Why a bath holds more heat than a match, and how heat travels by conduction, convection and radiation: explained step by step with diagrams, animations and worked examples.
A lit match and a bathtub of warm water: which contains more heat energy? The match is far hotter, yet the bath holds much more thermal energy, because it contains vastly more particles. This is the key to understanding the topic: temperature tells you how hot something is, while heat is energy moving from a hotter place to a colder one. People mix the two words up in daily speech, but in physics they mean different things, and separating them explains everything from why a metal spoon feels colder than a wooden one to why coastal cities have milder weather.
All matter is made of particles in constant motion. Temperature is a measure of the average kinetic energy of those particles. When a substance gets hotter, its particles vibrate or move faster on average. Temperature does not depend on how much of the substance there is: a spark and a furnace can both be very hot.
The total energy of all the moving and interacting particles in an object is its internal energy. It depends on the temperature and on the number of particles. That is why the bath has more internal energy than the match, even though the match is hotter.
Three scales are in common use:
| Scale | Symbol | Freezing point of water | Boiling point of water* | Used for |
|---|---|---|---|---|
| Celsius | °C | 0 | 100 | Everyday use in most countries, school science |
| Kelvin | K | 273.15 | 373.15 | The SI unit; scientific work and gas laws |
| Fahrenheit | °F | 32 | 212 | Everyday use in the USA and a few other places |
*At standard atmospheric pressure.
T (K) = θ (°C) + 273.15 (often rounded to +273)
°F = (°C × 9 ÷ 5) + 32 and °C = (°F − 32) × 5 ÷ 9
The kelvin scale starts at absolute zero, −273.15 °C (0 K), the lowest temperature possible, where particles have the least possible energy. A temperature difference of 1 K equals a difference of 1 °C. Typical human body temperature is about 37 °C (98.6 °F), although it varies between people and during the day.
Convert (a) 25 °C to kelvin and (b) 25 °C to Fahrenheit.
(a) T = 25 + 273 = 298 K (298.15 K using 273.15).
(b) °F = (25 × 9 ÷ 5) + 32 = 45 + 32 = 77 °F.
Thermometers use a property that changes predictably with temperature. A liquid-in-glass thermometer (alcohol or mercury) uses the expansion of the liquid in a narrow tube. A digital thermometer uses a thermistor or thermocouple whose electrical behaviour changes with temperature. An infrared thermometer measures the thermal radiation coming from an object. A good scientific thermometer has a suitable range, is sensitive, and responds quickly. To calibrate a liquid-in-glass thermometer, you mark two fixed points, the ice point (0 °C) and the steam point (100 °C at standard pressure), and divide the space between into equal parts.
Heat is the energy transferred between two objects (or two parts of one object) because of a difference in temperature. Heat flows from the hotter region to the colder one until their temperatures are equal, a state called thermal equilibrium. It is measured in joules (J), the same unit as all other energy.
It is incorrect to say an object "contains heat". It contains internal energy; heat is the name for the energy in transit. When you hold a cold drink, heat flows from your hand to the drink, so the drink warms and your hand cools.
Different materials need different amounts of energy to warm up. The specific heat capacity (c) of a material is the energy needed to raise the temperature of 1 kg of it by 1 °C (or 1 K). It is measured in J/kg°C.
Q = m × c × ΔT
Q = heat energy transferred (J), m = mass (kg), c = specific heat capacity (J/kg°C), ΔT = change in temperature (°C).
How much energy is needed to heat 2.0 kg of water from 20 °C to 80 °C? How long would a 2000 W kettle take if all the energy went into the water?
Step 1. ΔT = 80 − 20 = 60 °C.
Step 2. Q = mcΔT = 2.0 × 4200 × 60 = 504 000 J (504 kJ).
Step 3. Power = energy ÷ time, so t = Q ÷ P = 504 000 ÷ 2000 = 252 s ≈ 4.2 minutes.
In real life some energy warms the kettle and the surroundings, so it takes a little longer.
0.20 kg of water at 80 °C is mixed with 0.30 kg of water at 20 °C. Assuming no heat is lost, find the final temperature.
Step 1. Heat lost by hot water = heat gained by cold water. Let the final temperature be T.
Step 2. 0.20 × c × (80 − T) = 0.30 × c × (T − 20). The c cancels.
Step 3. 16 − 0.20T = 0.30T − 6, so 22 = 0.50T and T = 44 °C.
Check: it lies between 20 °C and 80 °C, and closer to 20 °C because there is more cold water ✓.
High specific heat capacity matters in nature. Water warms and cools slowly, so oceans and large lakes moderate the climate of nearby land. Sand and soil have a much lower specific heat capacity, so a beach is scorching at midday yet cool at night.
To measure c in a lab, an electric heater is placed in a block of the material with a thermometer. The energy supplied is E = VIt, so c = VIt ÷ (mΔT). Insulating the block reduces heat loss and improves accuracy.
Heat moves between places by three processes:
When one end of a solid is heated, its particles vibrate more strongly. They pass energy to neighbouring particles through collisions and bonds, and the energy spreads along the object. Metals are excellent conductors because they also have free electrons; these move through the metal and carry energy rapidly. Non-metals such as wood, plastic and glass are poor conductors, called insulators. Gases, such as air, are very poor conductors because their particles are far apart. Air trapped in wool, feathers, foam and double glazing is what makes these good insulators.
A metal spoon feels colder than a wooden one at the same room temperature, not because it is colder but because it conducts heat away from your hand faster.
The rate at which heat is conducted through a slab depends on four things: the material (its thermal conductivity k), the area A (larger area means more heat flow), the temperature difference ΔT (larger means more flow) and the thickness d (thicker means less flow). Together:
Heat flow per second = k × A × ΔT ÷ d (in watts, with k in W/m·K)
Approximate thermal conductivities: copper ≈ 400, steel ≈ 50, glass ≈ 1, still air ≈ 0.026 W/m·K.
An idealised single glass pane has area 1.5 m², thickness 5.0 mm and a temperature difference of 10 K between its surfaces. Taking k = 1.0 W/m·K, find the heat flow.
Step 1. d = 5.0 mm = 0.0050 m.
Step 2. Rate = kAΔT ÷ d = (1.0 × 1.5 × 10) ÷ 0.0050 = 3000 W.
Real windows lose less than this, because thin layers of still air on each side reduce the temperature difference across the glass itself, but the example shows the principle. Double glazing traps a layer of air or gas, which conducts far less heat than glass, and reduces losses.
When part of a fluid is heated, its particles move faster and spread apart, so that region becomes less dense and rises. Cooler, denser fluid flows in to take its place and is heated in turn. This circulation is a convection current. Convection is why the top of a room is warmer than the floor, why radiators and electric heaters are placed low, why a freezer compartment sits at the top of a refrigerator, and why hot air balloons rise.
The sea breeze links two ideas from this article: land has a low specific heat capacity so it heats quickly, while water's high specific heat capacity keeps it cooler, and the temperature difference drives the convection current.
Thermal radiation is infrared (a type of electromagnetic wave) emitted by all objects. The hotter the object, the more it radiates. Radiation travels at the speed of light and needs no medium, so it is the only way heat reaches us from the Sun across empty space.
| Surface | Absorbs radiation | Emits radiation | Reflects radiation |
|---|---|---|---|
| Dull black | Very well | Very well | Poorly |
| Shiny, silvery or white | Poorly | Poorly | Very well |
This is why solar water heating panels are painted matt black, why people in hot climates wear light-coloured clothes and paint houses white, and why emergency "space blankets" are shiny: they reflect body heat back towards the person.
The vacuum flask (thermos) is designed to stop all three forms of heat transfer, keeping hot drinks hot or cold ones cold.
When a material is heated, its particles vibrate more strongly and push slightly further apart, so most materials expand. Gases expand the most, liquids less, and solids the least. For a solid, the increase in length is:
ΔL = α × L × ΔT
α is the coefficient of linear expansion (per kelvin). Approximate values: steel ≈ 12 × 10⁻⁶ /K, copper ≈ 17 × 10⁻⁶ /K, aluminium ≈ 23 × 10⁻⁶ /K.
A 30 m steel rail warms by 40 K. How much does it expand?
ΔL = αLΔT = 12 × 10⁻⁶ × 30 × 40 = 0.0144 m ≈ 14 mm.
This is why railways leave small gaps or use special joints, and why bridges have expansion joints. Without them, hot weather could buckle the tracks.
A bimetallic strip is made of two metals (such as brass and iron) bonded together. Because they expand by different amounts, the strip bends when heated. It is used in simple thermostats and fire alarms to switch circuits on and off. Water behaves unusually between 0 °C and 4 °C, as explained in the article on matter and its states.
Almost all of the Earth's energy comes from the Sun by radiation. The ground and oceans absorb sunlight and warm up, and they in turn emit infrared radiation. Some gases in the atmosphere, called greenhouse gases (including water vapour, carbon dioxide and methane), absorb part of that outgoing infrared and re-emit it in all directions, including back towards the surface. This natural greenhouse effect keeps the Earth's average surface temperature far warmer than it would otherwise be. Human activities that add greenhouse gases, such as burning fossil fuels, strengthen the effect, which is the main cause of present-day global warming. Space agencies and meteorological organisations publish up-to-date temperature records, which are worth consulting for current numbers.
Try each question before opening the answer.
The lake has far more internal energy because it contains vastly more particles, but the cup of boiling water has the higher temperature.
300 − 273 = 27 °C. °F = (50 × 9/5) + 32 = 122 °F.
Q = mcΔT = 0.50 × 390 × 40 = 7800 J.
The metal is a good conductor, so heat reaches the food quickly. Plastic is an insulator, so the handle stays cool enough to hold.
It warms the air next to it, which becomes less dense and rises, setting up a convection current that spreads warmth through the room.
A matt black surface absorbs thermal radiation very well, so more of the Sun's energy heats the water.
ΔL = 23 × 10⁻⁶ × 10 × 30 = 0.0069 m ≈ 6.9 mm.
The vacuum reduces conduction and convection. The shiny silvered walls reduce radiation. The stopper reduces conduction at the top.
Safe activities with low-temperature water: compare how fast a metal and a plastic spoon warm in a cup of hot (not boiling) water; investigate insulation by wrapping identical cups of warm water in different materials and recording the temperature every two minutes; watch convection by dropping a small crystal of food colouring into one side of a water tank heated gently from below (use adult supervision); measure the specific heat capacity of a metal block with an electric heater. Always supervise any use of hot water, kettles or flames. All numerical values are rounded; please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions and typical values were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: specific heat capacities, conductivities and expansion coefficients are rounded typical values. Please check them against your own syllabus or exam board specification before relying on them.
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