HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q32 Solution: Seven rods A, B, C, D, E, F and G are joined as shown in the…

QPages 98-102: Q32: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q32 Solution: Seven rods A, B, C, D, E, F and G are joined as shown in the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that because rod F has a uniform temperature (no temperature gradient along its length), no heat flows through it, effectively ignoring it in the network calculation. However, a uniform temperature only means the rod is isothermal; it can still act as a junction where heat enters from one side and exits the other, so it must be included in the Kirchhoff's current law (heat flow conservation) equations at the nodes.

Seven rods A, B, C, D, E, F and G are joined as shown in the figure. All the rods have equal cross-sectional area A and length l. The thermal conductivities of the rods are

K_A = K_C = K_0

K_B = K_D = 2K_0

K_E = 3K_0

K_F = 4K_0

and

K_G = 5K_0

. The rod E is kept at a constant temperature

T_1

and the rod G is kept at a constant temperature

T_2

T_2 > T_1

). a) Show that the rod F has a uniform temperature

T = T_1 + 2T_2)/3

. b) Find the rate of heat flowing from the source which maintains the temperature

T_2

Step-by-Step Verified Solution

**Answer:** (a) T_F = (T_ + 2T_)/3 (b) Rate = (4K_A/l)(T__T_). **Step-by-Step Explanation:** (a) By symmetry, rod F has uniform temperature. (b) Heat flows from G to E through the network. Solving the network gives the rate.

QPages 98-102: Q32: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q32 Solution: Seven rods A, B, C, D, E, F and G are joined as shown in the…

Step-by-Step Verified Solution

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