Which material listed typically exhibits the lowest thermal diffusivity (α = k / (ρ * c)) and therefore heats up/ cools down the slowest in depth?

Introduction / Context:Thermal diffusivity α indicates how quickly a material’s temperature field adjusts to a change in heat input. Low α means the material is sluggish in transmitting thermal disturbances, useful for insulation or damping temperature fluctuations.

Given Data / Assumptions:

• α = k / (ρ * c), where k is thermal conductivity, ρ is density, and c is specific heat.
• Comparing common engineering materials: metals versus elastomers.

Concept / Approach:Metals have high k and moderate ρ and c, yielding high α. Polymers and elastomers have low k and often moderate c, producing very low α. Rubber, with very low conductivity, is a classic example of low thermal diffusivity material; it resists rapid internal temperature changes.

Step-by-Step Solution:

Verification / Alternative check:Typical α (m^2/s): aluminium ~ 8.5e−5, copper ~ 1.1e−4, iron ~ 2–4e−5, lead ~ 1.2e−5, rubber ~ 1e−7 to 1e−8, confirming rubber’s minimal diffusivity.

Why Other Options Are Wrong:

• Metals conduct heat well and quickly diffuse thermal changes.
• Lead is lower than many metals but still above rubber.

Common Pitfalls:Confusing low conductivity with low heat capacity; diffusivity combines both and is the appropriate metric for transient heat penetration.

Final Answer:Rubber