Thermal Conduction
This topic explains how heat energy moves through objects by direct particle-to-particle contact, a process called conduction. You will need to understand why some materials are good conductors (like metals) and others are insulators (like air), and how to calculate changes in the rate of heat flow when dimensions or temperatures change.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Heat transfer by conduction occurs when vibrating particles collide with and transfer kinetic energy to their neighbours. It requires a medium; it cannot happen in a vacuum.
- Metals are excellent thermal conductors because their delocalised (free) electrons can move through the lattice, transferring energy much faster than atomic vibrations alone.
- Thermal insulators are materials that conduct heat very slowly. Gases are typically the best insulators because their particles are far apart, leading to infrequent collisions.
- In general, for a given substance, conductivity is highest in the solid state, lower in the liquid state, and lowest in the gaseous state due to particle spacing.
- The rate of heat conduction is directly proportional to the cross-sectional area and the temperature difference across the material.
- The rate of heat conduction is inversely proportional to the thickness or length of the material the heat has to travel through.
› Why does this happen?
Why metals are excellent conductors: The free electron 'super-highway'
In non-metals (insulators), heat energy is transferred slowly when vibrating particles bump into their neighbours, like a message passed down a line of people by tapping the next person on the shoulder. Metals also transfer heat this way via their vibrating positive ions, but they have a much faster method as well. When metal atoms form a structure, they release their outer electrons. These become 'delocalised' and are free to move throughout the entire metal. These fast-moving electrons gain kinetic energy at the hot end of the metal, travel to the colder end, and transfer this energy when they collide with the ions there. This 'super-highway' of free electrons transfers energy much more quickly than the vibrations alone, making metals fantastic thermal conductors.
Why insulators work: Spacing is key
Insulators are poor conductors because their particles are inefficient at passing energy along. For solids like plastic or wood, the lack of free electrons means they can only use the slow 'tapping the shoulder' method of particle vibrations. For gases, the problem is different: their particles are very far apart. For one particle to pass energy to another, it has to travel a long way to find one to collide with. This means collisions happen much less often, so the rate of energy transfer is very low. This is why materials that trap small pockets of air, like wool or the gap in double-glazing, are such effective insulators. Trapping the air stops it from moving and transferring heat by convection, leaving only the very slow process of conduction.
Formulae
Rate of heat transfer ∝ (Area × Temperature difference) / Thickness Use this proportionality to compare the rate of heat flow between two different setups, or to find the new rate of flow when a property of an object (like its length or area) is changed.
Definitions
- Thermal Conduction
- The transfer of thermal energy through a substance from a hotter region to a colder region, via the interaction of adjacent particles, without any net movement of the substance itself.
- Thermal Conductor
- A material that allows heat to flow through it rapidly. Metals are prime examples.
- Thermal Insulator
- A material that resists the flow of heat, transferring it very slowly. Examples include wood, plastics, and trapped air.
Worked example
A copper bar, Bar X, has a length L and a square cross-section of side length s. An identical temperature difference is maintained across the ends of both Bar X and a second copper bar, Bar Y. Bar Y has a length of 4L and a square cross-section of side length s/2. What is the ratio of the rate of heat conduction in Bar X to that in Bar Y?
- 1
First, establish the relationship for the rate of heat conduction:
Rate ∝ (Area × ΔT) / Length.
Since ΔT is the same for both bars, we can simplify this to Rate ∝ Area / Length.
- 2
Calculate the cross-sectional area for each bar.
For Bar X, AreaX = s2.
For Bar Y, AreaY = (s/2)2 = s2 / 4.
- 3
Write the proportionality for Bar X:
RateX ∝ s2 / L.
- 4
Write the proportionality for Bar Y:
RateY ∝ AreaY / LengthY = (s2 / 4) / (4L) = s2 / (16L).
- 5
To find the ratio RateX / RateY, divide the two expressions:
(s2 / L) / (s2 / 16L).
- 6
The terms s2 and L cancel out, leaving 1 / (1/16), which is 16.
The ratio is 16:1.
Answer: 16
Common mistakes
- ×Forgetting that rate is INVERSELY proportional to thickness. Doubling the thickness of an insulator halves the rate of heat loss, it does not double it.
- ×Muddling area calculations. If a rod's radius or diameter is doubled, its cross-sectional area (πr2) increases by a factor of four, not two. This is a common source of being 'off by a factor'.
- ×Misinterpreting comparisons. Remember that a good conductor has high thermal conductivity, while a good insulator has low thermal conductivity.
- ×Forgetting gases are excellent insulators. Trapped air is the primary reason for the effectiveness of double glazing or fibre-glass insulation, not the solid material itself.
No-calculator tips
- ✓Think in factors, not formulae. If a question states length is tripled and area is doubled, think 'rate is multiplied by 2/3' immediately, without writing the full proportionality.
- ✓Cancel out constants early. If temperature difference is the same in two scenarios, ignore it in your ratio calculation from the start to simplify the problem.
- ✓Before finalizing an answer involving ratios, do a quick sanity check. 'The second rod is longer and thinner, so it should conduct heat much slower. My ratio shows this, so it's likely correct.'