Question

The dimension formula of thermal conductivity K given relation , $K=\frac{QL}{A∆T}$

Answer 1

Thermal conductivity: It is the property of the material to conduct heat through it.

Step 1: Given Data

Formula: $K=\frac{QL}{A∆T}$

Where $Q$ is the heat transferred through the material

$L$ is the length of the material.

$A$ is the area of the cross-section of the material

$∆T$ Is the temperature gradient.

Step 2: Calculate the Dimensions

Plug in the dimensional formula of the known variables

Dimensional formula of $Q$ is $M^1{L}^2{T}^{-2}$

Dimensional formula of $L$ is $M^0{L}^1{T}^0$

Dimensional formula of $A$ is $M^0{L}^2{T}^0$

Dimensional formula of $∆T$ is $M^0{L}^0{T}^0{K}^1$

⇒ The dimensional formula of $K$ is $\frac{\left[M^1{L}^2{T}^{-2}\right]\left[M^0{L}^1{T}^0\right]}{\left[M^0{L}^2{T}^0\right]\left[M^0{L}^0{T}^0{K}^1\right]}$

⇒ The dimensional formula of $K$ is $M^1{L}^1{T}^{-2}{K}^{-1}$