Verified Solution • 2025–26 Session moderate

QPages 98-102: Q33: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q33 Solution: Find the rate of heat flow through a cross section of the rod…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly apply the standard slab formula $Q/t = KA\Delta T/L$ by substituting an average area, which fails for conical geometries where area varies with length. The correct derivation requires integrating $dQ = K A(x) dT/dx$, resulting in a logarithmic term $\ln(r_2/r_1)$ in the denominator rather than a linear length term.

Find the rate of heat flow through a cross section of the rod shown in figure

\theta_2 > \theta_1

). Thermal conductivity of the material of the rod is K.

Step-by-Step Verified Solution

**Answer:** Q/t = �K(_____)/ln(r_/r_). **Step-by-Step Explanation:** For a truncated cone (rod with varying cross-section), the rate of heat flow is:

\frac{Q}{t} = \frac{\pi K (\theta_2 - \theta_1)}{\ln(r_2/r_1)}

for a conical rod.

All Questions in this Chapter

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