Two metal rods $\mathrm{P}$ and $\mathrm{Q}$ have same length and same temperature difference between their…
Two metal rods $\mathrm{P}$ and $\mathrm{Q}$ have same length and same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$, also cross-sectional areas $A_1$ and $A_2$ respectively. If the rate of flow of heat through rod $Q$ is three times that in rod $P$, then
Concept: the rate of heat flow through the rod is given by
$\dot{\mathrm{Q}}=\frac{\mathrm{KA} \Delta \theta}{\mathrm{l}}$
Where $\mathrm{K}$ is the conductivity, $\Delta \mathrm{Q}$ is the temperature difference across, $\mathrm{A}$ is the area of cross-section and 1 is the length of the rod.
$\begin{aligned}
& \therefore(\dot{\mathrm{Q}})_{\mathrm{Q}}=(\dot{\mathrm{Q}})_{\mathrm{P}} \\
& \Rightarrow \frac{\mathrm{K}_2 \mathrm{~A}_2}{\mathrm{l}}=\frac{3 \mathrm{~K}_1 \mathrm{~A}_1}{\mathrm{l}} \\
& \Rightarrow \mathrm{K}_2 \mathrm{~A}_2=3 \mathrm{~K}_1 \mathrm{~A}_1
\end{aligned}$