Which statement best captures the definition of thermal conductivity k for a homogeneous material?

Introduction / Context:Thermal conductivity k quantifies a material’s ability to conduct heat. It appears in Fourier’s law of conduction and is essential for sizing insulation, walls, and heat exchangers. A clear, general definition avoids ambiguity in units and geometry.

Given Data / Assumptions:

• Fourier’s law (one-dimensional steady conduction): q = −k * A * (dT/dx).
• Unit area and unit thickness provide a normalized definition.

Concept / Approach:The most general definition: k is the heat flow rate per unit area for a unit temperature gradient. Equivalently, it is the heat flow per unit time across unit area with unit thickness when the faces differ by 1°C (or 1 K). This avoids specific centimeter-based units and is independent of particular geometry choices beyond “unit.”

Step-by-Step Solution:

Verification / Alternative check:Dimensional analysis yields k with units W/(m·K) in SI, consistent with the chosen statement.

Why Other Options Are Wrong:

• (a) and (b) use centimeter-based special cases and are less general.
• (d) is too broad; not all are equally precise.
• (e) defines specific heat, not conductivity.

Common Pitfalls:Mixing up specific heat (energy to raise temperature) with conductivity (rate of heat transfer through a material).

Final Answer:Heat conducted per unit time across unit area through unit thickness when the temperature difference across faces is unity