Question

The dimension formula for thermal conductivity is (here $K\text{denotes the temeperature}$)

• A. $ML{T}^{-2}K$
• B. $ML{T}^{-2}{K}^{-2}$
• C. $ML{T}^{-3}K$
• D. $ML{T}^{-3}{K}^{-1}$

Answer 1

The correct option is D $ML{T}^{-3}{K}^{-1}$

Using , $\frac{dQ}{dt}=kA\frac{dT}{dx}$

$\Rightarrow k=\frac{\left(\frac{dQ}{dt}\right)}{A\left(\frac{dT}{dx}\right)}$

$\left[k\right]=\frac{\left[M{L}^2{T}^{-3}\right]}{\left[L^2\right]\left[K{L}^{-1}\right]}=\left[ML{T}^{-3}{K}^{-1}\right]$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.