The big idea: A metal pan heats up in seconds on the hob, but a pan of water on the same ring takes ages to get hot — some things need far more energy to warm up than others.
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).
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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.
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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 |
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.
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How this is tested — Q = mcΔT is one of the most-used equations in Theme B:
Paper 1A
- Quick MCQs — 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.
The 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.
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.
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