Question

What is the unit of the coefficient of thermal conductivity $K$?

Answer 1

Hint: The coefficient of anything can be calculated from its formula. And formula can only be understood after having a proper idea of the definition of the term. And we know that the thermal conductivity of a material is measured by the quickness of that material to transfer heat energy from one end to the other end per second.

Complete answer:
To calculate the coefficient of thermal conductivity let us first express thermal conductivity in terms of the distance between the isothermal planes of the material, the amount of heat transferred, the area of the surface and the temperature difference.
$K=\dfrac{Qd}{A\vartriangle T}$
Where, $K$ = Thermal conductivity, $Q$ = amount of heat transferred per second, $d$ = distance between two isothermal planes, $A$ = area of the surface and $\vartriangle T$ = difference in temperature

Using the formula, now we will put the units of the individual terms and derive the unit of thermal conductivity. Now, putting the units of the individual terms in the formula,
$K=\dfrac{wm}{{{m}^{2}}k} \\
\therefore K=w{{m}^{-1}}{{k}^{-1}}$
The meter unit in the numerator gets cancelled by the denominator and we are left with the unit of thermal conductivity, which is $w{{m}^{-1}}{{k}^{-1}}$.Here, $w$ is watt (joule per second), $m$ means meter and $k$ is kelvin.

Therefore, the unit of thermal conductivity is watts per meter-kelvin.

Note: In some platforms, the unit can also be expressed in terms of Joules. The only difference is that we calculated the unit of thermal conductivity per second and they calculated the unit by considering time as a variable. Also, we know that watt is defined as joules per second.