Thermal conductivity trends — With increase in temperature, the thermal conductivity of non-metallic amorphous solids generally:

Introduction:
Thermal conduction in solids arises mainly from lattice vibrations (phonons) for non-metals. The temperature dependence differs between crystalline and amorphous materials because phonon scattering and mean free path respond differently to disorder.

Given Data / Assumptions:

• Material class: non-metallic amorphous solids (e.g., glasses).
• Temperature range: below softening/glass-transition for stability.
• No significant radiative contribution in the stated range.

Concept / Approach:
In amorphous solids, the phonon mean free path is already limited by structural disorder and is relatively insensitive to additional phonon–phonon scattering as temperature rises. Meanwhile, heat capacity increases toward the Dulong–Petit limit. As a result, thermal conductivity commonly exhibits a gradual increase with temperature in many amorphous non-metals.

Step-by-Step Solution:
Identify conduction carriers: phonons in non-metals.Note strong disorder in amorphous materials limits mean free path at low T.As T increases, effective thermal conductivity typically increases moderately.

Verification / Alternative check:
Data for common glasses (e.g., silica-based) show k rising from low to moderate temperatures before plateauing near the softening region, supporting option (b).

Why Other Options Are Wrong:

• (a) Decrease with T is more characteristic of crystalline non-metals at high T.
• (c) and (e) are not generally correct over the normal operating range.
• (d) does not reflect typical amorphous behavior.

Common Pitfalls:
Confusing trends for metals (k often decreases slightly with T due to electron–phonon scattering) and crystalline ceramics with those for amorphous solids.

Final Answer:
Increases