Pick the incorrect statement about refractories and their properties or applications.

Introduction / Context:
Muffle furnaces isolate the load from combustion gases using a refractory “muffle” chamber. For efficient operation, the muffle walls must transfer heat rapidly and uniformly from the heat source to the charge. This item asks you to identify which statement is incorrect among several general truths about refractories.

Given Data / Assumptions:

• Muffle walls should favor heat transmission, not insulation.
• Electrical resistivity of many refractories decreases with temperature (semiconducting behavior).
• Higher controlled porosity and good firing can improve spalling resistance.
• RUL is typically lower than the pyrometric cone equivalent (softening without load).

Concept / Approach:
For muffles, high thermal conductivity is desirable to transmit heat to the workpiece quickly and evenly; silicon carbide is a classic choice because of its high thermal conductivity and thermal-shock resistance. Therefore, the assertion that muffle-furnace refractories should have “low thermal conductivity” is incorrect. The other statements align with standard materials science of refractories: resistivity declines with temperature; increased porosity can cushion thermal stress; and RUL is indeed less than PCE due to the applied load.

Step-by-Step Solution:
Assess muffle requirement: prioritize heat transfer → high conductivity preferred.Check resistivity trend: ρ_electrical ↓ as T ↑ for many refractories → statement (b) correct.Evaluate spalling: well-fired, more porous structures resist spalling → statement (c) correct.Compare RUL vs PCE: RUL < PCE → statement (d) correct.Thus, (a) is the incorrect statement.

Verification / Alternative check:
Handbooks cite SiC muffles and radiant tubes specifically for their high thermal conductivity, supporting the conclusion that high, not low, conductivity is advantageous in muffle applications.

Why Other Options Are Wrong (i.e., not the incorrect one):
(b) Correct generalization for many ceramic refractories.(c) Correct; porosity can absorb thermal stresses and reduce spalling.(d) Correct; load accelerates softening so RUL is lower.(e) Correct; microstructural design mitigates thermal shock.

Common Pitfalls:
Confusing furnace lining (insulating backup) with the muffle itself (heat-transmitting component).Assuming one property trend applies universally without regard to application.

Final Answer:
Refractories used in muffle furnaces should have low thermal conductivity.