Question

Thermal diffusivity of a wall is influenced by the choice of building material. Identify the statement(s) that is/are correct.

• A. Thermal diffusivity is inversely proportional to thermal conductivity.
• B. Increase in specific heat capacity increases the thermal diffusivity.
• C. Materials with low thermal diffusivity have a high amplitude dampening effect.
• D. Thermal diffusivity is inversely proportional to the density of material.

Hint:

Thermal diffusivity = \(\frac{k}{\rho c}\). Materials with low \(\alpha\) act as good insulators against temperature fluctuations.

Answer 1

The Correct Option is C, D

Step 1: Formula of thermal diffusivity.
\[ \alpha = \frac{k}{\rho c} \] where: - \( \alpha \) = thermal diffusivity
- \( k \) = thermal conductivity
- \( \rho \) = density
- \( c \) = specific heat capacity

Step 2: Check each statement.
- (A) Inverse relation with \(k\)? No, it is directly proportional. ✗
- (B) Higher \(c\) → denominator increases → diffusivity decreases. Not increases. ✗
- (C) Low diffusivity = slower heat transfer = higher dampening of temperature waves. ✓
- (D) Higher density → denominator increases → diffusivity decreases → inverse relation. ✓

Final Answer: \[ \boxed{(C) \; \text{and} \; (D)} \]