Question

A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turn to white hot. The correct explanation for the above observation is possible by using

• A. Stefan's Law
• B. Wien's displacement La
• C. Kirchoff's Lave
• D. Newton's Law of cooling

Answer 1

The Correct Option is B

The question pertains to the observation of a piece of iron that undergoes color changes as it is heated. To understand this phenomenon, we must consider the emission spectrum of a black body, which is described by Wien's Displacement Law.

Wien's Displacement Law states that the wavelength at which the emission of a black body spectrum is the most intense is inversely proportional to its temperature. Mathematically, this is given by:

\lambda_{\text{max}} = \frac{b}{T}

where \lambda_{\text{max}} is the peak wavelength, T is the absolute temperature in Kelvin, and b is Wien's constant, approximately 2.898 \times 10^{-3}\, \text{m}\,\text{K}.

As the temperature increases, the peak wavelength decreases, which causes a shift in the visible light spectrum observed:

• At lower temperatures, the iron appears dull red because the peak emission is in the red part of the visible spectrum.
• As the temperature increases, the peak shifts to shorter wavelengths (reddish-yellow).
• At even higher temperatures, the peak reaches the part of the spectrum where white light dominates, leading to a "white hot" appearance.

Thus, Wien's Displacement Law explains the colors observed as the piece of iron is heated. Here's why the other options are less relevant in this context:

• Stefan's Law: Describes the total energy radiated per unit area of a black body, not specifically the wavelength of emission.
• Kirchoff's Law: Relates to blackbody radiation in terms of absorbance and emission spectra equivalence, not the color change with temperature.
• Newton's Law of Cooling: Involves the rate of cooling of an object, not relevant to emission wavelength.

Therefore, the correct answer is that the observation is explained by Wien's Displacement Law.