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: Thermal Diffusivity Formula.
\n\[\n\alpha = \frac{k}{\rho c}\n\] \nDefinitions: \n- \( \alpha \) denotes thermal diffusivity
\n- \( k \) denotes thermal conductivity
\n- \( \rho \) denotes density
\n- \( c \) denotes specific heat capacity \n\n \n

Step 2: Evaluate each assertion.
\n- (A) Is there an inverse relationship with \(k\)? No, it is directly proportional. ✗
\n- (B) An increase in \(c\) causes the denominator to rise, thus decreasing diffusivity, not increasing it. ✗
\n- (C) Low diffusivity indicates slower heat transfer, leading to greater dampening of temperature waves. ✓
\n- (D) An increase in density causes the denominator to rise, thus decreasing diffusivity, indicating an inverse relationship. ✓
\n\n \n

Conclusion: \n\[\n\boxed{(C) \; \text{and} \; (D)}\n\]