PYQ NEET- Units Of Measurement L-10

Question: The unit of thermal conductivity is :#

A) $\mathrm{Jm}^{-1} \mathrm{~K}^{-1}$

B) $\mathrm{WmK}^{-1}$

C) $\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1}$

D) $\mathrm{J} \mathrm{m} \mathrm{K}^{-1}$

Answer: $\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1}$#

Solution:#

The rate of heat flow through a conductor of length $L$ and area of cross-section $A$ is given by $$ \frac{d Q}{d t}=K A \frac{\Delta T}{L} \mathrm{~J} / \mathrm{s} \text { or watt } $$ where, $K=$ coefficient of thermal conductivity and $\Delta T=$ change in temperature $$ \begin{aligned} \Rightarrow \quad K & =\frac{L}{A \Delta T} \frac{d Q}{d t} \ \therefore \text { Unit of } K & =\frac{\text { metre }}{\left(\text { metre }^2 \times\right. \text { kelvin }} \times \text { watt } \ & =W m^{-1} K^{-1} \end{aligned} $$