Thermal conductivity
Definition
Thermal conductivity
A measure of how quickly energy is transferred through a material by conduction.
Definition
Thermal insulator
A material through which energy is transferred only slowly by heating.
- Every material conducts energy, but different materials do it at very different rates.
- The thermal conductivity of a material describes how quickly energy is conducted through it when one side is hotter than the other.
- A material with a high thermal conductivity lets energy pass through it quickly, so a metal saucepan handle soon becomes too hot to hold.
- A material with a low thermal conductivity lets energy pass through it only slowly, which makes it a good thermal insulator.
- Metals such as copper, aluminium and steel have the highest thermal conductivities, because as well as vibrating particles passing energy on, they contain free electrons that move through the metal and carry energy quickly from the hot side to the cold side.
- Building materials such as concrete, stone, brick and glass have much lower thermal conductivities than metals.
- Wood has a lower thermal conductivity than brick, which is why a wooden door feels warmer to the touch than the brick wall beside it.
- Insulating materials such as mineral wool and polystyrene foam have very low thermal conductivities, because they are mostly trapped air, and the particles in a gas are too far apart to pass energy on quickly.
- Comparing materials by thermal conductivity is only fair when the samples are the same thickness, because the thickness also changes how quickly energy gets through.
How a building cools
Definition
Rate of cooling
The decrease in temperature of an object per unit time.
- In winter the inside of a heated house is warmer than the air outside, so energy is transferred out of the house by heating.
- Energy leaves through the walls, the roof, the windows and the floor, and much of it is conducted through the walls from the warm inner surface to the cold outer surface.
- The outer surface of the wall then warms the air outside, so the energy is dissipated to the surroundings.
- While the heating is on, the boiler has to replace this energy as fast as it is conducted out, or the rooms cool down.
- When the heating is switched off, the temperature inside falls, and how quickly it falls is the rate of cooling of the building.
- The rate of cooling is greatest when the inside is much warmer than the outside, and it slows down as the temperature difference gets smaller.
- A building with a low rate of cooling stays warm for longer after the heating goes off and needs less fuel to keep it at a comfortable temperature.
- The two properties of a wall that decide the rate of cooling through it are its thermal conductivity and its thickness.
Effect of thermal conductivity
- For walls of the same thickness, a wall made from a material with a lower thermal conductivity conducts energy through it more slowly.
- Less energy is transferred out each second, so the building has a lower rate of cooling.
- A wall made from a material with a higher thermal conductivity conducts energy out more quickly, so the inside of the building cools faster.
- This is why a modern wall is built with a layer of foam insulation inside it, because the foam has a far lower thermal conductivity than the brick and concrete around it.
- Glass has a higher thermal conductivity than brick and is used in thin sheets, so a large single-glazed window lets energy out much faster than the same area of wall.
Effect of wall thickness
- For walls made from the same material, a thicker wall gives energy a greater distance of material to be conducted through.
- The energy has to be passed along many more layers of particles to reach the outside, so it is conducted through a thicker wall more slowly.
- Less energy is transferred out each second, so the building has a lower rate of cooling.
- A thinner wall of the same material conducts energy out more quickly, so the building cools faster.
- Old stone cottages with walls more than half a metre thick stay at a steadier temperature than a garden shed with thin wooden walls.
- The lowest rate of cooling comes from walls that are both thick and made from a material with a low thermal conductivity.
- The highest rate of cooling comes from walls that are both thin and made from a material with a high thermal conductivity.
- Thickness and thermal conductivity can work against each other, so a thin layer of a very good insulator can keep a building warmer than a much thicker layer of brick.
Practical
Cooling of insulated copper cans
- Aim: to compare how quickly hot water cools in a copper can wrapped in insulation and in an identical can with no insulation.
- Apparatus: two identical copper cans, two thermometers or temperature probes, a kettle, a 250 cm3250\ \text{cm}^3250 cm3 measuring cylinder, a stopwatch, an insulating material such as cotton wool, bubble wrap or felt, elastic bands, two card lids with a hole for the thermometer, two heatproof mats and eye protection.
- Method, preparing the cans:
- Wrap one copper can in 333 layers of the insulating material, holding them in place with elastic bands, and leave the other can bare.
- Stand both cans on heatproof mats on the same bench, away from windows, radiators and draughts.
- Boil water in the kettle and use the measuring cylinder to pour exactly 200 cm3200\ \text{cm}^3200 cm3 into each can.
- Fit a card lid on each can and push a thermometer through the hole so that its bulb sits in the middle of the water, clear of the bottom and sides.
- Method, taking readings:
- Stir the water gently with the thermometer and wait until both cans read the same starting temperature, for example 80 ∘C80\ ^\circ\text{C}80 ∘C.
- Start the stopwatch at that moment and record both starting temperatures.
- Record the temperature of each can every minute for 151515 minutes, reading each thermometer with your eye level with the top of the liquid.
- Repeat the experiment with fresh hot water to check that the results are repeatable.
- Variables: the independent variable is whether the can is insulated, the dependent variable is the temperature of the water over time, and the control variables are the volume of water, the starting temperature, the size and material of the cans, the lids and the surroundings.
- Results: plot temperature on the vertical axis against time on the horizontal axis for both cans on the same grid, and draw a smooth cooling curve through each set of points, which will be steepest at the start and less steep for the insulated can throughout.
- Maths: find the fall in temperature over the same time for each can, then divide by the time to compare rates, so a fall from 80 ∘C80\ ^\circ\text{C}80 ∘C to 58 ∘C58\ ^\circ\text{C}58 ∘C in 101010 minutes is a mean rate of 2210=2.2 ∘C\dfrac{22}{10} = 2.2\ ^\circ\text{C}1022=2.2 ∘C per minute.
- Taking it further: the same set-up can compare different numbers of layers of the same insulator, which tests the effect of thickness, or the same thickness of different materials, which tests the effect of thermal conductivity.
- Watch out: starting the two cans at different temperatures makes the comparison unfair, a missing lid lets convection and evaporation dominate the cooling, and a thermometer touching the copper reads the temperature of the can instead of the water.
- Safety: wear eye protection, pour boiling water slowly with the can standing on the mat rather than held in your hand, and let the cans cool before handling them.
Example
Comparing two cooling rates
- In the copper can investigation, both cans start at 80 ∘C80\ ^\circ\text{C}80 ∘C.
- After 101010 minutes the bare can is at 58 ∘C58\ ^\circ\text{C}58 ∘C and the insulated can is at 71 ∘C71\ ^\circ\text{C}71 ∘C.
- Fall in temperature of the bare can:
- Fall in temperature of the insulated can:
- The mean rates of cooling are 2.2 ∘C2.2\ ^\circ\text{C}2.2 ∘C per minute and 0.9 ∘C0.9\ ^\circ\text{C}0.9 ∘C per minute, so the insulation has cut the rate of cooling to less than half, because the trapped air in the insulating layer has a very low thermal conductivity.
Example
Ranking three walls
- Wall A is a single layer of brick 10 cm10\ \text{cm}10 cm thick, wall B is a single layer of brick 20 cm20\ \text{cm}20 cm thick, and wall C is 10 cm10\ \text{cm}10 cm of brick with 10 cm10\ \text{cm}10 cm of foam insulation behind it.
- Walls A and B are made of the same material, so the thicker wall B conducts energy out more slowly than wall A.
- Walls B and C are the same total thickness, but half of wall C is foam, which has a far lower thermal conductivity than brick.
- Wall C therefore conducts energy out most slowly, wall B comes next and wall A conducts energy out fastest.
- A room behind wall C has the lowest rate of cooling, and a room behind wall A has the highest.
Common Mistake
- Do not write that a thick or well-insulated wall stops energy escaping, because it only reduces the rate at which energy is conducted through it.
- Do not confuse temperature, which measures how hot something is, with the energy in its thermal energy store.
- Do not compare materials of different thicknesses and give the difference to thermal conductivity alone, because thickness changes the rate of cooling too.
Exam technique
Explaining the rate of cooling
- Build the answer as a chain that links the property of the wall to how quickly energy is conducted through it and then to the rate of cooling.
- Use comparative words such as thicker, lower thermal conductivity, more slowly and lower rate of cooling, because the marks are for the direction of each change.
- In a practical question, compare the temperatures of the cans after the same time, or compare the gradients of the cooling curves, rather than only saying that one can is hotter.
Self review
- Define thermal conductivity.
- State the effect on the rate of cooling of a building of making its walls thicker.
- Explain why a wall containing foam insulation cools a house more slowly than a solid concrete wall of the same thickness.
- Name the independent and dependent variables in the copper can investigation.
- Explain how a cooling curve shows which can is cooling faster.
