Why does a metal spoon burn your hand while a wooden one does not, and how does the Sun warm you across empty space?

How to use this simulation

1. Start in Conduction with the copper rod. One end sits in a 100 °C bath and the other in a 20 °C bath. The white dots are the particles of the rod: they shake harder at the hot end. The amber dots are packets of energy being passed along. The reading says 24.6 W flows.
2. Click Wood. The rod looks the same, but the rate falls to 0.008 W and only a couple of amber dots crawl along. Now click the other materials and compare the four bars underneath. They are drawn on a log scale because copper and wood differ by a factor of thousands.
3. Drag the length and the area. Double L and the rate halves. Double A and it doubles. Raise the hot-end temperature and the rate grows in proportion to ΔT.
4. Switch to Convection. Raise the temperature at the bottom and watch the water at the heater turn red and rise on the left, then cool and sink on the right. The density readings show why: warmer water is lighter, so it floats up through the cooler water around it.
5. Switch to Radiation. Slide the temperature up and watch the body go from dull grey to red, orange and yellow-white. Compare the radiated power at your temperature with the reading "P if T were doubled": it is always sixteen times bigger.
6. Lower the emissivity to 0.05 and the same hot body radiates almost nothing. That is the shiny surface of a thermos flask. Finally, check the peak wavelength: the hotter the body, the shorter the wavelength at which it glows most.

Heat is energy moving because of a temperature difference

Put a hot cup of tea on a cold table and the tea cools while the table warms. Nothing is added or lost from the pair of them: thermal energy has moved from the hotter object to the cooler one. That moving energy is what we call heat, and it always flows from hot to cold until the temperatures match.

How it moves depends on what lies between the two objects. If they touch, particles hand the energy on to their neighbours: that is conduction. If there is a fluid between them that is free to flow, the fluid can carry the energy with it: that is convection. And if there is nothing at all, the energy can still cross as electromagnetic waves: that is radiation.

Most real situations use all three at once. A kettle heats its water by conduction through the metal base, then convection stirs that heat through the water, while the outside of the kettle sends radiation to your face as you stand next to it. Learning the three separately is how you learn to work out which one matters.

Conduction: passing it on, particle to particle

Hold one end of a metal rod over a flame and, after a while, the other end becomes too hot to hold. Nothing moved along the rod. The particles at the hot end vibrate more violently, bump into their neighbours and shake them harder, and so on down the line. Energy travels; the material stays put. In the animation, look at the white dots: they shake with a bigger swing near the hot end and a smaller swing near the cold end, and the amber packets are the energy being passed along.

Three things decide how fast it goes. A bigger temperature difference ΔT between the ends pushes harder. A thicker rod (larger area A) offers more routes. A longer rod (larger length L) means more particles to relay the energy through, so slower. And the material matters through a number k, the thermal conductivity. Together: Q/t = kAΔT/L, the rate of heat flow in watts.

With the animation’s default rod, L = 0.50 m, A = 4 cm² and ΔT = 80 K, the copper rod carries 24.6 W. In steady state the temperature drops evenly along the rod, which is why the colour shades smoothly from red to blue. The temperature gradient is ΔT/L = 160 K/m, so the middle of the rod sits at 60 °C, exactly halfway.

Good conductors, bad conductors and the role of electrons

Metals conduct heat so well because they have free electrons that roam through the whole piece. These electrons carry energy across the metal far faster than vibrating atoms can pass it hand to hand. This is also why good conductors of heat (copper, aluminium, silver) are good conductors of electricity. Glass and wood have no free electrons, so they rely on the slow atom-to-atom relay.

Gases are the worst conductors of all, because the particles are far apart and collide rarely. Still air conducts even worse than wood, and it is the secret behind a woolly jumper, double-glazed windows and the fluffy filling of a quilt: they trap air in tiny pockets so that it cannot move and cannot convect either.

So a metal spoon in hot soup feels hotter than a wooden one, even though both are at the same temperature. Your fingers feel the rate at which heat arrives. Copper delivers it quickly, so your skin warms quickly; wood hands it over so slowly that your skin barely notices. The same reason makes a tile floor feel colder than a carpet on a winter morning.

Convection: the fluid carries the heat

Heat a pan of water from below and the water at the bottom warms up first. Warm water expands, so a given volume of it is lighter than the same volume of cooler water. The cooler water around it pushes it upward, in the same way a cork rises in a bucket. The warm water travels up, meets the cooler surface, loses heat to the air and the water above, and sinks again down the other side. The result is a circulating current, a convection current, and in the animation the particles trace it as one big loop.

The current is driven by a density difference. For 80 °C water at the bottom against 20 °C water above, the table below gives the densities, and the buoyant push on the warm water per kilogram is g′ = g (ρcold − ρhot) / ρhot. It is a small fraction of g, but it acts all the time and moves the whole pan’s worth of water around in a minute or so. Move the slider and the current speeds up or slows down in step with that figure.

This is why a radiator heats a room: warm air near it rises to the ceiling, cool air from the floor flows in to replace it, and the whole room turns over. It is also why a heater belongs at the bottom of a room and an air conditioner high up. Sea breezes work the same way: land warms faster than water in the afternoon, so air rises over land and the cooler sea air flows in to fill the gap.

Convection needs a fluid and needs gravity. It cannot happen in a solid, because the particles cannot flow, and it cannot happen in a vacuum, because there is nothing to flow.

Radiation: heat with no medium at all

The Sun’s heat crosses about 150 million kilometres of vacuum to reach you. There are no particles out there to conduct it and no fluid to convect it. It comes as electromagnetic waves, mostly visible and infrared light, and you feel warm when your skin absorbs them. Every object above absolute zero radiates, from a glowing coal to your own body (which sends out infrared that night-vision cameras can see).

How much a body radiates depends strongly on its temperature. Stefan’s law says the power is P = εσAT⁴, where T is in kelvin, A is the surface area, σ = 5.67 × 10⁻⁸ W/(m²·K⁴) and ε is the emissivity between 0 and 1. A perfect radiator (a black body) has ε = 1; a polished mirror-like surface has ε close to 0.

The fourth power is dramatic. Double the temperature in kelvin and the power rises sixteen times. With the animation’s defaults (T = 1,000 K, ε = 0.9, A = 0.5 m²) the body radiates 25.5 kW. Do not forget that the surroundings radiate back: the net loss is εσA(T⁴ − T₀⁴), with T₀ the temperature of the surroundings.

The colour changes too. Wien’s law says the wavelength where a body radiates most is λ = 2.898 × 10⁻³ / T metres. At 1,000 K that is 2.90 µm, which is infrared, so the body looks only dull red because just the short-wavelength tail of its glow reaches the visible range. Turn the temperature up and the peak slides toward the visible, so the glow goes through red, orange and yellow to white.

Shiny, dark, white: what the surface does

A good absorber is also a good emitter. A matte black surface takes in most radiation that hits it and gives out a lot when hot. A shiny surface reflects most radiation and emits little. That is why radiators and car engine fins are painted dark, why fire-fighters’ and mountaineers’ emergency blankets are silvered, and why people in hot countries wear light-coloured clothing: white reflects the Sun’s visible light.

A vacuum flask (thermos) puts all three modes to work at once. The double-walled glass has the air removed from between the walls, which stops conduction and convection across the gap. The glass surfaces are silvered, so very little radiation crosses either. The plastic stopper is a poor conductor so no heat leaks out through the top. What is left is a very slow leak, which is why a good flask keeps tea hot for hours.

A greenhouse has a different trick. Glass lets the Sun’s short-wavelength light in, but blocks the longer infrared that the warm ground sends back out, and it also stops the warm air from rising away. Conduction, convection and radiation are all being managed to keep the heat inside.

Solved problems

Each answer uses the same functions as the animation, so you can check any of them by setting the sliders.

Mistakes that cost marks

Check this list before the exam. Each one has cost someone a mark.

• Putting temperatures in Celsius into Stefan’s law. T must be in kelvin. In Q/t = kAΔT/L, a difference in °C equals a difference in K, so there you are safe.
• Forgetting to convert the area to m² or the thickness to metres. A cross-section of 4 cm² is 4 × 10⁻⁴ m², and 5 mm is 5 × 10⁻³ m.
• Saying that particles travel along the rod in conduction. They only vibrate in place and pass the energy on. In convection the particles do move.
• Claiming that convection can happen in solids or in a vacuum. It needs a fluid.
• Saying that heat rises. Hot fluids rise because they are less dense. Heat itself goes from hot to cold in any direction.
• Forgetting that the surroundings radiate back. Net power uses T⁴ − T₀⁴, not just T⁴.
• Treating a vacuum flask as if one feature does the job. It needs the vacuum, the silvering and the stopper together.

Where else you meet it

Chip designers worry about conduction through heat sinks, power stations about convection in boilers, and astronomers read the temperature of stars from their colour using Wien’s law. A cooking pot has a copper base for fast conduction and a wooden or plastic handle to slow it. A heat-seeking camera simply measures how much radiation each patch of a scene gives off.

If you want to see how particles carry sound rather than heat, try the wave animations. For how hot gas pushes on a piston, head to the gas-laws pages when they appear in this collection.

Frequently asked questions