Physics · 2 Thermal physics

2.3.1 Conduction

Before you start

Thermal energy is transferred from a hotter region to a colder one.
The particle model: in a solid the particles are close together in fixed positions, in a liquid they are close together but move past one another, in a gas they are far apart and move randomly.
Raising the temperature of a substance increases the average kinetic energy of its particles.
Atoms contain electrons.
What a fair test is: change one variable, measure one, keep the rest the same.

Syllabus objectives covered (4)

Describe experiments to demonstrate the properties of good thermal conductors and bad thermal conductors (thermal insulators)
Describe thermal conduction in all solids in terms of atomic or molecular lattice vibrations and also in terms of the movement of free (delocalised) electrons in metallic conductors
Describe, in terms of particles, why thermal conduction is bad in gases and most liquids
Know that there are many solids that conduct thermal energy better than thermal insulators but do so less well than good thermal conductors

Part 1 of 7

What conduction is, and what good and bad conductors do

Thermal energy always moves from a hotter place to a colder one. Conduction is one of the ways it travels: energy passes through a material from particle to particle, while the material as a whole stays where it is.
That last part is what separates conduction from convection, which you meet next. In convection the material itself moves and carries the energy with it. In conduction it does not.
A good thermal conductor lets thermal energy pass through it quickly. Metals are good thermal conductors; copper and aluminium are the standard examples.
A bad thermal conductor lets thermal energy pass through it only slowly. The syllabus also calls it a thermal insulator. The two names mean the same thing, so you can use either.
Wood, plastic, wool, expanded polystyrene and air are thermal insulators.
Notice the word slowly. An insulator does not stop thermal energy. It only slows the transfer down. Every material conducts at least a little.
This subtopic has no equation to recall. The marks come from describing an experiment, reading its results, explaining what particles do and placing a material on the conductor scale, so the wording is what you practise.

Part 2 of 7

Experiment: racing energy along rods of different materials

The standard way to compare conductors is to heat one end of several rods in exactly the same way and see how quickly energy reaches the other end.
Take rods of copper, aluminium, steel and glass, all the same length and the same diameter. Fix a drawing pin to each rod with a small blob of wax, the same distance from one end, using the same amount of wax each time.
Heat the other end of every rod in the same way at the same time — for example, arrange the rods like the spokes of a wheel with their bare ends meeting in one Bunsen flame. Start a stopwatch when heating starts.
apparatus diagram — not drawn yet
Four horizontal rods of equal length and diameter labelled copper, aluminium, steel and glass, arranged like the spokes of a wheel with their inner ends meeting in a single Bunsen flame and their outer ends resting on a support ring; near the outer end of each rod a drawing pin hangs from the underside, held on by a small blob of wax, every pin the same distance from the flame.
Same size, same heating, same distance to the wax: the material is the only thing that differs.
Record the time for each pin to drop. A pin drops when energy conducted along the rod has melted its wax.
The best conductor is the rod whose pin drops first. The shortest time means energy reached the far end fastest. For these rods the order is copper, then aluminium, then steel.
The pin on the glass rod drops much later than the metal ones, or not at all in the time you allow. Glass is a far worse conductor than any of the metals.
Each controlled variable is there so that the material is the only thing that changes: same length, same diameter, same heating, same amount of wax, same distance of the wax from the heated end.
Here is why each one matters. A shorter rod gives energy less distance to travel, and a thicker rod lets more energy through at once. If the rods differed in size, you could not tell whether the material or the size caused the difference in times.
You can measure the same thing with a thermometer instead of wax. Fix a thermometer or temperature sensor at the far end of each rod and compare the temperature rise after a fixed time. The largest rise marks the best conductor.

Part 3 of 7

Three more demonstrations: paper, ice and your hand

Paper on a wood-and-metal rod. Use a rod that is wood for half its length and metal, such as brass, for the other half. Wrap one sheet of paper tightly around the join so it covers both halves, then hold it in a flame.
apparatus diagram — not drawn yet
A horizontal rod made of a wooden half joined end to end with a brass half, with a single strip of paper wrapped tightly around the join so it covers part of each half, held in a Bunsen flame directly under the join; the paper over the wood is shown scorched brown and the paper over the brass is shown unmarked.
The paper burns only where it sits on the bad conductor.
The paper over the wood scorches, while the paper over the metal is still unmarked.
The reason: the metal is a good conductor, so it carries thermal energy away from the paper quickly and the paper stays below the temperature at which it chars. The wood is a bad conductor, so energy stays in the paper above it and that paper's temperature rises until it scorches.
Ice in a tube of water. Hold a small piece of ice at the bottom of a test tube of water by wrapping it in metal gauze — ice floats, so it needs weighing down. Hold the tube at an angle and heat it near the top.
apparatus diagram — not drawn yet
A test tube of water held at an angle by a clamp, with a lump of ice wrapped in metal gauze at the bottom, and a Bunsen flame heating the tube near its top; bubbles of boiling are drawn in the water at the top while the ice at the bottom is intact.
Boiling at the top, ice still there at the bottom.
The water at the top boils while the ice at the bottom stays almost unmelted. This shows that water is a bad thermal conductor.
The tube is heated at the top on purpose. Hot water floats on cold water, so the heated water stays at the top and does not move down to the ice. The main way left for energy to reach the ice is conduction down through the water, and the unmelted ice shows how slow that is.
The touch test. A metal rail and a wooden bench left outside on the same cold day are at the same temperature, yet the metal feels much colder.
The metal is a good conductor, so it conducts thermal energy away from your hand faster than the wood does. What you feel is your own skin cooling faster, not a lower temperature in the rail.

Part 4 of 7

Inside every solid: lattice vibrations

In a solid the particles (atoms or molecules) are held close together in fixed positions by the forces between them. The syllabus calls this arrangement a lattice.
The particles cannot move from place to place, but each one vibrates about its fixed position.
Heat one end of the solid. The particles there gain kinetic energy, so they vibrate more vigorously, with a larger amplitude.
Each particle is linked to its neighbours by the forces between them. As it vibrates harder it pushes and pulls on them, so they start to vibrate harder too. They then do the same to the particles beyond them.
So energy is passed along the solid from particle to particle, from the hot end towards the cold end. The particles themselves stay in their positions; only the energy travels.
This happens in all solids — metals, glass, wood, plastic, ice. In most solids it is a slow way to move energy, because each particle has to hand the energy on to the next one.

Part 5 of 7

Metals: free electrons as well

A metal conducts by lattice vibrations, like every other solid. It also has something extra: free (delocalised) electrons.
In a metal, some electrons are not tied to any one atom. They move freely and randomly through the whole metal, between the positive ions of the lattice.
At the hot end, the free electrons gain kinetic energy and move faster.
Because they are free to move, these electrons travel through the metal and collide with ions and other electrons further along, transferring some of their energy there.
Free electrons carry energy along much faster than lattice vibrations alone can. That is why metals are good thermal conductors.
The objective asks for both mechanisms: lattice vibrations in all solids, and also free electrons in metals. So when you explain conduction in a metal, describe both. An answer about a metal that mentions only one of them leaves half the explanation out.
The free electrons are also why metals conduct electricity. The same particles do both jobs.

Part 6 of 7

Why gases and most liquids conduct badly

Conduction depends on particles passing energy to their neighbours. How well that works depends on how close the particles are and how they are held.
Gases. The particles are far apart, with large spaces between them, and they move about randomly.
A particle can pass energy to another particle only when the two collide. Because gas particles are far apart, these collisions are infrequent, so energy is passed on slowly.
A gas has no lattice and no free electrons, so neither of the routes a solid metal uses is available. Gases, including air, are bad thermal conductors.
This is why many insulators — wool, feathers, foam, fibreglass — are full of small pockets of trapped air. The trapped air is the bad conductor, and the fibres or foam stop that air from moving about.
Liquids. The particles are close together, but they are not held in fixed positions in a lattice. They slide past one another and move about randomly.
So energy is not handed along a fixed chain of linked neighbours as it is in a solid. The particles keep moving about, and energy is passed from one to the next much less effectively.
Most liquids also have no free electrons. The exception is a liquid metal, such as mercury, which does have free electrons and conducts much better than other liquids. That is why the objective says most liquids.

Part 7 of 7

The middle of the scale

Good conductor and insulator are the two ends of a scale, not two boxes. Many solids sit in between.
Glass, brick, concrete and stone all conduct thermal energy better than thermal insulators such as wool, expanded polystyrene or air, but much less well than good conductors such as metals.
In particle terms you can explain the top of their range: they have no free electrons, so they conduct by lattice vibrations only and cannot match a metal. Wood and plastic also have no free electrons yet are insulators, so 'no free electrons' alone does not place a material in the middle. The syllabus asks you only to know that these in-between solids exist.
The glass rod in the rod experiment is an example. Its pin drops far later than the metals' pins, yet glass still conducts better than a true insulator such as polystyrene.
So if a question asks you to place a material like glass, do not call it a good conductor and do not put it in the same class as polystyrene. Say what the syllabus says: it conducts better than thermal insulators but less well than good thermal conductors.

Worked examples

Example 1. Describe an experiment to show that copper is a better thermal conductor than steel.

Show the working

Choose what you compare: a copper rod and a steel rod of the same length and the same diameter. The size must match, because a shorter or thicker rod would let energy through faster whatever it was made of.
Fix a drawing pin to each rod with the same amount of wax, the same distance from one end. This makes the 'finish line' the same for both rods.
Heat the other ends equally and at the same time — both in the same Bunsen flame — and start a stopwatch.
Record the time for each pin to drop. A pin drops when energy conducted along the rod melts the wax.
State the conclusion from the measurement, not from memory: the pin on the copper rod drops first, so energy is conducted along copper faster, so copper is the better thermal conductor.

Answer: Use copper and steel rods of the same length and diameter, each with a drawing pin fixed by the same amount of wax at the same distance from one end. Heat the other ends equally at the same time and time how long each pin takes to drop. The copper pin drops first, so energy is conducted along copper faster and copper is the better thermal conductor.

Example 2. A student heats one end of five rods of the same size in the same way. A thermometer at the far end of each rod reads 20.0 °C at the start. After 5 minutes the readings are: copper 52.0 °C, aluminium 41.0 °C, steel 26.0 °C, glass 22.5 °C, wood 20.5 °C. (a) Determine the temperature rise for each rod. (b) Deduce the order of the materials from best to worst thermal conductor. (c) Comment on whether glass belongs with the metals or with the wood.

Show the working

(a) Temperature rise = final reading − starting reading. Copper: 52.0 − 20.0 = 32.0 °C. Aluminium: 41.0 − 20.0 = 21.0 °C. Steel: 26.0 − 20.0 = 6.0 °C. Glass: 22.5 − 20.0 = 2.5 °C. Wood: 20.5 − 20.0 = 0.5 °C.
(b) The rods were the same size and heated the same way for the same time. So a bigger rise at the far end means more energy was conducted along that rod, which means a better conductor.
Rank by rise, largest first: copper (32.0 °C), aluminium (21.0 °C), steel (6.0 °C), glass (2.5 °C), wood (0.5 °C).
(c) Look at where glass falls. Its rise of 2.5 °C is far smaller than that of even the poorest metal here (6.0 °C), but it is larger than the wood's 0.5 °C, and wood is a thermal insulator.
So glass belongs with neither group. It is one of the many solids that conduct better than insulators but less well than good conductors.

Answer: (a) Copper 32.0 °C, aluminium 21.0 °C, steel 6.0 °C, glass 2.5 °C, wood 0.5 °C. (b) Copper, aluminium, steel, glass, wood. (c) Glass belongs with neither: it conducts better than the wood (an insulator) but much less well than the metals.

Example 3. Explain, in terms of particles, why a copper rod conducts thermal energy much better than a glass rod of the same size.

Show the working

Start with what the two rods have in common. Both are solids, so both conduct by lattice vibrations: the particles at the hot end vibrate with a larger amplitude and pass the vibration on to neighbouring particles.
Now the difference. Copper is a metal, so it also has free (delocalised) electrons. Glass has none.
At the hot end of the copper, the free electrons gain kinetic energy, move quickly through the metal and collide with ions further along, transferring energy to them.
This transfer by free electrons is much faster than lattice vibrations alone. Glass has only the slower lattice-vibration route, so it conducts much less well.

Answer: Both rods conduct by lattice vibrations: particles at the hot end vibrate more and pass energy to their neighbours. Copper also has free (delocalised) electrons, which gain kinetic energy at the hot end, move quickly through the metal and transfer energy in collisions with ions further along. Glass has no free electrons, so it conducts only by the slower lattice vibrations.

Example 4. A winter jacket is filled with feathers that trap a large amount of air. Explain, in terms of particles, why the trapped air reduces the conduction of thermal energy away from the body.

Show the working

Most of the filling is trapped air, so the air is what you explain.
Air is a gas, so its particles are far apart.
Energy passes from one particle to another only when they collide. Far-apart particles collide infrequently, so energy is passed on slowly.
A gas has no lattice and no free electrons, so it has neither of the faster routes that a solid metal uses.

Answer: Air is a gas: its particles are far apart, so they collide infrequently. Energy is passed between particles only in collisions, so thermal energy is conducted very slowly through the trapped air.

Where people go wrong

Mistake: Saying the metal rail is colder than the wooden bench because it feels colder.

Instead: Both are at the same temperature. The metal feels colder because it conducts thermal energy away from your hand faster.

Your skin senses its own cooling. A good conductor cools it faster, which feels like 'colder'.

Mistake: Writing that the particles at the hot end of a solid travel along to the cold end.

Instead: In a solid the particles stay in their fixed positions and only vibrate. Energy is passed along from particle to particle; the particles do not travel.

Material moving from place to place and carrying energy with it is convection, which happens only in liquids and gases. In a metal it is the free electrons, not the atoms, that move through the material.

Mistake: Explaining that gases conduct badly because their particles move slowly.

Instead: Gas particles move quickly. Gases conduct badly because the particles are far apart, so they collide infrequently.

Energy passes between particles only in collisions. Speed is not the problem; the distance between particles is.

Mistake: Explaining conduction in a metal with free electrons only, or with vibrations only.

Instead: A metal uses both: lattice vibrations, as in every solid, and also the movement of free (delocalised) electrons.

The objective names both mechanisms. Free electrons are the extra that makes a metal a good conductor; they do not replace the vibrations.

Mistake: Putting every material into one of two boxes: conductor or insulator.

Instead: Many solids, such as glass, brick and concrete, conduct better than insulators but less well than good conductors.

Conduction is a scale, not two boxes. These solids have no free electrons, so they cannot match a metal, but they still conduct much better than insulators such as wool or polystyrene.

Check yourself

In the rod experiment with wax and drawing pins, how do you tell which rod is the best thermal conductor?
Answer
Its pin drops first. The shortest time means energy reached the wax fastest.
State three things that must be the same for every rod in that experiment.
Answer
Any three from: the length of the rod, the diameter of the rod, the amount (and type) of wax, the distance of the wax from the heated end, the way and time each rod is heated (same flame, same part of the flame), the starting temperature of the rods.
Why does a metal rail feel colder than a wooden bench on the same cold day?
Answer
They are at the same temperature, but the metal is a better conductor, so it conducts thermal energy away from your hand faster and your skin cools faster.
In the ice-in-a-tube demonstration, why is the tube heated near the top rather than at the bottom?
Answer
Hot water floats on cold water, so the heated water stays at the top and cannot carry energy down to the ice by moving. Energy can then reach the ice only by slow conduction down through the water (and the glass wall), so the experiment tests how well water conducts.
Name the two ways thermal energy is conducted along a metal rod.
Answer
Lattice vibrations passed from particle to particle, and the movement of free (delocalised) electrons that carry energy through the metal and transfer it in collisions.
A plastic rod conducts by only one of those two ways. Which one, and why?
Answer
Lattice vibrations only. Plastic is not a metal, so it has no free electrons.
Why does the objective say 'most liquids' rather than 'all liquids'?
Answer
A liquid metal, such as mercury, has free electrons, so it conducts much better than other liquids.
Name one solid that conducts thermal energy better than a thermal insulator but less well than a good thermal conductor.
Answer
Any one of: glass, brick, concrete, stone.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. A student compares four rods of the same length and diameter, made of copper, aluminium, steel and glass. A drawing pin is fixed with wax near one end of each rod. The other ends are heated in the same Bunsen flame. The times for the pins to drop are: copper 50 s, aluminium 80 s, steel 270 s. The pin on the glass rod had not dropped after 1200 s.

(a) Apart from the length and diameter of the rods, state two variables the student must keep the same for the test to be fair. 2 marks No calculator

Mark scheme

B1 any one from: the amount of wax on each rod / the type of wax / the distance of each pin from the heated end / the size or mass of the pins / each rod heated in the same flame (same part of the flame, same length of rod in the flame) for the same time / the same starting temperature of the rods, owtte
B1 a second, different point from the same list; the length or diameter of the rods does not count, as the question excludes them

(b) Deduce which material is the best thermal conductor. Give a reason from the results. 2 marks No calculator

Mark scheme

B1 copper
B1 its pin dropped first / in the shortest time (50 s), so energy reached the wax fastest, owtte

(c) The student concludes that glass is a thermal insulator. Comment on this conclusion. 2 marks No calculator

Mark scheme

B1 the results show only that glass conducts much less well than the metals (its pin had not dropped after 1200 s); no thermal insulator was tested (a known insulator such as wood or polystyrene would be needed for comparison), so the experiment cannot show glass is one, owtte
B1 glass conducts better than thermal insulators such as polystyrene, wool or air, but less well than good conductors, so it lies between the two

Question 2. A copper rod is heated at one end. Thermal energy is conducted along the rod to the cold end.

(a) Explain, in terms of particles, how thermal energy is transferred along the copper rod. 4 marks No calculator

Mark scheme

B1 atoms / ions / particles / molecules at the hot end gain kinetic energy and vibrate more (faster or with larger amplitude)
B1 the vibrations (energy) are passed on to neighbouring atoms / ions / particles along the lattice, owtte
B1 free (delocalised) electrons at the hot end gain kinetic energy and move through the metal
B1 the electrons collide with atoms / ions (or other electrons) further along the rod and transfer energy to them

(b) A glass rod of the same size is heated in the same way. Explain why it conducts thermal energy much less well than the copper rod. 2 marks No calculator

Mark scheme

B1 glass has no free (delocalised) electrons
B1 so it conducts by lattice vibrations only, which transfer energy more slowly than free electrons, owtte

Question 3. A piece of ice is wrapped in metal gauze and held at the bottom of a test tube of water. The tube is heated near the top. After a few minutes the water at the top is boiling, but the ice at the bottom has hardly melted.

(a) State what this experiment shows about water. 1 mark No calculator

Mark scheme

B1 water is a bad (poor) thermal conductor / a thermal insulator

(b) Explain, in terms of particles, why thermal conduction in water is bad. 2 marks No calculator

Mark scheme

B1 the particles are not held in fixed positions in a lattice / are (on average) further apart than in a solid / have weaker forces between them, so vibrations (energy) are not passed on efficiently from particle to particle, owtte
B1 water has no free (delocalised) electrons to carry energy through it

(c) A double-glazed window has a layer of air between two sheets of glass. Explain, in terms of particles, why the layer of air reduces the transfer of thermal energy through the window by conduction. 2 marks No calculator

Mark scheme

B1 the particles in air (a gas) are far apart
B1 so they collide infrequently, and energy is passed between particles only in collisions, so it is transferred slowly, owtte

How this is examined

Describing a fair experiment that ranks materials as thermal conductors: a three- or four-mark Describe, built around rods of different materials, a heat source and wax or thermometers, which can be followed by a results table Rods of the same length and diameter; one end of each heated in the same way; wax (or a pin fixed with wax) at the same distance from the heated end; time measured until the wax melts or the pin drops; the shortest time shows the best conductor.
How energy is passed along a metal: vibrations plus free electrons: an Explain of three or four marks about a metal rod heated at one end Particles at the hot end vibrate with larger amplitude and pass the vibration to neighbouring particles; free (delocalised) electrons gain kinetic energy, move through the metal and collide with ions further along, transferring energy. Both mechanisms must be there.
Why gases and most liquids are bad conductors, in particle terms: a two-mark Explain 'in terms of particles', which may be set in an insulation context such as a jacket or a double-glazed window Gas: particles far apart, so they collide infrequently, so energy is passed on slowly. Liquid: particles not held in fixed positions in a lattice, and no free electrons.
Reading a conduction results table: a one- or two-mark Deduce or Identify after a table of times or temperature rises Name the material and quote the evidence from the table: the shortest time for the wax to melt, or the largest temperature rise at the far end.
Placing a material such as glass between conductors and insulators: a one- or two-mark State or Comment asking you to classify a non-metal solid Glass (or brick, concrete, stone) conducts better than thermal insulators such as polystyrene or air but less well than good conductors such as metals; it has no free electrons, so it conducts by lattice vibrations only.

Words to know

Thermal conduction: The transfer of thermal energy through a material from particle to particle, without the material as a whole moving.
Good thermal conductor: A material that lets thermal energy pass through it quickly, such as a metal.
Thermal insulator: A bad thermal conductor: a material that lets thermal energy pass through it only slowly, such as wool, polystyrene or air.
Lattice: The arrangement of particles held close together in fixed positions in a solid.
Lattice vibrations: The vibrations of the particles of a solid about their fixed positions; passing them from particle to particle conducts energy in every solid.
Free (delocalised) electrons: Electrons in a metal that are not tied to any one atom and can move through the whole metal, carrying thermal energy (and electric charge) with them.

All Physics lessons Next: 2.3.2 Convection