# Thermal conductivity

(Redirected from Watt per metre-kelvin)
In physics, thermal conductivity, λ, is the intrinsic property of a material which relates its ability to conduct heat.
It is the quantity of heat, Q, transmitted through a unit thickness, L, in a direction normal to a surface of unit area, A, due to a unit temperature gradient, ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.
thermal conductivity = heat flow rate × distance / (area × temperature gradient)
λ = Q × L / (A × ΔT)

(Halliday, 1997 p.470)

 Contents

## Units

In the SI system of units, thermal conductivity is measured in watts per metre-kelvin, W·m-1·K-1 or W/(m·K)

where

watt is the unit of power

metre is the unit of distance

kelvin is the unit of temperature

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

In old literature you may find the following unit for thermal conductivity: cal/(m·h·°C). This stands for ((cal/h)/m)/°C. By multiplying this value by 0.001162 (=4.184/3600) it is converted to the SI unit (assuming the calories are the small or gram calories, not kilogram or food calories).

## 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:

MaterialThermal conductivity
W·m-1·K-1
Diamond1000-2600
Silver406
Copper385
Gold320
Aluminium205
Brass109
Platinum70
Steel50.2
Mercury8.3
Quartz8
Ice1.6
Glass0.8
Water0.6
Wood0.04-0.12
Wool0.05
Fiberglass0.04
Air (300 K, 100 kPa)0.026
Silica aerogel0.017
Styrofoam0.01

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-metres 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, 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 L this is λA/L, measured in W·K-1. This matches the relationship between electrical conductivity (A·m-1·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/L, measured in W·K-1
• thermal resistance = L/λA, measured in K·W-1
• heat transfer coefficient = λ/L, measured in W·K-1·m-2
• thermal insulance = L/λ, measured in K·m2·W-1.

The heat transfer coefficient is also known as thermal admittance. But thermal admittance may mean other things.

### Second definition (buildings)

When dealing with buildings, 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 L:

• thermal conductance = λ/L, measured in W·K-1·m-2
• thermal resistance (R value, thermal resistivity in scientific terms) = L/λ, measured in K·m2·W-1.
• thermal transmittance (U value)= 1/(Σ(L/λ)) + convection + radiation, measured in W·K-1·m-2

## Molecular origins

The thermal conductivity of a system is determined by how molecules comprising the system interact. There are no simple but correct expressions for the thermal conductivity. The simplest exact expression employs one of the Green-Kubo relations. Although this expression is exact, in order to calculate the thermal conductivity of a dense fluid or solid using this relation requires the use of molecular dynamics computer simulation (http://rsc.anu.edu.au/~evans/evansmorrissbook.htm).

## References

Halliday, David; Resnick, Robert; & Walker, Jearl(1997). Fundamentals of Physics (5th ed.). John Wiley and Sons, INC., NY ISBN 0-471-10558-9.ca:Conductivitat tèrmica de:Wärmeleitfähigkeit es:Conducción de calor fr:Conductivité thermique it:Conducibilità termica nl:Warmtegeleiding ja:熱伝導率 pl:Przewodność cieplna pt:Condutividade térmica ro:Conductibilitate termică ru:Теплопроводность sl:Toplotna prevodnost fi:Lämmönjohtavuus sv:Värmeledningsförmåga

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