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°C and 40°C respectively. Given the thermal conductivity of rodx is three times of that of rody, the temperature at junction points B and E are (close to):

Solution

Physics sir · 4 steps

Treat each rod as a thermal resistor, then solve it like a series and parallel circuit.

1. Thermal resistance. A rod has resistance Rₜₕ = L/kA. The dimensions are equal and kₓ = 3k_y, so if rod x has resistance R, rod y has 3R.
2. Reduce the network. Between B and E, the upper path y + y gives 6R and the lower path x + x gives 2R. In parallel these give (6R × 2R)/8R = 1.5R. Adding AB (R) and EF (3R) in series gives a total of 5.5R.

   H = (Δ T)/Rₜₒₜₐₗ = (100 - 40)/5.5R = 10.9/R °C

3. Junction temperatures. The drop across AB is H × R = 10.9°C, so T_B = 100 - 10.9 ≈ 89°C. The drop across EF is H × 3R = 32.7°C, so T_E = 40 + 32.7 ≈ 73°C.
4. So. B is at about 89°C and E is at about 73°C, which is option (c).

The idea to keep. Heat flow works like current: Δ T is the voltage and L/kA is the resistance. A higher conductivity means a lower resistance and so a smaller temperature drop across that rod.

Answer from the NTA final answer key. Solution by PrepWiser.