Question

Given below are two statements
Statement I: Increase in thermal conductivity increases thermal diffusivity
Statement II: Materials having higher specific heat possess lower thermal diffusivity
In light of the above statements, choose the most appropriate answer from the options given below

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is correct and Statement II is false
• D. Statement I is incorrect and Statement II is true

Hint:

$\alpha = \frac{\text{Heat conduction capability}}{\text{Heat storage capability}} = \frac{k}{\rho c_p}$. Direct with $k$, inverse with $c_p$ and $\rho$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Thermal diffusivity represents the rate at which heat transfers through a material relative to its ability to store thermal energy.
Key Formula or Approach:
\[ \alpha = \frac{k}{\rho \cdot c_p} \]
where \(k\) is thermal conductivity, \(\rho\) is density, and \(c_p\) is specific heat capacity.

Step 2: Detailed Explanation:
Analyzing each statement with the thermal diffusivity equation \(\alpha = \frac{k}{\rho c_p}\):
1. Statement I: Thermal diffusivity \(\alpha\) is directly proportional to thermal conductivity \(k\). Increasing \(k\) increases \(\alpha\). Hence, Statement I is true.
2. Statement II: Thermal diffusivity \(\alpha\) is inversely proportional to specific heat capacity \(c_p\). Materials with higher specific heat store more heat and diffuse thermal wavefronts slower, resulting in a lower \(\alpha\). Hence, Statement II is true.

Step 3: Final Answer:
Therefore, Both Statement I and Statement II are true, matching option (A).