Specific heat capacity
Some materials need far more energy than others to warm up by the same amount. Specific heat capacity puts a number on that, and one equation lets you find the energy, the mass, the temperature change or the specific heat capacity itself.
Part 1 of 3: Learn it
In short
- Specific heat capacity: the energy that warms 1 kg of a material by 1 °C.
- ΔE = m c Δθ, with Δθ the change in temperature, not the final temperature.
- In the practical, energy lost to the surroundings makes your value of c too high.
Where this is in your specification
Spec points: AQA 4.1.1.3 and its required practical, Edexcel Topic 14, OCR P1.2
| Board | Topic: Energy stores, transfers and efficiency |
|---|---|
| AQA 8463 | 4.1 (8463); 6.1 (8464) |
| Edexcel 1PH0 | Topics 3 and 8 (specific heat capacity: Topic 14) |
| OCR J249 | P7 and P8.2; P5 and P6.2 (specific heat capacity: P1.2) |
The equation
| Symbol | Quantity | Unit |
|---|---|---|
| ΔE | change in thermal energy | J |
| m | mass | kg |
| c | specific heat capacity | J/kg°C |
| Δθ | temperature change | °C |
The equation is on the equation sheet for AQA, Edexcel and OCR, and the question gives you the value of c. Water's is high, about 4200 J/kg°C, which is why a kettle takes minutes to boil while a metal pan heats up quickly (aluminium is about 900 J/kg°C, copper about 385 J/kg°C).
Rearranging
- Temperature change: Δθ = ΔE ÷ (m c)
- Mass: m = ΔE ÷ (c Δθ)
- Specific heat capacity: c = ΔE ÷ (m Δθ)
If a mass is given in grams, divide by 1000 first. If an energy is given in kJ, multiply by 1000.
The required practical
You measure c for a metal block (or water) by heating it with an electric heater and recording how its temperature rises.
- Measure the mass of the block on a balance and wrap it in insulation.
- Put the heater in one hole and a thermometer in the other.
- Record the starting temperature, switch on and start a stopwatch.
- Record the energy supplied (from a joulemeter, or from power × time) and the temperature at regular intervals.
- Work out c = ΔE ÷ (m Δθ), or plot temperature against energy supplied and use the gradient.
The independent variable is the energy supplied, the dependent variable is the temperature, and the mass of the block is kept the same. Edexcel calls this a core practical; AQA calls it a required practical.
How much energy does it take to heat 0.5 kg of water by 10 °C? (c = 4200 J/kg°C)
Show the answer
ΔE = 0.5 × 4200 × 10 = 21 000 J.
Part 2 of 3: See it worked
Worked examples
Example 1
A 2.0 kg aluminium block is heated from 20 °C to 45 °C. The specific heat capacity of aluminium is 900 J/kg°C. How much energy was transferred to the block?
- Δθ = 45 − 20 = 25 °C
- ΔE = m c Δθ = 2.0 × 900 × 25
- ΔE = 45 000 J
Answer: 45 000 J, which is 45 kJ.
Example 2
A 3 kW heater runs for 2 minutes and warms 1.5 kg of water. Assume all the energy goes into the water (c = 4200 J/kg°C). What is the temperature rise?
- Energy = power × time = 3000 × 120 = 360 000 J
- Δθ = ΔE ÷ (m c) = 360 000 ÷ (1.5 × 4200)
- Δθ = 360 000 ÷ 6300 = 57 °C (2 s.f.)
Answer: About 57 °C. In real life it would be a little less, because some energy heats the kettle and the air.
Common mistakes
- Putting the final temperature in for Δθ instead of the change.
- Leaving the mass in grams.
- Forgetting to change minutes to seconds before working out energy from power.
- Saying insulation makes the result 'more accurate' without saying why: it reduces energy lost to the surroundings, so less of the energy supplied is wasted.
- Expecting your measured c to be lower than the true value. Energy losses make it come out higher.
12 000 J raises the temperature of a 1 kg block by 30 °C. Find c.
Show the answer
c = 12 000 ÷ (1 × 30) = 400 J/kg°C.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
How much energy does it take to heat 0.5 kg of water by 10 °C? (c = 4200 J/kg°C)
ΔE = 0.5 × 4200 × 10 = 21 000 J.
12 000 J raises the temperature of a 1 kg block by 30 °C. Find c.
c = 12 000 ÷ (1 × 30) = 400 J/kg°C.
Why does wrapping the block in insulation improve the practical?
It reduces the energy transferred to the surroundings, so more of the energy supplied raises the block's temperature.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
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