Thermal conductivity and Required Practical 2

Buildings lose heat through walls, roofs and windows. Thermal conductivity measures how easily energy passes through a material by conduction. Lower conductivity = better insulator. The rate at which a building cools depends on the conductivity of its materials, the thickness of the walls, and the temperature difference inside vs outside.

Conduction in solids

Energy passes through a solid by:

1. Particles vibrate in their fixed positions; faster vibrations spread to neighbouring particles.
2. In metals also by free electron transfer — which is why metals conduct heat (and electricity) very well.

A material with high thermal conductivity transfers energy quickly:

• Copper: ~400 W/m K — excellent conductor.
• Brick: ~0.7 W/m K — moderate.
• Wood: ~0.15 W/m K — poor conductor (good insulator).
• Air: ~0.025 W/m K — very poor conductor; trapped air is a great insulator.

Rate of cooling — the factors

For a building (or any hot object):

• Greater thickness of walls → slower energy transfer → slower cooling.
• Lower thermal conductivity of walls → slower energy transfer → slower cooling.
• Larger temperature difference between inside and outside → faster transfer (greater rate of cooling).
• Larger surface area → faster transfer.

Required Practical 2 — investigating insulation

The aim is to compare different insulating materials, or different thicknesses of one material.

Apparatus

• Small can or beaker (the "house").
• Lid with a hole for a thermometer.
• Hot water (around 80 °C).
• Insulating material — bubble-wrap, cotton wool, fleece, newspaper.
• Stopwatch and digital thermometer.

Method

1. Wrap the can in one insulating material of fixed thickness.
2. Pour a measured volume of hot water (e.g. 200 ml) into the can; record starting temperature.
3. Replace the lid and start the stopwatch.
4. Record the temperature every minute for 10 minutes.
5. Repeat with a different insulating material (or different thickness) — same volume, same starting temperature.
6. Plot temperature against time on the same axes.

Variables

• Independent: type/thickness of insulator.
• Dependent: temperature after a fixed time (or rate of cooling).
• Control: volume of water, starting temperature, surrounding air temperature, lid type, can shape.

Sample data

Insulator	Initial T (°C)	T after 10 min (°C)	$\Delta T$
None	80	50	30
Newspaper	80	60	20
Bubble wrap	80	65	15
Cotton wool	80	68	12

Best insulator = smallest temperature drop. Cotton wool wins because it traps lots of small air pockets — air is a poor conductor.

Why air pockets matter

A "good insulator" doesn't actually work because of the material itself — wool, fleece and fibreglass are all just trapping air. The trick is that the trapped air can't circulate (so no convection) and air conducts very poorly anyway. Loose tightness matters: too tight and air is squeezed out.

Building applications

• Loft insulation — fibreglass with trapped air.
• Cavity-wall insulation — foam between two layers of brick reduces conduction and stops convection.
• Double glazing — gap of air or argon between panes.
• Thicker walls — slower energy transfer simply because there's more material to traverse.

Common pitfalls

1. Forgetting to use the same volume of water — different volumes have different heat capacities so they cool at different rates anyway.
2. Forgetting to put a lid on — convection from the open top will dominate over conduction through the wrapped sides.
3. Reporting after a long time when temperatures all converge to room temperature — pick a fixed time before equilibrium.
4. Not labelling axes (you lose marks).

Calculation example

A house loses 4000 J/s through its walls. The walls are doubled in thickness (everything else equal). What is the new rate of energy loss? 2000 J/s, because conductive loss is inversely proportional to thickness (for a given $\Delta T$ and area).