Wien's Displacement Law

Have you noticed that a metal object, upon heating, first turns red, then orange, and finally white with an increasing rise in temperature? Now, this change of colour, directly speaking, comes as the direct result of Wien's Displacement Law, which is one of the base laws in thermal physics. It was proposed by Wilhelm Wien and hence named after him. The law describes the relationship between the temperature of an object and its peak wavelength radiation. By understanding Wien's Displacement Law, we are going to be able to tell the temperature of stars, optimize the design of thermal cameras, and even boost the energy efficiency of a very wide range of technologies.

In this article, we will cover the concept of Wien's Displacement Law. This concept falls under the broader category of Properties of Solids and Liquids which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE and more.

Wien's Displacement Law

Wien's displacement law states that the wavelength (i.e λmax for which the emissive power of a black body is maximum is inversely proportional to the absolute temperature (T) of the black body.

Or Mathematically we can write that

λmax∗T=b=constant
Where b is a constant of proportionality which is known as Wien's displacement constant.

The value of b is given as b=2.89∗10−3mK

With the help of this law, we can say that

As the temperature of the body increases, the wavelength at which the spectral intensity (\left(E_\lambda\right)) is maximum shifts towards left, as shown in the below figure.

I.e

If T1<T2<T3
Then λm1>λm2>λm3

Wien's displacement law is useful for determining the temperatures of hot radiant objects such as stars, and it is also useful for the determination of the temperature of any radiant object whose temperature is far above that of its surroundings.

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Summary

Wien's Displacement Law states that the wavelength at which a black body spectrum is maximized is inversely proportional to its absolute temperature. This means that with an increase in temperature, the peak wavelength of radiation from an object changes to shorter wavelengths. It can be used in astrophysics to help in determining star temperatures from their colour, in the design of thermal imaging devices, and in increasing the efficiency of heating elements and lighting systems.