Thermal diffusivity — dependence on material properties Thermal diffusivity (alpha) indicates how quickly a material’s temperature field responds to a thermal disturbance. Which combined dependence is correct?

Introduction / Context:
Thermal diffusivity alpha is a key parameter in transient conduction, dictating the speed of temperature equalization inside solids, liquids, and gases. It combines the effects of how well a material conducts heat and how much energy it stores per unit volume.

Given Data / Assumptions:

• Definition: alpha = k / (rho * c_p).
• Isotropic, homogeneous material behavior assumed.

Concept / Approach:
The formula alpha = k / (rho * c_p) shows that materials with high thermal conductivity and low volumetric heat capacity (rho * c_p) respond more quickly to temperature changes. Metals often have high alpha; polymers and water have lower alpha due to higher heat capacity per unit volume and/or lower k.

Step-by-Step Solution:
Write the definition: alpha = k / (rho * c_p).Direct proportionality: larger k → larger alpha.Inverse proportionalities: larger rho or c_p → smaller alpha.Hence all three component statements are simultaneously true.

Verification / Alternative check:
Example: Aluminum (high k, moderate rho and c_p) has high alpha; water (low k, high rho*c_p) has low alpha, matching the dependence.

Why Other Options Are Wrong:
(a), (b), (c) are each partially true alone, but the comprehensive correct choice is the combination (d). (e) is false because alpha is defined entirely by material properties.

Common Pitfalls:
Confusing thermal diffusivity with thermal conductivity; conductivity alone does not capture thermal inertia effects from rho and c_p.

Final Answer:
All of the above