What are the units for thermal conductivity and why?
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$\begingroup$ What happens in thermal conductivity, and what factors determine the amount of energy transmitted? $\endgroup$– DJohnMCommented Sep 7, 2013 at 2:12
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3 Answers
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Thermal conductivity is, as Mark writes, is in SI units measured in $Wm^{-1}K^{-1}$, i.e. $\frac{power}{distance \times temperature}$
However, the $m^{-1}$ needs a little more explanation.
The rate of heat flow is proportional to the surface area, and inversely proportional to the thickness. So for the unit of thermal conductivity, thickness gives a $distance^1$ in the numerator, and surface area gives a $distance^2$ in the denominator.
Hence, thermal conductivity is $\frac{power \times distance}{distance^2 \times temperature}$.
And so when we cancel $distance^1$ from numerator and denominator, we get $\frac{power}{distance \times temperature}$
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Thermal conductivity has dimensions of $\mathrm{Power / (length * temperature)}$. Power is the rate of heat flow, (i.e.) energy flow in a given time. Length represents the thickness of the material the heat is flowing through, and temperature is the difference in temperature through which the heat is flowing.
In SI units, it is commonly expressed as $\mathrm{Watts / (meter * Kelvin)}$, and in US units, it is commonly given in $\mathrm{BTU/hr/(feet\ *\ ^oF)}$.
It expresses the rate at which heat is conducted through a unit thickness of a particular medium. That rate will vary linearly based on the temperature difference across the material, so it is expressed as a value per degree of temperature difference, thus Heat Rate per unit thickness per degree of temperature difference.
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$\begingroup$ This is incorrect, the distance in this unit is not thickness. There is a proper explanation in one of the answers below. The distance in this unit is essentially a mathematical abstraction, somewhat like acceleration being quoted as distance*time^2 (which is a mathematically correct reduction when limited to specific base units) but the general physical concept is (distance per time)*(time of action) which stands up to a mix of units and offers better visualization to many students. $\endgroup$ Commented May 14, 2020 at 21:27
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You might need to look up R-Value which is closely related to thermal conductivity and is being used in so many case instead.
The units are $ \frac{(ft^2.h.^{\circ}F)}{BTU} $ in US and $ \frac{(K.m^2)}{W} $ in SI.
These two units (Thermal conductivity and R-Value) can be converted to each-other very easily doing Say if x is our Thermal conductivity value for our material, hence R-Value will be,
a is the thickness in Meters
$$ \frac{1}{x}* (a) $$
