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QPages 98-102: Q31: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q31 Solution: Four identical rods AB, CD, CF and DE are joined as shown in…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently treat the temperature at a junction as the plain average of all prescribed end temperatures, assuming three equal rods meet there, even when the actual circuit connects only the rods that are physically attached to the node. Always write the heat‑balance equation using the conductances of the rods that join the node; the arithmetic mean is valid only when exactly three identical conductors meet the node.
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 temperature , and respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.
Step-by-Step Verified Solution
**Answer:** T_B = (T_ + T_ + T_)/3.
**Step-BY-Step Explanation:**
Four identical rods joined. By symmetry and conservation of heat flow at junction B:
T_B = (T_A + T_E + T_F)/3 = (T_ + T_ + T_)/3.
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