Question

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. $K_{1}A_{1}^{2} = K_{2}A_{2}^{2}$

Answer 1

Answer: (B)

$K_{1}A_{1} = K_{2}A_{2}$

Answer 2

$\left( \frac{Q}{t} \right)_{1} = \frac{K_{1}A_{1}(\theta_{1} - \theta_{2})}{l}$ and $\left( \frac{Q}{t} \right)_{2} = \frac{K_{2}A_{2}(\theta_{1} - \theta_{2})}{l}$

given $\left( \frac{Q}{t} \right)_{1} = \left( \frac{Q}{t} \right)_{2}$⇒ $K_{1}A_{1} = K_{2}A_{2}$