Question

When an iron rod is heated, the variation of colour from dull red to white can be explained by

• A. Boltzmann Law
• B. Newton's Law of Cooling
• C. Stefan's Law of Radiation
• D. Wien's Displacement Law

Hint:

Wien’s Displacement Law:

• Describes shift in peak wavelength with temperature.
• $\lambda_max \propto \frac1T$.
• Explains visible color change in heated objects (red $\rightarrow$ yellow $\rightarrow$ white).

Answer 1

The Correct Option is D

As a body is heated, the wavelength at which it emits maximum radiation shifts. This change in peak wavelength explains the color shift from red (longer wavelength) to white (shorter wavelength, mix of visible light).
Wien’s Law states: $\lambda_{max} = \frac{b}{T}$, where $b$ is a constant. As temperature increases, $\lambda_{max}$ decreases.
This explains why the rod glows dull red at lower temperatures and eventually white at higher temperatures.

Answer 2

Step 1: Understand the phenomenon
When an iron rod is heated, it glows and changes color as its temperature increases.

Step 2: Relationship between temperature and color
The color of the glowing iron depends on the wavelength of the maximum intensity of emitted radiation.
As temperature increases, this wavelength shifts.

Step 3: Wien's Displacement Law
Wien's Displacement Law states that the wavelength (λ_max) at which the emission of a blackbody spectrum is maximum is inversely proportional to the temperature (T):
λ_max = b / T
where b is Wien's constant.

Step 4: Explanation of color change
- At lower temperatures, the rod emits longer wavelengths corresponding to dull red.
- As temperature rises, λ_max shifts to shorter wavelengths, moving through orange, yellow, and eventually to white light at very high temperatures.

Step 5: Conclusion
The variation of color of the heated iron rod from dull red to white is explained by Wien's Displacement Law, which relates temperature to the peak wavelength of emitted radiation.