Question

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

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

Answer 1

The Correct Option is C

The observation in the question is about a piece of iron changing color as it is heated. This phenomenon occurs because of the relationship between temperature and the color of thermal radiation emitted by a hot object. The correct explanation for this is provided by Wien's Displacement Law.

1. Explanation of Wien's Displacement Law: Wien's Displacement Law states that the wavelength of the peak emission of a black body is inversely proportional to its absolute temperature. Mathematically, it can be expressed as:

   \[\lambda_{\text{max}} T = b\]

   where \(\lambda_{\text{max}}\) is the wavelength at which the emission of the black body is maximum, \(T\) is the absolute temperature, and \(b\) is Wien's constant, approximately equal to \(2.898 \times 10^{-3} \, \text{m K}\).

2. Color Change Explanation:

   • When the iron is heated, the temperature increases. According to Wien's law, as the temperature increases, the peak wavelength of the emitted radiation shifts towards shorter wavelengths (higher frequencies).
   • The progression of colors from dull red to reddish yellow and finally to white indicates that the peak emission wavelength shifts from the infrared region (dull red) to visible light with higher frequencies (yellow to white).
   • At higher temperatures, more components of visible light are emitted, resulting in the white-hot appearance, as nearly all visible wavelengths are being emitted.

3. Negation of Other Options:

   • Newton's Law of Cooling describes the rate at which an object cools and is not related to the emission color changes.
   • Stefan's Law (Stefan-Boltzmann Law) is about the total energy radiated per unit surface area of a black body, which does not explain color changes.
   • Kirchhoff's Law relates to the absorption and emission of radiation, but not specifically to the wavelength changes with temperature.

Therefore, the correct explanation for the change in color of the heated iron is given by Wien's Displacement Law, which correlates temperature with the color (wavelength) of emitted radiation.