Heat conduction in solids – Dependence of thermal conductivity For a conducting solid material (e.g., metals, ceramics, porous refractories), thermal conductivity may vary with which intrinsic or structural factors? Identify the best choice.

Introduction / Context:
Thermal conductivity k is not necessarily constant. In real solids, k often depends on temperature (phonon and electron transport effects) and on microstructure, including porosity. Recognizing these dependencies is important for furnace linings, insulation, and high-temperature equipment design.

Given Data / Assumptions:

• Homogeneous solid whose microstructure may include pores.
• Steady-state, one-dimensional conduction concepts apply.
• Temperature range may affect carriers (phonons/electrons).

Concept / Approach:
In metals, electron scattering increases with temperature, often reducing k at high T; in many ceramics, phonon scattering changes so k can decrease with T over practical ranges. Porosity introduces low-conductivity gas-filled regions and tortuous paths, decreasing effective k. Therefore, both temperature and porosity influence k in practice.

Step-by-Step Solution:

Verification / Alternative check:
Handbooks list k(T) curves; porous firebricks show order-of-magnitude lower k than dense ceramics at the same temperature.

Why Other Options Are Wrong:

• Single-factor options ignore well-documented dependencies.
• “Neither” contradicts extensive experimental data.

Common Pitfalls:
Using constant-k assumptions outside narrow temperature ranges; for accuracy, incorporate k(T) and porosity corrections in design calculations.

Final Answer:
both (a) & (b)