Question 88 of 126

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively. Given the thermal conductivity of $\operatorname{rod} x$ is three times of that of $\operatorname{rod} y$, the temperature at junction points $B$ and $E$ are (close to):

A$80^{\circ} \mathrm{C}$ and $70^{\circ} \mathrm{C}$ respectivelyB$80^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$ respectivelyC$60^{\circ} \mathrm{C}$ and $45^{\circ} \mathrm{C}$ respectivelyD$89^{\circ} \mathrm{C}$ and $73^{\circ} \mathrm{C}$ respectively

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Answer: (D) $89^{\circ} \mathrm{C}$ and $73^{\circ} \mathrm{C}$ respectively

Let $\left[ R = \dfrac{\ell}{3KA} \right]$

$\left[ H = \dfrac{100 - 40}{\dfrac{11R}{2}} \right]$ ...(1)
$H = \dfrac{100 - T_B}{R}$ .....(2)
$H = \dfrac{T_E - 40}{3R}$ .....(3)
using (1) and (2)
$120 = 1100 - 11T_A$
$T_B = 89°C$
using (1) and (3)
$T_E = 73°C$