Question

If $K$ denotes coefficient of thermal conductivity, $d$ the density and $C$ the specific heat, the unit of $X$, where $X=\frac{K}{dC}$ will be,

• A. $cm{s}^{-1}$
• B. $c{m}^2{s}^{-2}$
• C. $cms$
• D. $c{m}^2{s}^{-1}$

Answer 1

The correct option is D

$c{m}^2{s}^{-1}$

Step 1: Given and known values

We know, units of $K$,$d$ and $C$ are,

$$\begin{gathered} K=cal{s}^{-1}c{m}^{-1}°C^{-1} \\ d=gc{m}^{-3} \\ C=cal{g}^{-1}°C^{-1} \end{gathered}$$

Step 2: Solution

Unit of $X$,

$X=\frac{K}{dC}$

$K$ denotes the coefficient of thermal conductivity

$d$ is the density

$C$ is the specific heat

Substituting their units, we get

$$\begin{gathered} \Rightarrow X=\frac{cal{s}^{-1}c{m}^{-1}°C^{-1}}{gc{m}^{-3}\times cal{g}^{-1}°C^{-1}} \\ \Rightarrow X=c{m}^2{s}^{-1} \end{gathered}$$

Therefore, the unit of $X$ is $c{m}^2{s}^{-1}$.

Hence, option D is correct.