5th  Top materials properties 
In physics, thermal conductivity, k, is the property of a material that indicates its ability to conduct heat. It appears primarily in Fourier's Law for heat conduction. Thermal conductivity is measured in watts per kelvin per metre (W·K^{−1}·m^{−1}). Multiplied by a temperature difference (in kelvins, K) and an area (in square metres, m^{2}), and divided by a thickness (in metres, m) the thermal conductivity predicts the power loss (in watts, W) through a piece of material.
The reciprocal of thermal conductivity is thermal resistivity.
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Generally speaking, there are a number of possibilities to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. A distinction may be observed between steadystate and transient techniques.
In general, steadystate techniques perform a measurement when the temperature of the material measured does not change with time. This makes the signal analysis straightforward (steady state implies constant signals). The disadvantage is that a wellengineered experimental setup is usually needed. The Divided Bar (various types) is the most common device used for consolidated rock samples.
The transient techniques perform a measurement during the process of heating up. The advantage is that measurements can be made relatively quickly. Transient methods are usually carried out by needle probes.
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] An alternative traditional method using real thermometers is described at [3]. A brief review of new methods measuring thermal conductivity, 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.
The reciprocal of thermal conductivity is thermal resistivity, usually measured in kelvinmetres 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.
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 kelvin. For a plate of thermal conductivity k, area A and thickness L this is kA/L, measured in W·K^{−1} (equivalent to: W/°C). Thermal conductivity and conductance are analogous to 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 kelvin. The reciprocal is thermal insulance. In summary:
The heat transfer coefficient is also known as thermal admittance
When thermal resistances occur in series, they are additive. So when heat flows through two components each with a resistance of 1 °C/W, the total resistance is 2 °C/W.
A common engineering design problem involves the selection of an appropriate sized heat sink for a given heat source. Working in units of thermal resistance greatly simplifies the design calculation. The following formula can be used to estimate the performance:
where:
For example, if a component produces 100 W of heat, and has a thermal resistance of 0.5 °C/W, what is the maximum thermal resistance of the heat sink? Suppose the maximum temperature is 125 °C, and the ambient temperature is 25 °C; then the ΔT is 100 °C. The heat sink's thermal resistance to ambient must then be 0.5 °C/W or less.
A third term, thermal transmittance, incorporates 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 Uvalue is another synonym.
In summary, for a plate of thermal conductivity k (the k value ^{[4]}), area A and thickness t:
In metals, thermal conductivity approximately tracks electrical conductivity according to the WiedemannFranz law, as freely moving valence electrons transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in nonmetals. As shown in the table below, highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator.
Thermal conductivity depends on many properties of a material, notably its structure and temperature. For instance, pure crystalline substances exhibit very different thermal conductivities along different crystal axes, due to differences in phonon coupling along a given crystal axis. Sapphire is a notable example of variable thermal conductivity based on orientation and temperature, with 35 W/(m·K) along the caxis and 32 W/(m·K) along the aaxis.[12]
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 gasfilled pockets which prevent largescale convection. Examples of these include expanded and extruded polystyrene (popularly referred to as "styrofoam") and silica aerogel. Natural, biological insulators such as fur and feathers achieve similar effects by dramatically inhibiting convection of air or water near an animal's skin.
Light gases, such as hydrogen and helium typically have high thermal conductivity. Dense gases such as xenon and dichlorodifluoromethane have low thermal conductivity. An exception, sulfur hexafluoride, a dense gas, has a relatively high thermal conductivity due to its high heat capacity. Argon, a gas denser than air, is often used in insulated glazing (double paned windows) to improve their insulation characteristics.
Thermal conductivity is important in building insulation 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 kvalues, see the references.
This is a list of approximate values of thermal conductivity, k, for some common materials. Please consult the list of thermal conductivities for more accurate values, references and detailed information.
Material  Thermal conductivity W/(m·K) 
Silica Aerogel  0.004  0.04 
Air  0.025 
Wood  0.04  0.4 
Hollow Fill Fibre Insulation Polartherm  0.042 
Alcohols and oils  0.1  0.21 
Polypropylene  0.25 ^{[5]} 
Mineral oil  0.138 
Rubber  0.16 
LPG  0.23  0.26 
Cement, Portland  0.29 
Epoxy (silicafilled)  0.30 
Epoxy (unfilled)  0.59 
Water (liquid)  0.6 
Thermal grease  0.7  3 
Thermal epoxy  1  7 
Glass  1.1 
Soil  1.5 
Concrete, stone  1.7 
Ice  2 
Sandstone  2.4 
Stainless steel  12.11 ~ 45.0 
Lead  35.3 
Aluminium  237 (pure) 120—180 (alloys) 
Gold  318 
Copper  401 
Silver  429 
Diamond  900  2320 
Graphene  (4840±440)  (5300±480) 
Heat flux is exceedingly difficult to control and isolate in a laboratory setting. Thus at the atomic level, there are no simple, correct expressions for thermal conductivity. Atomically, the thermal conductivity of a system is determined by how atoms composing the system interact. There are two different approaches for calculating the thermal conductivity of a system.
A kinetic theory of solids follows naturally from the standpoint of the normal modes of vibration in an elastic crystalline solid (see Einstein solid and Debye model)—  from the longest wavelength (or fundamental frequency of the body) to the highest Debye frequency (that of a single particle). There are simple equations derived to describe the relationship of these normal modes to the mechanisms of thermal phonon wave propagation as represented by the superposition of elastic waves—both longitudinal (acoustic) and transverse (optical) waves of atomic displacement. ^{[6]} ^{[7]} ^{[8]} ^{[9]}
The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the thermal conductivity which levels out temperature differentials between compressed and expanded volume elements. For example, the thermal properties of glass are interpreted in terms of an approximately constant mean free path for lattice phonons. Furthermore, the value of the mean free path is of the order of magnitude of the scale of structural (dis)order at the atomic or molecular level. ^{[10]}^{[11]}^{[12]}
Thus, heat transport in both glassy and crystalline dielectric solids occurs through elastic vibrations of the lattice. This transport is limited by elastic scattering of acoustic phonons by lattice defects. These predictions were confirmed by the experiments of Chang and Jones on commercial glasses and glass ceramics, where mean free paths were limited by "internal boundary scattering" to length scales of 10^{−2} cm to 10^{−3} cm. ^{[13]}^{[14]}
The phonon mean free path has been associated directly with the effective relaxation length for processes without directional correlation. Thus, if V_{g} is the group velocity of a phonon wave packet, then the relaxation length is defined as:
where t is the characteristic relaxation time. Now, since longitudinal waves have a much greater group or "phase velocity" than that of transverse waves, V_{long} is much greater than V_{trans}, the relaxation length or mean free path of longitudinal phonons will be much greater. Thus, thermal conductivity will be largely determined by the speed of longitudinal phonons. ^{[13]}^{[15]}
Regarding the dependence of wave velocity on wavelength or frequency (aka "dispersion"), lowfrequency phonons of long wavelength will be limited in relaxation length by elastic Rayleigh scattering. This type of light scattering form small particles is proportional to the fourth power of the frequency. For higher frequencies, the power of the frequency will decrease until at highest frequencies scattering is almost frequency independent. Similar arguments were subsequently generalized to many glass forming substances using Brillouin scattering. ^{[16]}^{[17]} ^{[18]} ^{[19]}
Often in heat transfer the concept of controlling resistance is used to determine how to either increase or decrease heat transfer. Heat transfer coefficients represent how much heat is able to transfer through a defined region of a heat transfer area. The inverse of these coefficients are the resistances of those areas. If a wall can be considered, it would have a heat transfer coefficient representing convection on each side of the wall, and one representing conduction through the wall. To obtain an overall heat transfer coefficient, the resistances need to be summed up.
Due to the nature of the above reciprocal relation, the smallest heat transfer coefficient (h) or the largest resistance is generally the controlling resistance as it dominates the other terms to the point that varying the other resistances will have little impact on the overall resistance:
Thus the controlling resistance can be used to both simplify heat transfer calculations and manipulate a system to a desired resistance value.
First, we define heat conduction, H:
where is the rate of heat flow, k is the thermal conductivity, A is the total cross sectional area of conducting surface, ΔT is temperature difference, and x is the thickness of conducting surface separating the 2 temperatures. Dimension of thermal conductivity = M^{1}L^{1}T^{3}K^{1}
Rearranging the equation gives thermal conductivity:
(Note: ΔT / x is the temperature gradient)
I.E. It is defined as the quantity of heat, ΔQ, transmitted during time Δt through a thickness x, in a direction normal to a surface of area A, per unit area of A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.
Alternatively, it can be thought of as a flux of heat (energy per unit area per unit time) divided by a temperature gradient (temperature difference per unit length)
Typical units are SI: W/(m·K) and English units: Btu/(h·ft·°F). To convert between the two, use the relation 1 Btu/(h·ft·°F) = 1.730735 W/(m·K). [Perry's Chemical Engineers' Handbook, 7th Edition, Table 14]
Thermal conductivity is the ability of a material to conduct heat. Metals are good at moving heat. They are good conductors of heat. Gases are also good at moving heat. They are also good conductors of heat. Thermal resistivity is the opposite of thermal conductivity. Thermal conductivity is often represented by the Greek letter "kappa", $\backslash kappa$. The units of thermal conductivity are watts per meterKelvin. Watts are a measure of power, meters are a measure of length, and Kelvins are a measure of temperature. From the units, we can see that thermal conductivity is a measure of how much power (in watts) moves through a distance (in meters) due to a temperature difference (in Kelvin).
