Specific heat capacity (E = m c Δθ)
AQA GCSE Physics calculation · part of the free Calculation Climb
The energy to change something’s temperature: E = m c Δθ (mass × specific heat capacity × temperature change). Joules.
How to do it — step by step
- Work out the temperature change: Δθ = final − starting temperature. (This is the step examiners flag most — see below.)
- Check units: mass in kg (convert grams: ÷1000), energy in J (convert kJ: ×1000).
- E = m c Δθ. Rearrange when needed: m = E ÷ (c Δθ), or Δθ = E ÷ (m c).
- The equation is on the Physics Equations Sheet in the exam — you don't need to memorise it, you need to use it.
Worked examples — from real AQA papers
Straight substitution. Braking raises the temperature of a bicycle's brake pads by 50 °C. The pads have mass 0.040 kg and specific heat capacity 480 J/kg °C.
E = 0.040 × 480 × 50 = 960 J
Everything is already in the right units, so it's substitute-and-multiply for both marks.AQA GCSE Physics Paper 1, Foundation, 2018 — 2 marks
Find Δθ first. A kettle heats 0.50 kg of water from 20 °C to 100 °C (c = 4200 J/kg °C).
Δθ = 100 − 20 = 80 °C → E = 0.50 × 4200 × 80 = 168 000 J
The first mark is for Δθ = 80. Substituting 100 (the final temperature) instead of 80 (the change) is the classic error on this question type.AQA GCSE Physics Paper 1, Foundation, 2020 — 3 marks
Rearranging for the temperature change. A water tank holds 80 kg of water and the change in thermal energy is 8 400 000 J. Find the temperature change.
Δθ = 8 400 000 ÷ (80 × 4200) = 25 °C
The examiner report on this one is blunt: despite the equation being on the sheet and c given in the question, over 5% of students didn't attempt it and more than half scored zero. Write the equation down, substitute what you know, and rearrange — the method marks are there even if the arithmetic slips.AQA GCSE Combined Science Physics Paper 1, Foundation, 2021 — 3 marks
Higher tier: linked to power. A 2.53 kW coffee machine heats water from 20 °C to 90 °C. What mass of water can it heat in 14 seconds?
E = P t = 2530 × 14 = 35 420 J → m = 35 420 ÷ (4200 × 70) = 0.12 kg
Two equations chained: energy from power and time, then E = m c Δθ rearranged for mass. Higher papers like combining this calculation with P = E ÷ t or with efficiency.AQA GCSE Physics Paper 1, Higher, 2018 — 5 marks
Where students lose marks — from the examiner reports
- Using the final temperature instead of the temperature change. On the 2022 Foundation paper, students who put 62.5 °C into the equation instead of Δθ = 12.5 °C got 31 500 J instead of 6 300 J — and dropped the answer marks.
- Leaving the mass in grams. The 2021 deuterium question gave 4.0 g; the first mark was for converting to 0.004 kg. c is in J/kg °C, so the mass must be in kg.
- Leaving the energy in kJ. The 2022 Higher paper gave 10.5 kJ; converting to 10 500 J was the first mark.
- Not attempting it at all. The 2021 report notes over 5% left it blank even though the equation was on the sheet and c was in the question. This is one of the most attempt-friendly calculations on the paper.
- Misreading graph scales. The 2022 question made you read start and final temperatures off a cooling graph first; the report says students "struggled to interpret the scale", losing the first mark before the calculation began.
How often it comes up on AQA papers
From Science Street's database of real AQA questions, E = m c Δθ has appeared on these Paper 1s since 2018:
| Paper | Marks | What you had to do |
|---|---|---|
| Physics Paper 1 Foundation 2018 | 2 | Substitute: brake pads, E = 960 J |
| Physics Paper 1 Higher 2018 | 5 | Chain with P = E ÷ t, rearrange for mass → 0.12 kg |
| Physics Paper 1 Foundation 2020 | 3 | Δθ = 80 °C first, then E = 168 000 J |
| Physics Paper 1 Foundation 2021 | 3 | Convert 4.0 g → kg, then E = 1.04 × 10⁹ J (fusion) |
| Combined Science Physics Paper 1 Foundation 2021 | 3 | Rearrange for Δθ → 25 °C |
| Physics Paper 1 Foundation 2022 | 4 | Read Δθ = 12.5 °C off a graph, then E = 6 300 J |
| Physics Paper 1 Higher 2022 | 3 | Convert kJ → J, rearrange for mass → 0.125 kg |
The pattern: it lives on Paper 1, appears at both tiers, and the mark scheme almost always pays one mark for a unit conversion or for finding Δθ before the substitution. At Higher, expect it chained with power or efficiency. It also anchors the specific heat capacity required practical, so it can turn up inside practical questions too.
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