Thermal Conduction (DP IB Physics)

Thermal Conduction

• 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

Temperature Gradient Equation

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