Question

Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperature. Which one will conduct most heat?

• A. $r=1cm,l=1m$
• B. $r=1cm,l=\frac{1}{2}m$
• C. $r=2cm,l=2m$
• D. $r=2cm,l=\frac{1}{2}m$

Answer 1

The correct option is D $r=2cm,l=\frac{1}{2}m$

Heat conducted by rod, $Q=\frac{KAt\Delta T}{l}$ where $A=\pi r^2$

$⟹$ $Q=a\frac{r^2}{l}$ where $a=Kt\pi \Delta T=$ constant

(A) : $Q_A=a\frac{(0.01{)}^2}{1}={10}^{-4}a$

(B) : $Q_B=a\frac{(0.01{)}^2}{1/2}=2\times {10}^{-4}a$

(C) : $Q_C=a\frac{(0.02{)}^2}{2}=2\times {10}^{-4}a$

(D) : $Q_D=a\frac{(0.02{)}^2}{1/2}=8\times {10}^{-4}a$

Hence rod D conducts the most heat.