 25 K. Calculate the specific heat capacity of aluminium.
Solution
- Start with the given formula:
- Rearrange to make c the subject:
- Put in the numbers (Q = 9.0 × 10³, m = 0.40, ΔT = 25):
- Work it out — keep the unit:
Final answer
c = 9.0 × 10² J kg⁻¹ K⁻¹ (about 900 — the accepted value for aluminium).