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 T₁, T₂ and T₃ respectively. Assuming no loss of heat to the atmosphere, final the temperature at B.

Question

Philoid · Accepted Answer

Let’s redraw the diagram

Let the temperature at junction B be T.

Let Q_A, Q_C and Q_B be the heat currents, i.e. rate of flow of heat per unit time in AB, BCE and BDF, respectively.

From fig.

At point B

Q_A = Q_C + Q_B

Now, rate of flow of heat is given by –

= +

⇒ = +

⇒ T =