Example 1: energy needed
How much energy heats 0.80 kg of water from 15 °C to 65 °C?
- ΔT = 65 − 15 = 50 °C.
- E = 0.80 × 4200 × 50 = 168 000 J.
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IB DemystifiedMYP Sciences
Specific heat capacity
On a summer afternoon the sand burns your feet while the sea stays cool, even though both have had the same sunshine. Different materials need very different amounts of energy to warm up, and that difference shapes climates, cooking and how we store energy.
Recommended for MYP 4 · eAssessment priority · About 3 lessons · Criteria A, B, C and D
On this page
- Learning objectives
- Before you start
- Key vocabulary
- Understanding specific heat capacity
- Using E = m × c × ΔT
- Specific heat capacity in the real world
- Worked examples
- In the eAssessment
- Check your understanding
- Practice questions
- Investigation
- Criterion-linked questions
- Challenge questions
- Topic check
- Review your mistakes
- Your progress
Learning objectives
By the end of this topic you should be able to:
- explain what specific heat capacity means and state its unit
- use E = m × c × ΔT, including rearranging it
- use energy = power × time with heating data
- measure specific heat capacity and explain why results differ from data-book values
- explain everyday and environmental effects of water's high specific heat capacity
- evaluate uses of thermal energy storage
Before you start
You will use these skills. If any feel shaky, review them first.
- thermal energy transfer (see Thermal energy transfer)
- energy = power × time (see Electrical power)
- rearranging equations
Key vocabulary
- Specific heat capacity (c)
- The energy needed to raise the temperature of 1 kg of a material by 1 °C, in J/kg °C.
- Temperature change (ΔT)
- Final temperature minus starting temperature.
- Thermal energy store
- Energy stored in an object because of its temperature.
- Joulemeter
- A meter that measures the electrical energy supplied, in joules.
- Thermal mass
- How much energy a large object can store, depending on its mass and specific heat capacity.
Understanding specific heat capacity
What is it?
Specific heat capacity tells you how much energy each kilogram of a material needs for each degree its temperature rises. Water needs 4200 J per kg per °C; copper needs only 385.
Why do materials differ?
When a material is heated, energy goes into making its particles move and vibrate faster. Materials differ in the mass and bonding of their particles, so the energy needed per kilogram per degree varies. Water's strong attractions between molecules give it an unusually high value.
How do we know?
An electric heater supplies a measured amount of energy (power × time, or a joulemeter reading) to a known mass, and the temperature rise is measured. Then c = E ÷ (m × ΔT). Joseph Black first distinguished heat from temperature in the 1760s.
Why does it matter?
Water's high specific heat capacity makes oceans moderate coastal climates, makes water an excellent coolant and store of energy, and helps keep our bodies at a steady temperature.
What does it connect to?
Specific heat capacity links to thermal transfer, power and efficiency in physics; to energy changes in reactions in chemistry; to body temperature in biology; and to climate and ocean currents in Earth science.
Using E = m × c × ΔT
E = m × c × ΔT, where E is energy (J), m is mass (kg), c is specific heat capacity (J/kg °C) and ΔT is temperature change (°C).
- To find energy: multiply. To find ΔT: ΔT = E ÷ (m × c). To find c: c = E ÷ (m × ΔT).
- With an electric heater, energy supplied = power × time (in seconds).
- Measured values of c are usually higher than data-book values, because energy is lost to the surroundings.
Specific heat capacity in the real world
Car engines are cooled by water pumped through them, and hot-water tanks store energy from solar heaters or cheap night-time electricity. Traditional buildings in hot, dry regions use thick walls with a large thermal mass to keep rooms cool by day and warm at night.
Worked examples
Example 2: finding c
A 2.0 kg block warms by 12 °C when a 60 W heater runs for 6 minutes. Find c.
- E = 60 × 360 = 21 600 J.
- c = 21 600 ÷ (2.0 × 12) = 900 J/kg °C (aluminium).
In the eAssessment
Specific heat capacity questions are usually calculations set in a practical or everyday context. Expect:
- Calculate and rearrange E = m × c × ΔT, often combined with energy = power × time.
- Interpret heating graphs, linking steepness to mass and specific heat capacity.
- Evaluate experiments, explaining why measured values are usually too high.
- Explain effects such as sea breezes, coastal climates and cooling systems.
Common ways to lose marks: confusing specific heat capacity with conductivity; using minutes instead of seconds; using the final temperature instead of the temperature change; and forgetting to convert grams to kilograms.
Check your understanding
Quick questions on the ideas above. Try each one before using a hint.
Practice questions
Investigation: does wet sand warm up more slowly than dry sand?
Partially guided investigation · about 50 minutes · pairs
- Research question
- How does the percentage of water mixed into sand (0, 10, 20 and 30% by mass) affect the temperature rise of 200 g of sand under a lamp in 15 minutes?
- Scientific background
- Water has a much higher specific heat capacity than dry sand, so adding water to sand should increase the energy needed to warm it. This helps explain why wet soils and beaches warm up more slowly.
- Hypothesis
- Write your own prediction, with a scientific justification.
- Variables
- Identify your independent, dependent and control variables, and explain how you will control them.
- Apparatus
- Dry sand, water, balance, four identical shallow dishes, a desk lamp (or sunlight), thermometers or temperature probes, stopwatch, ruler.
- Method
- Mix water into sand to make each percentage, and put 200 g of each mixture into a dish.
- Place the dishes the same distance under the lamp, with thermometers at the same depth.
- Record the temperature every 3 minutes for 15 minutes.
- Repeat and calculate the mean temperature rise for each mixture.
Safety. Lamps become hot: do not touch the bulb and keep water away from the lamp and cable. Wash hands after handling sand.
Then evaluate: apart from specific heat capacity, what else might make wet sand warm more slowly (think about evaporation)?
Criterion-linked questions
Criterion B: inquiring and designing
Criterion C: processing and evaluating
Criterion D: reflecting on the impacts of science
Challenge questions
Harder problems in unfamiliar contexts. Plan before you calculate.
Topic check
Five questions picked at random from the whole topic. Take a new set whenever you like.
Review your mistakes
Questions you got wrong on this device appear here so you can try them again. Answer one correctly and it leaves the list.
Your progress
Tracked separately for each skill, on this device only.
| Skill | Correct | Status |
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