Question

The dimensions of the coefficient of thermal conductivity are

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\text{For bar of cross-sectional area A,length (l) and having temperatures}{\theta }_1\text{and}{\theta }_2\text{at its two ends, the amount of heat energy Q flowing normally across the bar in time (t) is given by}Q=\frac{KA(\theta 1-\theta 2)t}{l}$ $\text{Where K is the coefficient of thermal conductivity . Therefore,}K=\frac{Ql}{A(\theta 1-\theta 2)t}\therefore ofk=\frac{dimensionsofQ\times dimensionsofl}{dimensionsofA\times of({\theta }_1-{\theta }_2)\times dimensionsoft}=\frac{M{L}^2{T}^{-2}\times L}{L^2\times K\times T}=ML{T}^{-3}{K}^{-1}$ $\text{Hence the correct choice is (d)}$