Thermal conductivity

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In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat.

It is defined as the quantity of heat, Q, transmitted through a thickness L, in a direction normal to a surface of area A, due to a temperature difference 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 difference)

k = Q × L / (A × ΔT)

1 Examples
2 Some typical thermal conductivities (k values)
- 2.1 References and additional sources of k values
3 Measurement
4 Related terms
- 4.1 First definition (general)
- 4.2 Second definition (buildings)
5 Textile industry
6 Molecular origins
7 See also
8 External links
9 References

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Examples

In metals, thermal conductivity approximately tracks electrical conductivity, as the freely moving valence electrons transfer not only electric current but also heat. However, this correlation does not apply to some materials, as shown in the table below, where highly electrically conductive silver is shown to be less thermally conductive than diamond, which is an electrical semiconductor.

Thermal conductivity is not a simple property, and depends intimately on structure and temperature. For instance, pure, crystalline substances also exhibit highly variable thermal conductivities along different crystal axes. One particularly notable example is sapphire, for which the CRC Handbook reports a thermal conductivity perpendicular to the c-axis of 2.6 W·m^-1·K^-1 at 373 K, and 6000 W·m^-1·K^-1 at 35 K for an angle of 36 degrees to the c-axis.

Air and other gases are generally good insulators, in the absence of convection. Therefore, many insulating materials function simply by having a large number of gas-filled pockets which prevent large-scale convection. Examples of these include polystyrene (styrofoam) and silica aerogel.

Thermal conductivity is clearly an important quantity for construction and related fields. However, materials used in such trades are rarely subjected to chemical purity standards. Several construction materials' k values are listed below. These should be considered approximate due to the uncertainties related to material definitions.

The following table is meant as a small sample of data to illustrate the thermal conductivity of various types of substances. For more complete listings of measured k-values, see the references.

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Some typical thermal conductivities (k values)

	Thermal conductivity (W·m^-1·K^-1)	Temperature (K)	Notes
Diamond	1,000†	273	type I diamond
Silver	429†	300	Highest electrical conductivity of any metal
Iron, pure	80.2†	300
Stainless Steel	14†	273
Limestone	1.3††
Ice	2.2†	273
Soil (dirt)	0.2-1.1†††
Oak	0.16†	298
Rubber (92%)	0.16†	303
Polystyrene	0.033†	98-298
Nitrogen	0.026†	300
Air (100 kPa)	0.0262†	300
Silica aerogel	0.003†	98-298

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References and additional sources of k values

†CRC handbook of chemistry and physics †† Marble Institute ††† Soil Sci Journals

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Measurement

For good conductors of heat, Searle's bar method can be used [1]. For poor conductors of heat, Lees' disc method can be used [2]. VELA is an old data logging machine. An alternative traditional method using real thermometers is described at [3]. A brief review of relatively new class of dynamic methods that are measuring thermal conductivtiy, thermal diffusivity and specific heat within a single measurement is available at [4]

A thermal conductance tester, one of the instruments of gemology, determines if gems are genuine diamonds using diamond's uniquely high thermal conductivity, which is higher still for natural blue diamond.

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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.

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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 k, area A and thickness L this is kA/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 = kA/L, measured in W·K^-1
- thermal resistance = L/kA, measured in K·W^-1
heat transfer coefficient = k/L, measured in W·K^-1·m^-2
- thermal insulance = L/k, measured in K·m²·W^-1.

The heat transfer coefficient is also known as thermal admittance, but this term has other meanings.

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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 k, area A and thickness L:

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

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Textile industry

In textiles, a tog value may be quoted instead of thermal resistance.

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Molecular origins

The thermal conductivity of a system is determined by how molecules comprising the system interact. There are no simple, correct expressions for 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.

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