Question

Two rods $P$ and $Q$ of equal lengths have thermal conductivities $K_{1}$ and $K_{2}$ and cross-sectional areas $A_{1}$ and $A_{2}$ respectively. If the temperature difference across the ends of each rod is the same, then the condition for which the rate of flow of heat through each of them will be equal, is

• A. $\frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}}$
• B. $\frac{A_{1}}{A_{2}}=\frac{K_{1}}{K_{2}}$
• C. $\frac{A_{1}}{A_{2}}= \, \sqrt{\frac{K_{1}}{K_{2}} \, }$
• D. $\frac{A_{1}}{A_{2}}=\left( \, \frac{K_{2}}{K_{1}}\right)^{2}$

Answer 1

Answer: (A)

$\left(\frac{\Delta Q}{\Delta t}\right)_{P}=\left(\frac{\Delta Q}{\Delta t}\right)_{Q}$
$K_{1}A_{1}\frac{\left(T_{1} - T_{2}\right)}{l}=K_{2}A_{2}\frac{\left(T_{1} - T_{2}\right)}{l}$
Or $K_{1}A_{1}=K_{2}A_{2}$ or $\frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}}$