Question

Three bars of equal lengths and equal areas of cross-section are connected in series. Their thermal conductivities are in the ratio of $2 : 4 : 3$. If the open ends of the first and the last bars are at temperatures $ 200^{\circ} C $ and $ 18^{\circ} C $ respectively in the steady state, the temperature of the two junctions is

• A. $60^{\circ}C, 50^{\circ}C$
• B. $116^{\circ}C, 74^{\circ}C$
• C. $55^{\circ}C, 65^{\circ}C$
• D. $160^{\circ}C, 80^{\circ}C$

Answer 1

Answer: (B)

The rate of flow of heat is same

$H =(2 K) A \frac{\left(200-\theta_{1}\right)}{L} $
$=(4 K) A \frac{\left(\theta_{1}-\theta_{2}\right)}{L} $
$=(3 K) A \frac{\theta_{2}-18^{\circ}}{L} $
$\Rightarrow 2\left(200^{\circ}-\theta_{1}\right) =4\left(\theta_{1}-\theta_{2}\right) $
$=3\left(\theta_{2}-18^{\circ}\right)$
$\Rightarrow \theta_{1} =116^{\circ} C , \theta_{2}=74^{\circ} C$