Four identical rods $A B, C D, C F$ and $D E$ are connected as shown in figure. The length, cross-sectional area and thermal conductivity of each rod are $L, A, K$ respectively. The ends $A, E, F$ are maintained at temperature $T_{1}, T_{2}$ and $T_{3}$ respectively. Assuming no loss of heat to the atmosphere, calculate the temperature at $B [C B = B D]$ .
(Consider $T_{3}$ as higher temperature)

\frac{T_{1} + T_{2} + T_{3}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 T_{1} + 3 T_{2} + 5 T_{3}}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 T_{1} + 2 T_{2} + 2 T_{3}}{7}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{T_{1} + 2 T_{2} + 3 T_{3}}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{3 T_{1} + 2 T_{2} + 2 T_{3}}{7}$
Heat flow in the fiven system can be represented by following diagram

Let the temperature at B be $x$
In steady state ,
${(\frac{Q}{t})}_{3} = {(\frac{Q}{t})}_{1} + {(\frac{Q}{t})}_{2}$
$\frac{(T_{3} - x)}{(\frac{3 l}{2 K A})} = \frac{x - T_{1}}{\frac{l}{K A}} + \frac{(x - T_{2})}{\frac{3 l}{2 K A}} [K and A gets cancelled]$
$T_{3} - x = \frac{3}{2} (x - T_{1}) + (x - T_{2})$
$T_{3} + T_{2} + \frac{3}{2} T_{1} = x + \frac{3}{2} x + x$
$2 (T_{3} + T_{2}) + 3 T_{1} = 7 x$
Temperature at $B$ is $x = \frac{3 T_{1} + 2 T_{2} + 2 T_{3}}{7}$

Suggest Corrections

Similar questions

Q. Four identical rods AB, CD, CF and DE are joined as shown in figure (28-E8). The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature T₁, T₂ and T₃ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross -sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures $T_{1}, T_{2}$ and $T_{3}$ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.