Specific Heat Capacity

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 5.2 — Use the unit J/kg °C (bold P statement — Paper 2 only)
• 5.12 — Specific heat capacity defined, in J/kg °C (bold P statement — Paper 2 only)
• 5.13 — Use Q = m × c × ΔT (bold P statement — Paper 2 only)
• 5.14 — Practical: investigate the specific heat capacity of water and some solids (bold P statement — Paper 2 only) (required practical)

Specification section 5(b) Density and pressure — also taught in Density, Pressure, and Pressure in Liquids, Particles and Changes of State.

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

On a hot day the sand is unbearable underfoot while the sea a few metres away is cold enough to make you gasp. Both have been in the same sunshine for the same hours. The difference is that sand and water need very different amounts of energy to warm up by the same amount, and the quantity that measures this is SPECIFIC HEAT CAPACITY.

The definition is worth learning exactly, because it is a mouthful and every word earns its place: the specific heat capacity of a substance is the energy required to raise the temperature of ONE KILOGRAM of it by ONE DEGREE CELSIUS. The unit follows straight from the definition — joules per kilogram per degree Celsius, J/kg °C, which statement 5.2 asks for by name.

Water has an unusually high specific heat capacity: about 4200 J/kg °C. Sand is around 800, and most metals are lower still — copper is about 385. So warming a kilogram of water by one degree takes more than five times as much energy as warming a kilogram of sand, which is exactly why the beach heats up in an hour and the sea takes all summer.

Think of it like filling containers of different widths

Imagine pouring water at a steady rate into a narrow measuring cylinder and into a wide bucket. The level in the cylinder shoots up; the level in the bucket barely moves. Nothing about the pouring differs — what differs is how much water each container needs per centimetre of level. Specific heat capacity is that width. Sand is the narrow cylinder: a little energy and the temperature leaps. Water is the bucket: pour energy in all day and the level creeps. And the analogy carries over to cooling, too, which is the half people forget — the bucket takes just as long to empty, which is why the sea is still relatively warm in October when the sand has long gone cold.

The equation is Q = m × c × ΔT, where Q is the energy transferred in joules, m is the mass in kilograms, c is the specific heat capacity in J/kg °C, and ΔT is the CHANGE in temperature in degrees Celsius. That triangle symbol simply means 'change in' — it is the final temperature minus the starting temperature, not the temperature itself, and using 80 °C rather than a 60 °C rise is one of the most common errors in the topic.

The equation used forwards and backwards

(a) How much energy is needed to heat 2.5 kg of water from 20 °C to 80 °C? Take c as 4200 J/kg °C. (b) A 0.50 kg block of metal is given 9000 J and rises by 40 °C. Find its specific heat capacity.

1. (a) ΔT = 80 − 20 = 60 °C. Note this is a CHANGE, not a temperature.
2. Q = m × c × ΔT = 2.5 × 4200 × 60 = 630 000 J.
3. (b) Rearrange: c = Q ÷ (m × ΔT) = 9000 ÷ (0.50 × 40) = 9000 ÷ 20.
4. = 450 J/kg °C, which is close to the value for iron.

Answer: 630 000 J, and a specific heat capacity of 450 J/kg °C.

The high specific heat capacity of water has consequences well beyond the beach. It makes water an excellent coolant, which is why it circulates through car engines and power stations — it can absorb a great deal of energy without its own temperature rising much. It moderates the climate of coastal regions, which have milder winters and cooler summers than places inland at the same latitude. And it is why a hot-water bottle works: a kilogram of water at 60 °C holds far more energy to give out than a kilogram of almost anything else at the same temperature.

A word about the practical, because there is a systematic error in it that cannot be removed and must instead be discussed. When you heat a block with an electric heater and measure the energy supplied, some of that energy inevitably warms the surroundings and the thermometer and the heater itself rather than the block. So the energy actually delivered to the block is LESS than the energy you measured — which makes the calculated specific heat capacity come out TOO HIGH. Insulating the block reduces it; nothing removes it entirely.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

Q = m × c × ΔT

Q is the energy transferred in joules (J), m is mass in kilograms (kg), c is specific heat capacity in J/kg °C, ΔT is the CHANGE in temperature in °C

Units: J, kg, J/kg °C, °C. Rearranged: c = Q ÷ (m × ΔT) and ΔT = Q ÷ (m × c). ΔT is a change, not a temperature.

Learn this definition · Specific heat capacity

The energy required to raise the temperature of one kilogram of a substance by one degree Celsius. It is measured in joules per kilogram per degree Celsius, J/kg °C.

Values worth recognising, and what follows from them

• WATER: about 4200 J/kg °C — unusually high, and the reason for most of what follows
• SAND: about 800 J/kg °C, so a beach heats and cools far faster than the sea beside it
• COPPER: about 385 J/kg °C; most metals are low, which is why a metal spoon heats quickly
• Water's high value makes it an excellent COOLANT in engines and power stations
• It also MODERATES COASTAL CLIMATES — milder winters and cooler summers than inland

Required practical 5.14 — measuring specific heat capacity

1. For a solid, take a metal block of known mass with holes drilled for an electric immersion heater and a thermometer.
2. Insulate the block, put a little oil in the thermometer hole for good thermal contact, and record the starting temperature.
3. Connect the heater through a joulemeter, or through an ammeter and voltmeter with a timer so that the energy can be calculated from E = I × V × t.
4. Switch on and record the temperature every minute for about ten minutes, then switch off and record the highest temperature reached.
5. Calculate the temperature rise, and use c = Q ÷ (m × ΔT).
6. For water, use a known mass of water in an insulated container with the same heater arrangement, stirring throughout.

Variables

Independent (changed) — The substance being heated
Dependent (measured) — The temperature rise produced for a measured energy input

Sources of error

Using Q = m × c × ΔT without going wrong

1. Work out ΔT as the CHANGE in temperature: final minus initial, not the final temperature.
2. Convert the mass to kilograms if it is given in grams.
3. Identify which quantity is missing and rearrange BEFORE substituting.
4. Substitute and calculate, keeping the units attached.
5. Check the answer is plausible: heating water takes large numbers of joules, because c is 4200.

Temperature against energy — why a spark does not burn you

A. TEMPERATURE is a measure of the average kinetic energy of the particles. A spark from a firework can be at over 1000 °C.

B. ENERGY transferred depends on the MASS as well, through Q = m × c × ΔT. A spark has almost no mass, so it carries almost no energy and cannot burn you — while a bath of water at 60 °C certainly can.

Model answer [4 marks]

Calculate the energy needed to raise the temperature of 3.0 kg of water from 15 °C to 45 °C. The specific heat capacity of water is 4200 J/kg °C. [4]

The change in temperature is ΔT = 45 − 15 = 30 °C. Using Q = m × c × ΔT, the energy needed is 3.0 × 4200 × 30 = 378 000 J.

Model answer [4 marks]

Explain why the sand on a beach becomes much hotter than the sea on the same sunny day. [4]

Sand has a much lower specific heat capacity than water — about 800 J/kg °C compared with 4200 J/kg °C. This means far less energy is needed to raise the temperature of a kilogram of sand by one degree than to raise a kilogram of water by the same amount. Both receive a similar amount of energy from the Sun, so from Q = m × c × ΔT the temperature rise of the sand is much greater than that of the water. The same property works in reverse at night, so the sand also cools much faster than the sea does.

Not this: Water heats up slowly because it is a poor conductor.

This: Conduction affects how fast energy SPREADS through it. What makes water slow to warm is its high SPECIFIC HEAT CAPACITY — it takes 4200 J to raise one kilogram by one degree, which is more than five times what sand needs.

Mark-losing trap. ΔT is the CHANGE in temperature — final minus initial. Not the final temperature.

Mark-losing trap. Mass must be in KILOGRAMS. A mass in grams gives an answer a thousand times too small.

Mark-losing trap. In the practical the calculated value comes out TOO HIGH, because some energy warms the surroundings.

Mark-losing trap. Water's c is about 4200 J/kg °C. Recognising that number explains coolants, climate and hot-water bottles.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · State [1 mark] — What is the unit of specific heat capacity?
2. Grade 7 · Explain [2 marks] — Explain why sand on a beach becomes much hotter than the sea on the same sunny day.
3. Grade 8 · Calculate [4 marks] — Calculate the energy needed to raise the temperature of 2.0 kg of water from 20 °C to 70 °C. The specific heat capacity of water is 4200 J/kg °C.
4. Grade 9 · Calculate [4 marks] — A 0.80 kg metal block is supplied with 14 400 J of energy and its temperature rises by 40 °C. Calculate the specific heat capacity of the metal.
5. 9+ · Analyse [6 marks] — A student measures the specific heat capacity of an aluminium block and gets 1100 J/kg °C, against an accepted value of 900 J/kg °C. Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one whose thermometry made the measurement possible at all, and the one who needed these numbers to build a working engine. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

James Prescott Joule — the one whose thermometry made the measurement possible at all

The practical on this page is essentially Joule's experiment with an electric heater instead of falling weights, and it depends on exactly the skill he was famous for: measuring very small temperature changes reliably. His paddle-wheel work required detecting a rise of a fraction of a degree, and his contemporaries dismissed the results partly because they did not believe thermometry that fine was possible. He is also the person who established that the electrical energy from a heater and the mechanical energy from a falling weight are the same currency, which is what lets the practical measure energy with a joulemeter at all.

• “How did you measure a temperature rise of a fraction of a degree?”
• “Why did other scientists doubt your thermometry?”
• “How do you know a heater delivers the energy you think it does?”
• “Where does the energy go that never reaches the thing you are heating?”
• “Why does the same work always produce the same warming?”

James Watt — the one who needed these numbers to build a working engine

Watt's decisive insight came from precisely this quantity. The Newcomen engine cooled its cylinder with water on every stroke and then reheated it with steam, and the metal's heat capacity meant most of the steam was consumed doing that rather than pushing the piston. He was working at Glasgow alongside Joseph Black, whose measurements of latent and specific heats were the framework he thought in — and the separate condenser is what you build once you can see how much energy the cylinder itself is swallowing.

• “How much of the steam was going into reheating the cylinder?”
• “What did Joseph Black's work tell you that you could use?”
• “Why does the heat capacity of the metal matter so much?”
• “How do you measure where an engine is losing its energy?”
• “What made you realise the cylinder had to stay hot?”

Carry on through the course

• Previous lesson: Particles and Changes of State
• Next lesson: Gas Pressure and Absolute Zero
• Density — Not how heavy something is, but how much of it is packed into the space it occupies.
• Pressure, and Pressure in Liquids — Why a drawing pin works, why pressure at a point pushes every way at once, and why depth is the only thing that matters underwater.
• Particles and Changes of State — What the particles are doing in each state — and why a boiling pan stays at 100 °C however hard you heat it.
• Gas Pressure and Absolute Zero — Where the pressure of a gas actually comes from, and why the temperature scale has to start somewhere else.
• The Kinetic Theory of Gases — One picture — fast random molecules bouncing off walls — that predicts everything a gas does.
• All of Physics · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification