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 can be obtained using which of the following?

• A. Wein’s displacement law
• B. Stefan’s law
• C. Kirchhoff’s law
• D. Newton’s law of cooling

Answer 1

The correct option is A

Wein’s displacement law

Explanation for correct option :

1. Option $\left(\mathrm{A}\right)$ Wein’s displacement law is the correct option.
2. The Wein's displacement law states that the black body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.
3. ${\lambda }_{\text{peak}}=\frac{b}{T}$ where T is the absolute temperature. b is a constant of proportionality called Wien's displacement constant, equal to $2.897771955...\times {10}^{-3}m\cdot K$
4. This mean that the wavelength of radiation caused by thermally heating of the body is inversely proportional to the temperature of the radiation emitted by the body.
5. Thus, when temperature of the iron rod is increased continuously, its wavelength keeps on decreasing continuously, and this will cause visible change in color in the piece of iron from dull red to reddish yellow to finally white hot.

An illustrative diagram of Wien's law :

The explanation for incorrect option :

1. Stefan’s law states that the total radiation emitted by black body per unit area per unit time is directly proportional to the fourth power of its absolute temperature. As the radiation emitted by the black body is directly proportional to the fourth power of temperature and not its wavelength. Hence, option $\left(\mathrm{B}\right)$ is incorrect.
2. Kirchhoff's law states that at any given temperature, the emissivity of a body is equal to its coefficient of absorption. It states that good emitter is good absorber too. Hence, option $\left(\mathrm{C}\right)$ is incorrect.
3. Newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surrounding. Hence option $\left(\mathrm{D}\right)$is incorrect.

Hence, option A is correct.