Thermal Conduction (SL IB Physics)

• Thermal energy can be transferred from a hotter area to a cooler area through one of the following mechanisms:
  • Conduction
  • Convection
  • Radiation

Thermal conduction, convection and radiation in a mug of tea

• Objects will always lose heat until they are in thermal equilibrium with their surroundings
  • For example, a mug of hot tea will cool down until it reaches room temperature

Conduction

• Conduction is the main method of thermal energy transfer in solids
• Conduction occurs when:

Two solids of different temperatures come in contact with one another, thermal energy is transferred from the hotter object to the cooler object

• Metals are the best thermal conductors
  • This is because they have a high number of free electrons

• Non-metals, such as plastic or glass, are poor at conducting heat
  • Poor conductors of heat tend to also be poor conductors of electricity
  • This suggests a link between the mechanisms behind both types of conduction

• Liquids and gases are even poorer thermal conductors
  • This is because the atoms are further apart

Conduction of Heat in a Metal

During conduction, the atoms in a solid vibrate and collide with each other

• Conduction can occur through two mechanisms:
  • Atomic vibrations
  • Free electron collisions

• When a substance is heated, the atoms, or ions, start to move around, or vibrate, more
  • The atoms at the hotter end of the solid will vibrate more than the atoms at the cooler end
  • As they do so, they bump into each other, transferring energy from atom to atom
  • These collisions transfer internal energy until thermal equilibrium is achieved throughout the substance
  • This occurs in all solids, metals and non-metals alike

• Metals are especially good at conducting heat due to their high number of delocalised electrons
  • These can collide with the atoms, increasing the rate of transfer of vibrations through the material
  • This allows metals to achieve thermal equilibrium faster than non-metals

Thermal Conductivity

• The conductivity of a material can be quantified by its thermal conductivity
• Thermal conductivity is defined as

The ability of a substance to transfer heat via conduction

• It is denoted by the symbol k and has units of W m⁻¹ K⁻¹
• The thermal conductivities of some common materials are shown in the table below

• Excellent thermal conductors...
  • Have high values of thermal conductivity
  • Transfer thermal energy at a fast rate
  • (Usually) contain a large number of delocalised electrons (diamond being the obvious exception)

• Poor thermal conductors (insulators)...
  • Have low values of thermal conductivity
  • Transfer thermal energy at a slow rate
  • Contain few delocalised electrons

Temperature Gradient Formula

• When there is a temperature difference between two points, thermal energy will flow from the region of higher temperature to the region of lower temperature
  • This is known as a temperature gradient

• The rate of the heat transfer via conduction is given by

• Where
  • = flow of thermal energy per second (W)
  • k = thermal conductivity of the material (W m⁻¹ K⁻¹)
  • A = cross-sectional area (m²)
  • ΔT = temperature difference (K or °C) 
  • Δx = thickness of the material (m)
• The flow of thermal energy per second can be considered to be uniform across a temperature gradient, provided A is constant, regardless of material
  • This is analogous to electrical current being constant throughout a series circuit, even though the components may have different resistances

Conduction of thermal energy through a solid

Thermal energy flows down a temperature gradient. The rate of energy transfer depends on the properties of the material