Thermal conductivity

The thermal conductivity of a material is equivalent to the quantity of heat that passes in unit time through unit area of a plate, when its opposite faces are subject to unit temperature gradient (e.g. one degree temperature difference across a thickness of one unit).

Thermal conductivity = Heat flow rate ÷ (Area × Temperature gradient)

Table of contents

1 Units 2 Examples 3 Related terms 3.1 First definition (general) 3.2 Second definition (buildings) 4 See Also

Units

In the SI system of units, thermal conductivity is measured in watts per meter-kelvin, (W·m^-1·K^-1) where a

• watt is the unit of power
• meter is the unit of distance
• kelvin is the unit of temperature

Thermal conductivity should not be confused with thermal conductance, which is explained below.

Examples

In general thermal conductivity tracks electrical conductivity, metals being good thermal conductors. There are exceptions, the most outstanding is that of diamond which has a high thermal conductivity, between 1000 and 2600 W·m^-1·K^-1, while the electrical conductivity is low.

Thermal conductivity of other common materials:

• Silver 430 W·m^-1·K^-1
• Copper 390
• Gold 320
• Aluminium 236
• Platinum 70
• Quartz 8
• Glass 1
• Water 0.6
• Wool 0.05
• Expanded polystyrene ("Styrofoam") 0.03

Thermal conductivity changes with temperature. For most materials it decreases slightly as the temperature rises.

Since diamond has such a high thermal conductivity, natural blue diamond much higher still, one may test gems to determine if they are genuine diamonds using a thermal conductance tester, one of the instruments of gemology. Diamonds of any size are notably cool to the touch because of their high thermal conductivity, perhaps the origin of the term "ice."

Related terms

The reciprocal of thermal conductivity is thermal resistivity, measured in kelvin-meters per watt (K·m·W^-1).

When dealing with a known amount of material, its thermal conductance and the reciprocal property, thermal resistance, can be described. Unfortunately there are differing definitions for these terms.

First definition (general)

For general scientific use [2]class="external">[1, thermal conductance is the quantity of heat that passes in unit time through a plate of particular area and thickness when its opposite faces differ in temperature by one degree. For a plate of thermal conductivity λ, area A and thickness T this is &lambda/em>, measured in W·K^{-1electrical conductivity}·V^-1) and electrical conductance (A·V^-1).

There is also a measure known as heat transfer coefficient: the quantity of heat that passes in unit time through unit area of a plate of particular thickness when its opposite faces differ in temperature by one degree. The reciprocal is thermal insulance. In summary:

• thermal conductance = λA/T, measured in W·K^-1
  • thermal resistance = T/λA, measured in K·W^-1
• heat transfer coefficient = λ/T, measured in W·K^-1·m^-2
  • thermal insulance = T/λ, measured in K·m²·W^-1.

The heat transfer coefficient is also known as thermal admittance. But thermal admittance may mean other things (e.g. [1], page 5).

Second definition (buildings)

When dealing with buildings ([1], thermophysics FAQ 5)[1], thermal resistance or R value means what is described above as thermal insulance, and thermal conductance means the reciprocal. For materials in series, these thermal resistances (unlike conductances) can simply be added to give a thermal resistance for the whole.

A third term, thermal transmittance, incoporates the thermal conductance of a structure along with heat transfer due to convection and radiation. It is measured in the same units as thermal conductance and is sometimes known as the composite thermal conductance. The term U value is another synonym.

The term K value is a synonym for thermal conductivity.

In summary, for a plate of thermal conductivity λ, area A and thickness T:

• thermal conductance = λ/T, measured in W·K^-1·m^-2
  • thermal resistance (R value) = T/λ, measured in K·m²·W^-1.
• thermal transmittance (U value)= 1/(&Sigma(T/λ)) + convection + radiation, measured in W·K^-1·m^-2

See Also

• conduction