Heat is energy, temperature is not: the fall of caloric
By the end of this lesson you will be able to
- Distinguish heat from temperature: temperature as a measure of the average kinetic energy of particles, heat as energy transferred because of a temperature difference.
- Explain, with the particle model, why a bath of warm water stores more thermal energy than a cup of boiling tea.
- Outline the caloric theory, the evidence from Rumford (1798) and Joule (1843–1850) that overturned it, and the meaning of the mechanical equivalent of heat.
- Convert between joules, kilojoules, calories and kilocalories, and calculate the energy transferred by a falling mass.
- Apply the rule that heat flows from hot to cold until the temperatures are equal, in everyday and unfamiliar situations.
The puzzle
A sparkler burns at about 1000 °C, yet a spark that lands on your hand barely stings. A bath of water at 40 °C is far cooler, yet leave a block of ice in it and the ice is gone in minutes; drop the same ice in front of a thousand sparks and it hardly melts. The spark is hotter. The bath does more. What is the difference between being hot and having a lot of heat?
Predict which of these pairs holds more thermal energy, and say what you are comparing when you decide: a cup of tea at 80 °C or a swimming pool at 25 °C; a red-hot needle or a mug of warm water; the air in a classroom at 30 °C or a 1 kg block of iron at 30 °C.
Compare your answer
The pool, the mug and the classroom air. Temperature tells you how fast the particles are moving on average; thermal energy also depends on how many particles there are and what they are made of. A pool has millions of times more water particles than a cup, so even though each one moves more slowly, the total energy stored is enormously greater. The needle is hot, but it is tiny. The classroom holds more energy than the iron block because the air has far more mass than 1 kg. This lesson separates the two words that everyday English mixes up.
The science — structured notes
1.1 Two words, two different things
Everyday English says “turn up the heat” when it means raise the temperature, and “it is 35 degrees of heat” when it means a hot day. Physics keeps the words apart, and the exam expects you to.
| Temperature | Heat | |
|---|---|---|
| What it is | A measure of how hot something is — of the average kinetic energy of its particles | Energy transferred from a hotter object to a cooler one because of the temperature difference |
| Unit | °C (or K) | J (joule) |
| Measured with | A thermometer | Calculated from a temperature change and a mass, or from the energy supplied |
| Depends on the amount of stuff? | No — a drop and a bath from the same kettle have the same temperature | Yes — the bath can transfer far more energy than the drop |
| Belongs to an object? | Yes — an object has a temperature | No — heat is energy on the move; an object stores thermal energy, it does not “contain heat” |
1.2 The particle picture
Every substance is made of particles that never stop moving: vibrating in a solid, sliding past each other in a liquid, flying freely in a gas. The faster they move, the higher the temperature. Temperature is a measure of the average kinetic energy of the particles. Not the total — the average. A single fast particle and a billion equally fast particles are at the same temperature.
The total energy stored in the motion and positions of all the particles is the object’s thermal energy (physicists call it internal energy). It depends on three things: the temperature, the mass, and what the substance is (Lesson 4 gives that third factor a name and a number).
A cup holds 0.2 kg of tea at 80 °C; a bath holds 100 kg of water at 40 °C. Compare them.
Temperature: the tea is hotter — its water particles have, on average, more kinetic energy than the bath’s.
Thermal energy: the bath stores far more, because it has 500 times the mass. Above room temperature (20 °C) the tea holds roughly 0.2 × 60 = 12 units of “mass × degrees” and the bath 100 × 20 = 2000 units — about 170 times as much.
Heat: put a cold spoon in each. The spoon in the tea warms further, because heat flows down the larger temperature difference; but the bath could warm ten thousand spoons before its temperature noticeably fell. The tea has the higher temperature; the bath has the larger store of energy.
A spark from a sparkler is at about 1000 °C. Explain, using particles, why it does not burn your skin the way a splash of water at 80 °C would.
Reveal answer
Temperature measures the average kinetic energy of the particles, and the spark’s iron particles are moving very fast — it is genuinely hot. But the spark has a mass of a fraction of a milligram, so the total energy it can transfer to your skin is tiny; it warms a speck of skin by a little and cools instantly. A splash of water at 80 °C is at a lower temperature but has a mass of grams — millions of times more particles — so it transfers thousands of times more energy into your skin before reaching equilibrium with it. Burns depend on energy transferred, not on temperature alone.
1.3 Caloric — the theory that almost worked
Until the 1840s most scientists thought heat was a substance: an invisible, weightless fluid called caloric that flowed from hot objects to cold ones. It was not a foolish idea. Caloric explained why heat flows downhill in temperature (like water flowing downhill), why a big object needs more of it to warm up, why things expand when heated (caloric squeezing between the particles), and why mixing hot and cold water gives a temperature in between. Its one iron rule was that caloric was conserved — it could move, but it could never be created.
That rule is what broke it. If caloric cannot be created, then rubbing two objects together can only release caloric already inside them — and there should be a limit to how much comes out.
| Year | Who | What they did | Why it hurt caloric |
|---|---|---|---|
| 1798 | Count Rumford (Benjamin Thompson), Munich | Watched cannon barrels being bored with a blunt drill; put a barrel in a box of water and turned it with horses — the water boiled in about two and a half hours | The heat kept coming for as long as the horses walked; a barrel cannot hold an endless supply of a fluid. Rumford concluded heat is motion. |
| 1799 | Humphry Davy, Cornwall | Rubbed two blocks of ice together and reported that they melted | Melting needs heat; nothing but friction supplied it |
| 1842 | Julius Robert Mayer, Germany | Calculated from the heating of gases that a fixed amount of work always gives a fixed amount of heat | The first published number for the exchange rate, though his paper was ignored |
| 1843–1850 | James Prescott Joule, Manchester | Measured the exchange rate directly: electric currents, water forced through pipes, and finally falling weights spinning a paddle wheel in water | Always the same answer: about 4.2 J of work for every calorie of heat. Work and heat were two faces of one thing — energy. |
1.4 The mechanical equivalent of heat — and the units
Joule’s result is usually written as: 4.18 J of work produces the same effect as 1 calorie of heat, where one calorie is the energy that warms 1 g of water by 1 °C. Today we simply say heat is energy and measure it in joules; the calorie survives on food labels and in nutrition.
| Unit | Symbol | Equals | Where you meet it |
|---|---|---|---|
| joule | J | The SI unit of energy: the work done by a 1 N force moving 1 m | All physics calculations |
| kilojoule | kJ | 1000 J | Food labels (first number), fuel, electricity |
| calorie | cal | 4.18 J — warms 1 g of water by 1 °C | Old chemistry and physics books |
| kilocalorie (food “Calorie”) | kcal | 1000 cal = 4180 J = 4.18 kJ — warms 1 kg of water by 1 °C | Food labels (second number), diet apps |
| kilowatt-hour | kWh | 3 600 000 J | Your BPC electricity bill |
A packet of biscuits says “per 100 g: 2100 kJ / 502 kcal”. Check that the two numbers agree, and find how many joules one biscuit (12 g) supplies.
Convert kilocalories to kilojoules: 502 kcal × 4.18 = 2098 kJ ≈ 2100 kJ. The label is consistent.
Energy per gram: 2100 kJ100 g = 21 kJ per gram.
One 12 g biscuit: 12 × 21 = 252 kJ = 252 000 J — enough to lift a 60 kg person about 400 m, if the body could turn all of it into work (it cannot; most becomes heat, which is why you get warm when you exercise).
In Joule’s apparatus two weights of total mass 10 kg fall 1.0 m, twenty times, spinning a paddle in 0.50 kg of water. Calculate the energy transferred and the temperature rise (g = 9.8 N/kg; 4180 J warms 1 kg of water by 1 °C).
Energy per drop = m × g × h = 10 × 9.8 × 1.0 = 98 J.
Twenty drops: 20 × 98 = 1960 J.
Energy needed per degree for 0.50 kg of water: 0.50 × 4180 = 2090 J per °C.
Temperature rise = 19602090 = 0.94 °C. Small — which is why a thermometer reading to 0.01 °C is needed, and why a single drop (0.05 °C) would be lost in the noise.
A cyclist uses 1200 kJ of energy from food in an hour of riding.
(a) Express this in kilocalories.
(b) Her body converts about a quarter of the food energy into useful work; the rest becomes heat. If the heat warmed 50 kg of water instead of her body, by how much would it rise?
(c) Explain why she sweats.
Reveal answer
(a) 1 200 000 J4180 J per kcal = 287 kcal ≈ 290 kcal.
(b) Heat = 0.75 × 1 200 000 = 900 000 J. For 50 kg of water, 50 × 4180 = 209 000 J is needed per degree, so the rise is 900 000209 000 = 4.3 °C.
(c) Her body is roughly 50 kg of water, so without cooling she would warm by over 4 °C an hour — a dangerous fever. Sweat evaporates from her skin, and evaporation takes energy from the skin (the fastest particles leave the liquid), carrying away the excess heat and holding her temperature near 37 °C.
1.5 Heat flows one way
Heat flows from a higher temperature to a lower one, and the flow stops when the temperatures are equal. “Cold” is not something that flows: a cold drink does not “let the cold out” — heat from the room flows in. A fridge does not make cold; it moves heat from the inside to the coils at the back, which is why the back of a fridge is warm.
| Situation | Hotter | Colder | Heat flows… | Ends when… |
|---|---|---|---|---|
| Ice in a drink | Drink (25 °C) | Ice (0 °C) | From drink into ice, melting it | All the ice has melted and the drink is at one temperature |
| Hand on a metal rail in winter | Hand (33 °C) | Rail (5 °C) | From hand into rail — fast, because metal conducts well | Never, in practice: the rail is huge and keeps taking heat |
| Kettle switched off | Water (100 °C) | Room (22 °C) | From water to the air, kettle body and table | Water reaches room temperature |
| Thermometer in a patient’s mouth | Mouth (37 °C) | Thermometer (22 °C) | Into the thermometer | Both at 37 °C — that is when you read it |
“When you hold an ice cube, cold flows from the ice into your hand.”
Reveal answer
False. Only heat flows, and only from hot to cold. Your hand at about 33 °C is hotter than the ice at 0 °C, so heat flows from your hand into the ice, melting it. Your hand feels cold because it is losing energy quickly; nothing is coming in. The correct phrasing is: “heat flows from my hand to the ice”.
Two identical copper blocks, one at 80 °C and one at 20 °C, are pressed together and wrapped in insulation. Predict the final temperature and describe what happens to the particles of each block. Then: what changes if the hot block has twice the mass of the cold one?
Reveal answer
Equal masses of the same material: the hot block loses exactly the energy the cold block gains, so the final temperature is midway, 50 °C. At the boundary the fast-vibrating copper particles of the hot block jostle the slower ones of the cold block and pass on energy; the hot block’s particles slow down on average, the cold block’s speed up, until the average kinetic energies match. With a hot block of twice the mass, the same temperature fall in the hot block releases twice the energy, so the cold block must rise twice as far as the hot block falls: it ends at 60 °C (the hot block falls 20 °C, the cold block rises 40 °C).
Try it — Joule’s paddle wheel
Wind up the weights and let them fall through 1.00 m; each drop spins the paddle and stirs the water. Change the number of drops from 0 to 20 in steps of 2 and read the thermometer to 0.01 °C. Then change the falling mass, and the mass of water, and see what each does to the gradient.
Suppose your means with 10 kg falling and 0.5 kg of water were: 0 drops → 0.00 °C, 4 → 0.19, 8 → 0.37, 12 → 0.57, 16 → 0.74, 20 → 0.94 °C.
(a) Describe the relationship, quoting values, and state whether it is proportional.
(b) Calculate the gradient and use it to find the energy per drop measured as heat. Compare with 98 J.
(c) Explain, at the particle level, how energy from a falling weight ends up as a temperature rise.
(d) Real values come out slightly below 98 J. Name one specific reason and say whether it is a random or a systematic error.
Reveal answer
(a) The temperature rise increases with the number of drops, from 0.00 °C at 0 drops to 0.94 °C at 20, by about 0.19 °C for every 4 drops. Doubling the drops from 8 to 16 doubles the rise from 0.37 to 0.74 °C, and the line passes through the origin, so the rise is directly proportional to the number of drops.
(b) Gradient = 0.94 − 0.0020 − 0 = 0.047 °C per drop. Energy per drop = 0.047 × 0.5 × 4180 = 98 J, matching m × g × h = 98 J. Work done by the falling weight equals heat gained by the water.
(c) The weight loses gravitational potential energy; the string turns the paddles; the paddles push against the water particles, making them move faster; the faster average motion of the water particles is a higher temperature. Energy has moved from a gravitational store to the kinetic energy of billions of particles, and nothing has been created or lost.
(d) Some of the water’s energy escapes to the copper can and the room air during the twenty drops (a systematic error: every reading is slightly low, and later readings more so), or the weights still have kinetic energy when they hit the floor, so not all m g h went into the paddle (systematic, all readings low). Friction in the pulley bearings is a third: the weights fall slower and warm the bearings rather than the water. Random errors — the thermometer read at a slightly different moment each time — scatter the points rather than shifting them.
Common mistakes to avoid
- “The object contains heat” — it stores thermal energy; heat is energy in transit because of a temperature difference.
- “Higher temperature means more heat energy” — a spark beats a bath on temperature and loses on energy; mass and material matter too.
- “Cold flows in” — only heat flows, from hot to cold; cold is the absence of it.
- “Temperature is the total energy of the particles” — it is the average kinetic energy; the total is the thermal energy.
- Calories and kilocalories — a food Calorie is a kilocalorie: 4180 J, not 4.18 J.
- “Rumford disproved caloric on his own” — his experiment raised the doubt; Joule’s numbers, fifty years later, settled it.
How we found out — a cannon in Munich and a brewer in Manchester
Benjamin Thompson was born in Massachusetts in 1753, spied for the British in the American War of Independence, fled to Europe, reorganised the Bavarian army and was made Count Rumford by the Elector of Bavaria. In 1798, supervising the boring of cannon at the Munich arsenal, he noticed how hot the brass became under a blunt drill. Caloric theory said the drill was squeezing caloric out of the brass shavings; Rumford noticed that the shavings, once cool, were exactly as capable of being heated as fresh brass — nothing had been squeezed out of them. He sealed a cannon barrel in a wooden box of water, set two horses turning a blunt borer against it, and waited. After two and a half hours the water boiled, “to the astonishment of the bystanders”, and the heat kept coming for as long as the horses walked. A fluid that could be supplied without limit, he wrote, could not be a material substance: heat must be a kind of motion.
It took another fifty years for the argument to be won, and the man who won it was not a professor but the son of a Manchester brewer. James Prescott Joule had been taught by the chemist John Dalton, had a laboratory in the brewery, and from 1843 set about measuring exactly how much work made how much heat. He drove currents through wires, forced water through narrow tubes, and finally, in 1845, built the apparatus in the lab above: falling weights spinning brass paddles in a copper can of water, with thermometers of his own design that read to a two-hundredth of a degree. Every method gave the same exchange rate, about 4.2 joules for each calorie. When he presented the result at Oxford in 1847 the chairman asked him to be brief; a young physicist in the audience, William Thomson (later Lord Kelvin), stood up and asked questions instead, and the two became collaborators. Joule is even said to have taken a thermometer on his honeymoon in the Alps to measure whether the water at the bottom of a waterfall was warmer than at the top. It is — by about a quarter of a degree for a 100 m fall — but the spray made it impossible to check. The unit of energy is named after him.
Rumford’s experiment and Joule’s both involved friction warming water. Explain why Joule’s was the more convincing evidence, referring to what each could and could not measure.
Reveal answer
Rumford showed that the supply of heat from friction had no limit, which contradicted the idea of a conserved fluid, but he could not say how much heat a given amount of work produced — his horses’ effort was unmeasured. A caloric theorist could still argue that something unknown was going on in the brass. Joule measured both sides of the exchange: the work (mass × g × height, known exactly) and the heat (mass of water × temperature rise, read to 0.005 °C), and found the same fixed rate whatever the method — falling weights, electric current, water through pipes. A fixed exchange rate between work and heat is what you expect if they are the same quantity, energy, in two forms; it is not what you expect from a fluid. Numbers that agree across different experiments are far harder to explain away than a single surprising observation.
Where it is used now
- Food and the body in Botswana and everywhere. Every food label carries kJ and kcal; a person needs roughly 8000–10 000 kJ a day, and the body turns most of it into heat — which is why a crowded classroom in Gaborone warms up even with the fans on.
- Morupule B power station, Palapye. Coal burns, the heat boils water, steam spins turbines: the whole plant is Joule’s experiment run backwards, heat into work, and only about a third of the heat becomes electricity — the rest is rejected to the air through the station’s air-cooled condensers, which Botswana uses in place of the wet cooling towers of wetter countries because water here is too scarce to evaporate.
- Brakes and bearings. A lorry descending the escarpment on the road from Francistown converts kinetic energy into heat in its brake discs, which can glow red; engineers size the discs from exactly the calculation in 1.4.
- Cooking with firewood. Much rural cooking in southern Africa still relies on wood, and a three-stone fire delivers only a tenth of its heat to the pot; improved stoves that direct more heat to the pot save fuel, time and trees.
- Calorimetry in industry. Food companies burn a sample in a sealed bomb calorimeter and measure the temperature rise of surrounding water to print the kJ on the label — Joule’s method, exactly.
Science now — and the scientist you need to be
What is happening in 2026
The largest new sources of waste heat on Earth are data centres. The chips running AI models turn almost all their electrical energy into heat, and a single large facility now needs as much cooling as a small town; the newest designs pump liquid directly over the processors and pipe the warm water into district heating, so that Joule’s exchange rate runs in both directions — electricity to heat in the server, heat to warm homes in the street outside. Heat pumps, which move heat from cold outdoor air into buildings using far less energy than they deliver, have overtaken gas boilers in several European countries, and the same technology cools buildings in Botswana’s summers. In physics laboratories, heat is measured at scales Joule could not have imagined: nanocalorimeters now detect energies of a few nanojoules from samples smaller than a grain of salt, and researchers are pushing that sensitivity towards the heat released by single molecules — not there yet, but closer every year. And the definition of the kilocalorie has not changed since Joule’s brewery — the apps that count them are still using his number.
The mindshift
What you need to be able to do
Criterion A questions in this unit start with the distinction between heat and temperature and expect the particle model in every explanation: average kinetic energy for temperature, energy transferred for heat, hot to cold until equal. Calculations use J, kJ and kcal, and the examiners’ reports single out unit conversion as the place marks are lost. The Think task below rehearses both.
See an example
Labels: maize meal 1530 kJ / 365 kcal (ratio 4.19), peanut butter 2530 kJ / 605 kcal (4.18), a fizzy drink 180 kJ / 43 kcal (4.19) — all consistent. Kettle: 1 litre took 3 min 10 s = 190 s at about 2000 W, so roughly 380 000 J = 380 kJ; warming 1 kg of water from 22 to 100 °C needs 78 × 4180 = 326 kJ, so about 85 % of the electrical energy went into the water and the rest into the kettle body and the air. The AI first said “heat is the energy an object has because of its temperature”; when challenged, it corrected itself to “thermal energy is stored; heat is energy transferred because of a temperature difference” — the version that earns the mark.
Key terms
| Temperature | A measure of how hot an object is: the average kinetic energy of its particles. Measured in °C or K with a thermometer. |
| Heat | Energy transferred from a hotter object to a cooler one because of the temperature difference between them. Measured in joules. |
| Thermal energy | The total energy stored in the motion and positions of an object’s particles; depends on temperature, mass and material. |
| Thermal equilibrium | The state in which two objects in contact are at the same temperature, so no net heat flows between them. |
| Caloric | The abandoned theory that heat is a conserved, weightless fluid flowing from hot to cold. |
| Mechanical equivalent of heat | The fixed exchange rate between work and heat measured by Joule: about 4.18 J per calorie. |
| Joule (J) | The SI unit of energy: the work done by a force of 1 N moving 1 m. |
| Calorie (cal) | The energy that warms 1 g of water by 1 °C; 4.18 J. |
| Kilocalorie (kcal) | 1000 calories, 4180 J; the “Calorie” on food labels. |
| Kinetic energy of particles | The energy of the particles’ motion — vibration, sliding or free flight — which rises with temperature. |
Think like a scientist
Criterion A A school in Maun runs a solar cooker for the boarding kitchen: a curved mirror focuses sunlight onto a black pot. On a clear day the pot receives about 600 W. The cook puts in 5.0 kg of water at 20 °C. A visitor says: “The mirror makes the sunlight hotter, so the pot fills up with heat until it boils.”
(a) State the difference between heat and temperature, and identify one error in the visitor’s sentence. [3]
(b) Explain, using the particle model, what happens inside the water as its temperature rises from 20 °C to 100 °C. [3]
(c) Calculate the energy needed to warm the 5.0 kg of water from 20 °C to 100 °C (4180 J warms 1 kg of water by 1 °C), and the minimum time the cooker would take at 600 W. Give your answer in minutes. [4]
(d) The cooker actually takes about 50 minutes. Explain why, referring to where the energy goes. [2]
(e) A cook notes that a 1 kg pot of maize porridge at 90 °C burns the hand far worse than a 0.05 kg cup of tea at 90 °C. Explain why, using the ideas of this lesson. [2]
(f) In the 1790s, caloric theory would have described the cooker as “collecting caloric from the Sun”. Outline one piece of experimental evidence that showed heat is not a conserved fluid, and explain why it was convincing. [3]
Model answer
(a) Temperature is a measure of the average kinetic energy of the particles of an object; heat is energy transferred from a hotter object to a cooler one because of a temperature difference. The visitor’s errors: the mirror does not make sunlight “hotter” — it concentrates the same energy onto a smaller area, so more energy arrives at the pot each second; and the pot does not “fill up with heat” — heat is not a substance that accumulates; the water’s thermal energy and temperature rise as energy is transferred in.
(b) Energy transferred into the water makes its particles move faster: they vibrate and slide past each other with more kinetic energy. Temperature is the average kinetic energy, so as the average rises the thermometer reading rises. Nothing about the particles themselves changes — they are the same water particles, just moving faster; near 100 °C the fastest particles have enough energy to escape the liquid altogether, which is boiling.
(c) Energy = mass × 4180 × temperature rise = 5.0 × 4180 × 80 = 1 672 000 J (1.67 MJ). Time = energy ÷ power = 1 672 000 ÷ 600 = 2787 s = 278760 ≈ 46 minutes.
(d) The 600 W is what the pot receives, but not all of it stays in the water: some warms the pot itself, and the hot pot loses energy to the air by conduction, convection and radiation, faster as it gets hotter. The energy reaching the water each second is therefore less than 600 J, so the heating takes longer than the minimum.
(e) Both are at the same temperature, so their particles have the same average kinetic energy, but the porridge has twenty times the mass and so stores about twenty times the thermal energy. When it touches the hand it can transfer far more energy before it cools to skin temperature — and porridge sticks, so the transfer continues. Burns depend on the energy transferred, not the temperature alone.
(f) Rumford (1798) bored a cannon barrel with a blunt drill in a box of water; the water boiled after about two and a half hours and heat kept being produced for as long as the horses turned the drill. A fluid contained in the brass would have run out, so an unlimited supply showed that friction was creating heat, not releasing it — heat must be motion. (Or: Joule, 1843–1850, measured that a fixed amount of work — falling weights, electric current — always produced the same amount of heat, 4.18 J per calorie; a fixed exchange rate across different methods is what two forms of one quantity, energy, would give, and not what a fluid would.)
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
Define temperature and heat in terms of particles and energy.
Reveal answer
Temperature is a measure of the average kinetic energy of the particles in an object [1]; heat is energy transferred from a hotter object to a cooler one because of the temperature difference between them [1].
A 5 kg mass falls 2.0 m and stirs 0.25 kg of water in Joule’s apparatus. Calculate the energy transferred and the temperature rise (g = 9.8 N/kg; 4180 J/kg °C).
Reveal answer
Energy = m g h = 5 × 9.8 × 2.0 = 98 J [1]; energy per degree for 0.25 kg = 0.25 × 4180 = 1045 J/°C [1]; rise = 98 ÷ 1045 = 0.094 °C ≈ 0.09 °C [1].
A student writes: “The iron block feels colder than the wooden block because it contains less heat, and the cold in the iron flows into my hand.” Identify three errors.
Reveal answer
Both blocks are at room temperature, so neither is colder than the other [1]; objects do not “contain heat” — they store thermal energy, and heat is energy in transfer [1]; cold does not flow — heat flows from the warmer hand into the iron, faster than into the wood because iron conducts better, and that rapid loss is what feels cold [1].
A chocolate bar is labelled 1250 kJ. Convert this to kilocalories and state which number is larger and why.
Reveal answer
1 250 000 ÷ 4180 = 299 kcal ≈ 300 kcal [1]; the kJ number is larger because a kilojoule is a smaller unit than a kilocalorie (1 kcal = 4.18 kJ), so more of them are needed to describe the same energy [1].
True or false, with a reason: “Two objects at the same temperature must store the same amount of thermal energy.”
Reveal answer
False [1]: temperature is the average kinetic energy per particle, but thermal energy is the total, which also depends on the mass and the material — a bath and a cup at 40 °C store very different amounts [1].
A 0.5 kg copper block at 100 °C is dropped into 0.5 kg of water at 20 °C in an insulated cup. The final temperature is about 27 °C, not 60 °C. Suggest what this tells you about copper compared with water, and explain in terms of energy.
Reveal answer
The copper fell by 73 °C while the water rose by only 7 °C, yet the energy lost by the copper equals the energy gained by the water [1]; so each kilogram of copper releases far less energy per degree than each kilogram of water absorbs — about a tenth as much [1]; water needs much more energy per kilogram per degree than copper (Lesson 4 calls this its specific heat capacity: 4180 against 385 J/kg °C) [1].
Summary
- Temperature measures the average kinetic energy of particles (°C, thermometer); heat is energy transferred because of a temperature difference (J).
- Thermal energy stored depends on temperature, mass and material — a warm bath holds far more than a hot spark.
- Heat flows from hot to cold until thermal equilibrium; cold does not flow.
- Caloric theory fell to Rumford’s endless cannon heat (1798) and Joule’s fixed exchange rate (1843–1850): 4.18 J of work per calorie of heat. Heat is energy.
- Units: 1 kcal = 1000 cal = 4180 J = 4.18 kJ; always convert before calculating, and quote the unit after.
Next time → Measuring temperature: thermometers, fixed points, Celsius, Kelvin and Fahrenheit, and why the coldest possible temperature is −273 °C.