Q. Two rods $A$ and $B$ are of equal lengths. Their ends are kept between the same temperature and their area of cross-sections are $A_{1}$ and $A_{2}$ and thermal conductivities $K_{1}$ and $K_{2}$. The rate of heat transmission in the two rods will be equal, if
A) $K_{1}A_{2} = K_{2}A_{1}$
B) $K_{1}A_{1} = K_{2}A_{2}$
C) $K_{1} = K_{2}$
D) $K_{1}A_{1}^{2} = K_{2}A_{2}^{2}$
Explanation
(b) $\left( \frac{Q}{t} \right)_{1} = \frac{K_{1}A_{1}(\theta_{1} - \theta_{2})}{l}$ and $\left( \frac{Q}{t} \right)_{2} = \frac{K_{2}A_{2}(\theta_{1} - \theta_{2})}{l}$
Given $\left( \frac{Q}{t} \right)_{1} = \left( \frac{Q}{t} \right)_{2} \Rightarrow K_{1}A_{1} = K_{2}A_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.