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
$(a)$ Stefan’s law
$(b)$ Wein’s displacement law
$(c)$ Kirchoff’s law
$(d)$ Newton’s law of cooling

Answer 1

Since, the color of iron rod is changing as time passes by, it means the wavelength of light emitting from the piece of iron is changing. This implies that the wavelength of the emitted light is changing continuously with time. Therefore, explanation will be given only by that law which defines temperature as a function of wavelength under normal conditions, that is room temperature and pressure.

Complete step by step answer:
The first option is Stefan's law. We know that the Stefan’s law is for black body radiation and its equation is given by:
$\Rightarrow \varepsilon =\sigma {{T}^{4}}$
Here, the radiation emitted by the black body is directly proportional to the fourth power of temperature and not its wavelength. Hence, the first option is incorrect.
The second option is, Wein’s displacement law which is given by:
$\Rightarrow {{\lambda }_{m}}T=b$
Where,
$T$ is the absolute temperature of material (in kelvin).
${{\lambda }_{m}}$ is the wavelength of radiation having maximum intensity at that temperature $T$ .
$b$ is the constant of proportionality also known as Wein’s displacement constant.
From, Wein’s displacement law, we can clearly see that, the wavelength of radiation caused by thermally heating the body is inversely proportional to the temperature of the body emitting radiation. Thus, when temperature of the iron rod is increased continuously, its wavelength keeps on decreasing continuously.
This results in visible change in color in the piece of iron from dull red to reddish yellow to finally white hot.
Hence, option $(b)$ is the correct option.
In the third option, we have Kirchoff’s law which is given by the equation:
$\Rightarrow a=e$
Where, (a) is the absorptivity of the body and (e) is the emissivity. Hence, it states that good emitters are good absorbers too. So, option $(c)$ is also incorrect,
Now, for the last option, that is Newton’s Law of cooling. It states that the rate of heat loss of a body is directly proportional to the difference in temperatures between the body and the surroundings. Hence, the last option is also incorrect.

So, the correct answer is “Option b”.

Note: The statement and definition of each and every law should be remembered thoroughly as they are applied not only in common numerical problems but are of a big help in conceptual problems also. We should also remember the value of all the different “constant of proportionality” terms that are commonly used as one could ask us their value or their dimensional formula.