Question

The unit of thermal diffusivity is________

• A. $W/m^2$
• B. $kJ/kg \cdot K$
• C. $m^2/s$
• D. $W/m \cdot K$

Hint:

Notice that Diffusivity (Thermal or Molecular) always has the dimensions of $[L^2/T]$. This is a good way to verify units for any diffusivity parameter in physics.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the SI unit of thermal diffusivity ($\alpha$). Thermal diffusivity is a physical property that describes the rate at which heat spreads through a material.
Key Formula or Approach:
The formula for thermal diffusivity is:
\[ \alpha = \frac{k}{\rho \cdot C_p} \] Where:
• $k$: Thermal conductivity ($W/m \cdot K$).

• $\rho$: Density ($kg/m^3$).

• $C_p$: Specific heat ($J/kg \cdot K$).

Step 2: Detailed Explanation:

• Dimensional Analysis:
Unit of $\alpha = \frac{[W/m \cdot K]}{[kg/m^3] \cdot [J/kg \cdot K]}$
Since $W = J/s$:
Unit of $\alpha = \frac{J/(s \cdot m \cdot K)}{(J/m^3 \cdot K)} = \frac{m^3}{s \cdot m} = m^2/s$.

• Physical Meaning: Thermal diffusivity represents the ratio of heat conduction to heat storage. A material with high $\alpha$ (like copper) conducts heat quickly while storing very little, allowing it to reach thermal equilibrium rapidly.

• Comparison:
• (A) is heat flux.

• (B) is specific heat.

• (D) is thermal conductivity.

Step 3: Final Answer:
The units for thermal diffusivity, as well as kinematic viscosity, are $m^2/s$. Option (C) is correct.