Question

The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40W$ in the arrangement (a). Find the rates of heat flow when the rods are joined as in arrangement (b). (Assume $K_{Al}=200W/m^{\circ }C$ and $K_{cu}=400W/m^{\circ }C)$

• A. 75 W
• B. 200 W
• C. 400 W
• D. 4 W

Answer 1

Answer: (C)

$\because$ The rods have identical dimensions.
Let their area of crossection be $=A$ and length be $=L$
So each rod would have heat resistance of
$R=\frac{L}{KA}$
$R_{\text{eff}}=R_1+R_2+R_3$
$=\frac{L}{K_{Al}A}+\frac{L}{K_{Cu}A}+\frac{L}{K_{Al}A}$
$R_{\text{eff }}=\frac{L}{A}\times \frac{5}{400}$
$\left[\because K_{Al}=200,K_{Cu}=400\right]$
$H_1=\frac{\Delta T}{R_{\text{eff }}}=\frac{100}{\frac{L}{A}\times \frac{5}{400}}...(i)$
(b) When rods are connected in parallel
$\frac{1}{R_{eff}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
$R_{eff}=\frac{L}{A}\times 800$
$H_2=\frac{100}{\frac{L}{A}\times 800}...(2)$
Dividng (2) by (1)
$\frac{40}{H_2}=\frac{400}{800\times 5}\Rightarrow H_2=400W$