Question: The unit of thermal conductivity is: [PMT/NEET-2019]
a. W m$^{-1}$ K$^{-1}$
b. J m K$^{-1}$
c. J m$^{-1}$ K$^{-1}$
d. W m K$^{-1}$

Answer: a. W m$^{-1}$ K$^{-1}$

Solution: Thermal conductivity $K$ is defined by Fourier’s law of heat conduction:

$
\frac{Q}{t} = -K \cdot A \cdot \frac{dT}{dx}
$

where $\frac{Q}{t}$ is the rate of heat transfer (Watt), $A$ is the area (m²), $\frac{dT}{dx}$ is the temperature gradient (K/m).

Rearranging for $K$:

$
K = \frac{\frac{Q}{t}}{A \cdot \frac{\Delta T}{\Delta x}}
$

Units:
$
K = \frac{W}{m^2 \cdot (K/m)} = \frac{W}{m \cdot K}
$

So,
$
[K] = W \, m^{-1} K^{-1}
$

Hence the unit of thermal conductivity is W m⁻¹ K⁻¹.