Thermal Conduction for the ESAT

Understanding Thermal Energy and Heat

All matter, whether solid, liquid, or gas, is composed of microscopic particles such as atoms, molecules, or ions. These particles are constantly in motion. In solids, they vibrate about fixed positions, whereas in fluids (liquids and gases), they are free to move from one place to another.

Thermal energy is the energy a substance possesses due to this microscopic motion. It is important to distinguish thermal energy from temperature: temperature is a measure of 'hotness', and while an increase in thermal energy usually leads to an increase in temperature, they are not identical. At higher temperatures, particles possess higher average kinetic energy and move faster.

When thermal energy moves from one location to another, it is referred to as heat. Heat always transfers from regions of higher temperature to regions of lower temperature.

The Mechanism of Conduction

Thermal conduction is the transfer of heat through a substance by the passing of kinetic energy between its microscopic particles. In solids and liquids, where particles are close together, this occurs most readily. Conduction can also occur between different states of matter if they are in physical contact.

In a solid, particles in a hotter region vibrate with greater energy. Over time, they collide with and pass energy to their neighbours, which then vibrate more vigorously. This process spreads through the material until the temperature rises even in areas far from the original heat source.

In liquids, energy is similarly transferred, but primarily through collisions between particles as they move past each other.

Thermal Conductors and Insulators

Materials differ in their ability to conduct heat. A good conductor allows heat to transfer relatively quickly. Metals are prime examples of good conductors in both solid and liquid states, with silver, gold, and copper being particularly efficient.

Poor conductors are known as insulators. They allow heat to transfer only slowly. Common insulators include wood, plastics, and gases like air. Materials that trap air, such as fibreglass or foam, are also excellent insulators. It is important to note that conduction cannot occur in a vacuum because there are no particles to pass on kinetic energy.

Conduction in Different States of Matter

The physical state of a substance significantly affects its conductivity:

1. Gases are the poorest conductors because their particles are far apart, making collisions infrequent.
2. Liquids conduct better than gases but usually worse than solids, as their particles are not held as tightly together as they are in solids, slowing the transfer of kinetic energy.
3. Solids are generally the best conductors due to the close proximity of their particles.

The Role of Free Electrons in Metals

Metals are exceptional conductors in both solid and liquid states because they contain free electrons. These electrons are not bound to specific atoms and can move throughout the lattice of metal ions.

When a metal is heated, both the ions and the free electrons gain kinetic energy. While the ions can only transfer energy slowly to their immediate neighbours, the free electrons move rapidly through the lattice, colliding with other electrons and ions. This allows for a much faster transfer of energy than in non-metals.

Worked Examples: Comparing Conductivities

Example 1: Ordering Substances

Write these substances in order of thermal conductivity, from the best insulator to the best conductor: liquid water, water vapour, solid aluminium, and ice (frozen water).

Solution: Aluminium is a metal and is therefore the best conductor. Ice is a non-metal solid and a poor conductor, but it is better than liquid water. Liquid water is a better conductor than water vapour because particles in a liquid are closer together than in a gas. The order from best insulator to best conductor is: water vapour, liquid water, ice, solid aluminium.

Example 2: Silver vs Rubber

Explain why liquid silver is a better thermal conductor than solid rubber.

Solution: Silver is a metal. It contains free electrons that move through the material in both solid and liquid states, transferring energy rapidly. Rubber is a non-metal with no free electrons, so it conducts heat much more slowly through ion vibration alone.

Factors Affecting the Rate of Conduction

Consider two objects at temperatures $T_1$ and $T_2$ connected by a material with a uniform cross section.

If $T_1$ is greater than $T_2$, heat flows from left to right. The rate of this heat transfer depends on several variables:

1. The temperature difference: A higher difference ($T_1 - T_2$) results in a higher rate of transfer.
2. The nature of the material: Substances that are better thermal conductors transfer heat more quickly.
3. The distance: A shorter distance (or thickness) between the two objects increases the rate of transfer.
4. The surface area: A larger area of contact between the objects and the connecting material increases the rate of transfer.

Surface Area and the Rate of Heat Loss

When an object is surrounded by a substance at a different temperature, the area of contact is its total surface area. Comparing two objects at the same temperature, the one with the larger surface area will lose or gain heat faster.

A larger surface area allows for more frequent collisions between the surface particles and the particles of the surrounding medium, leading to a higher rate of energy transfer.

Worked Example: Window Design

For each pair of changes to a double-glazed window, state and explain whether the changes could be made without changing the rate of thermal conduction through the window.

1. Increasing the glass thickness and decreasing the window area: No. Both changes decrease the rate of conduction individually, so the combined effect must be a decrease.
2. Replacing air with a gas that is a better insulator and increasing the window area: Yes. The better insulator decreases the rate, while the larger area increases it. These effects could cancel each other out.
3. Decreasing glass thickness and replacing air with a vacuum: No. Conduction is not possible through a vacuum, so the rate of conduction through the window must drop to zero.