Question

Which of the following has the highest thermal diffusivity:

• A. Iron
• B. Lead
• C. Concrete
• D. Wood

Hint:

Thermal diffusivity ($\alpha$) represents how fast a material responds to a change in temperature.
A high value means heat propagates quickly, which depends on both high conductivity ($k$) and low heat capacity ($\rho c_p$).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the material with the highest thermal diffusivity among the given options.

Step 2: Key Formula or Approach:
Thermal diffusivity ($\alpha$) is a material property that measures the rate of heat transfer from hot to cold regions. It is defined as:
\[ \alpha = \frac{k}{\rho c_p} \]
where:
$k$ is the thermal conductivity.
$\rho$ is the density.
$c_p$ is the specific heat capacity.

Step 3: Detailed Explanation:

• Let us compare the typical thermal diffusivity values ($\alpha$) of the given materials:
- Concrete: $\alpha \approx 1.0 \times 10^{-6}\text{ m}^2/\text{s}$ (non-metal, low conductivity).
- Wood: $\alpha \approx 1.0 \times 10^{-7}\text{ m}^2/\text{s}$ (thermal insulator).
- Iron: $\alpha \approx 2.3 \times 10^{-5}\text{ m}^2/\text{s}$ (metal).
- Lead: $\alpha \approx 2.4 \times 10^{-5}\text{ m}^2/\text{s}$ (metal with high diffusivity relative to its heat capacity).

• Although Iron has higher thermal conductivity than Lead, Lead has a much lower specific heat capacity ($c_p \approx 129\text{ J/kg}\cdot\text{K}$ for Lead compared to $c_p \approx 450\text{ J/kg}\cdot\text{K}$ for Iron).

• This extremely low heat capacity means Lead requires very little thermal energy to change temperature, giving it a higher thermal diffusivity value of around $2.4 \times 10^{-5}\text{ m}^2/\text{s}$.

Step 4: Final Answer:
Lead has the highest thermal diffusivity among the options.