Thermal conductivity

Thermal conductivity, frequently represented by [math]\kappa[/math], is a property that relates the rate of heat loss per unit area of a material to its rate of change of temperature. Essentially, it is a value that accounts for any property of the material that could change the way it conducts heat. In SI units, thermal conductivity is expressed in watts per meter kelvin [math]\left(\frac{W}{m K}\right)[/math] whereas in imperial units it can be expressed in BTU per hour per foot Fahrenheit [math]\left(\frac{BTU}{h ft ^{\circ}F}\right)[/math]. Materials with a higher thermal conductivity are good conductors of thermal energy.

Since heat transfer by conduction involves transferring energy without motion of the material, it is logical that the rate of the transfer of heat would depend only on the temperature difference between two locations and the thermal conductivity of the material.

For more information on thermal conductivity, see Hyperphysics.

Values for Common Materials

Thermal Conductivity, [math]\kappa[/math]

Material	Conductivity at 25oC
Acrylic	0.2
Air	0.024
Aluminum	205
Bitumen	0.17
Brass	109
Cement	1.73
Copper	401
Diamond	1000
Felt Insulation	0.04
Glass	1.05
Iron	80
Oxygen	0.024
Paper	0.05
Silica Aerogel	0.02
Vacuum	0
Water	0.58

From the table to the left, it can be seen that most materials generally associated with being good conductors have a high thermal conductivity. Mainly metals have very high thermal conductivity which compares well to what is known about metals. As well, insulating materials such as aerogel and insulation used in homes has a low thermal conductivity, indicating that they do not let heat pass through them easily. Thus a low thermal conductivity indicates a good insulating material.

Materials in between these have neither significant insulating or conducting properties. Cement and glass neither conduct extremely large amounts of heat nor do they insulate extremely well.

The idea that the thermal conductivity of certain materials are linked to how well they insulate provides a connection between thermal conductivity, and R-values/ U-values. Since U and R-values to express how well a certain material resists the flow of heat, thermal conductivity plays a role in shaping these values. However, the U and R values also are dependent on the thickness of the material whereas thermal conductivity does not account for this.

Thermal and Electrical Conductivity

The values for thermal conductivity and electrical conductivity of metals can be expressed and compared using a ratio known as the Wiedemann-Franz Ratio. This ratio is expressed as:

[math]L = \frac{\kappa}{\sigma T} = \frac{\pi^2k^2}{3e^2}[/math]

Where:

• [math]L[/math] is a constant known as the Lorentz number, equal to 2.44 x 10^-8 WΩ/K²
• [math]\kappa[/math] is the thermal conductivity of the material
• [math]\sigma[/math] is the electrical conductivity of the material
• [math]T[/math] is the temperature of the material, in Kelvin
• [math]k[/math] is the Boltzmann's constant
• [math]e[/math] is the elementary charge of an electron