Thermal resistance help with different units The equation for thermal resistance R is:
$$R=\frac{\Delta T}{q}=\frac{L}{k}$$
with

*

*T being the temperature difference (in kelvins)

*q being the heat flow rate (in W/m²)

*L being the thickness of the material (in metres)

*k being the thermal conductivity (in W/(mK), watts per metre kelvin)

Whether you use:

*

*temperature and q, kelvin / (watts × metres²) ⇒ (metres² × kelvin) / watts or


*L and k, metres / (watts / (metre × kelvin)) ⇒ (metres² × kelvin) / watts,
you obtain (metres² × kelvin) / watts. This makes sense, as (m² × K) / W is the units for thermal resistance.
So why do datasheets for electronic components give thermal resistance with units of °C/W? I understand °C/W likely means for every watt of power dissipated by the device, the device heats up by that temperature. But how can this parameter have two different units?
Is 8°C/W the same as 8 (m² × K) / W?
 A: The datasheets for electronic components have already incorporated the relevant area, turning the heating flux in W/m² into a heating rate in W. This saves you the effort of looking up the area for that component and correcting for it.
No, 8°C/W is not the same as 8 K-m²/W, but it is the same as 8 K/W because the intervals of the Celsius and Kelvin scales are identical.
A: To add to Chemomechanics' answer, yu can find two definitions of the thermal resistance, if you read papers related to this notion. Of is the one you show, with q being the heat flux and the other one with q being the just the thermal power, in watts. They seem to be both used by people working in the fields related to heat transfer. You just have to be careful to be consistent. I had the same problem when I satrted in a thermal properties project.
A: The defining equation with consistent units is
$$ R = \frac{\Delta T}{\dot{q}} = \frac{L}{k A} $$
where $\Delta T$ is a temperature difference $^o$C or $K$, $\dot{q}$ is heat flow (W) (not heat flux), $L$ is distance (m), $k$ is thermal conductivity (W/m $^o$C), and $A$ is area (m$^2$). The analogy is Ohm's law with $\Delta V = i R$ where $i$ is current flow not current flux.
The units become
$$ \frac{^oC}{W} = \frac{m}{(W/m\ ^oC)\ m^2} $$
and are thereby consistent.
An alternative form of thermal resistance is $R' = R A$ with units of m$^2$ $^o$C/W. The alternative form would be $R' = L/k$. The two forms for thermal resistance are not to be set equal to each other ($R \neq R'$). This is the root of the confusion on units. You can however take a basis unit of 1 in the area units (e.g. 1 m$^2$ or 1 ft$^2$) to compare values for $R$ and $R'$.
Finally, this conversion set shows how the units on temperature scales can be considered.
$$\Delta T = 0\ ^oC = 0\ K\ \mathrm{as\ a\ difference} \neq 0\ K\ \mathrm{as\ an\ absolute}$$
$$ T = 0\ ^oC = 273.15\ K$$
