Question

The unit of thermal conductivity is:
A. $W{m^{ - 1}}{K^{ - 1}}$
B. $Jm{K^{ - 1}}$
C. $J{m^{ - 1}}{K^{ - 1}}$
D. $Wm{K^{ - 1}}$

Answer 1

When attempting questions like the one given above, keep in mind the definition of thermal conductivity, how it is measured et cetera. Keep in mind where thermal conductivity’s concepts are applied in real life, and what factors affect thermal conductivity and what causes it to increase and decrease.

Complete answer:
We know that thermal conductivity is defined as the transportation of energy due to random movement of molecules across the temperature gradient. It can be defined as the measure of a material’s ability to conduct heat.
The ability to conduct heat through a solid is proportional to its thermal conductivity. A solid's ability to transfer heat through it will reduce if its heat conductivity is low.
The rate of heat conduction through a medium depends on following factors:-
Geometry of the medium,
its thickness, and
The material of the medium.
It also depends on the temperature difference across the medium
There have been many experiments to derive the formula of thermal conductivity, the results of such experiments show that for a given $\Delta T$;
The quantity of heat conducted is directly proportional to the area of each surface, i.e. $Q \propto A$
Quantity of heat conducted is directly proportional to the temperature gradient in direction of heat flow, i.e. $Q \propto \dfrac{{\Delta T}}{{\Delta x}}$(provided $\Delta T$ and $\Delta x$ are small )
Quantity of heat conducted is directly proportional to the time i.e. $Q \propto t$
So when we combine all the three points given above we get one formula for thermal conductivity, who’s unit for simplification we will call $k$.
So the derived formula will be;
$k = \dfrac{{QL}}{{A\Delta T}}$
Where $k$ is the thermal conductivity
The amount of heat transported through the material denoted by the letter $Q$
$A$ is the area of the body
$\Delta T$ is the temperature difference
So the unit of thermal conductivity comes out to be $W{m^{ - 1}}{K^{ - 1}}$
Hence, option (A) is true.

Note: When we talk about Thermal conductivity, there are chances we can confuse it with thermal resistivity. Thermal resistance, on the other hand, is the inverse of thermal conductivity. It is defined as the temperature difference by which a material can resist the heat flow, while thermal conductivity does not resist heat flow.