Question

Which property increases the thermal conductivity of metals?

• A. Higher density
• B. Smaller grain size
• C. Lower atomic mass
• D. Greater number of free electrons

Hint:

Because conduction electrons transport both charge and heat, materials that are excellent electrical conductors (like Copper and Silver) are also excellent thermal conductors.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks to identify the key physical parameter that enhances the thermal conductivity of a metallic material.

Step 2: Key Formula or Approach:
The relationship between electrical conductivity (\( \sigma \)) and thermal conductivity (\( K \)) of a metal is described by the Wiedemann-Franz Law:
\[ \frac{K}{\sigma} = L T \]
where:
\( K \) is thermal conductivity,
\( \sigma \) is electrical conductivity,
\( L \) is the Lorenz number, and
\( T \) is absolute temperature.

Step 3: Detailed Explanation:

• Role of Free Electrons: In metals, thermal energy is conducted through two main mechanisms: the movement of free conduction electrons and lattice vibrations (phonons).
In high-purity metals, the electronic contribution is far more dominant than the phonon contribution, accounting for over \( 90\% \) of total heat transfer.
An increase in the concentration of free electrons directly enhances the rate at which thermal kinetic energy is transported through the metal lattice.

• Influence of Microstructure: A smaller grain size (Option B) introduces more grain boundaries.
These boundaries act as scattering sites for both electrons and phonons, which actually decreases thermal and electrical conductivity.

• Mass and Density: Higher density (Option A) and lower atomic mass (Option C) influence phonon speed but have a negligible effect on the dominant electronic heat transfer compared to the free-electron concentration.


Step 4: Final Answer:
Therefore, a greater number of free electrons increases the thermal conductivity of metals, matching Option (D).