Wiens Displacement Law: Understanding the Relationship Between Temperature and Radiation Emission

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Wiens displacement law, formally known as Wiens displacement law, is a fundamental principle in physics named after the Austrian physicist Wilhelm Wien. This law, formulated in 1893, elucidates the relationship between the temperature of a black body and the wavelength at which it emits radiation most intensely. The law provides valuable insights into the behavior of black bodies under varying temperature conditions and forms the basis for understanding thermal radiation.

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Mathematical Expression

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Mathematically, Wiens displacement law can be expressed as:

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#955; _ max b T

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where #955;max is the peak wavelength, T is the absolute temperature in Kelvin, and b is Wiens displacement constant, approximately equal to 2898 mu;m K.

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Theoretical Background

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Wiens displacement law explains the inverse relationship of the peak wavelength of maximum intensity with the absolute temperature of a body. At lower temperatures, blackbody emissions consist of longer wavelength radiations. As the temperature of the blackbody increases, the peak of the blackbody curve shifts to shorter wavelengths. This displacement in the peak wavelength of a blackbody at varying temperature conditions is precisely what the law describes.

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Physical Interpretation

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The physical interpretation of Wiens displacement law is that when the temperature of a radiating body is increased, the point of maximum radiation intensity shifts towards shorter wavelengths. This can be visualized as the peak emission wavelength shifting to the left on the x-axis. Essentially, the law indicates that as the temperature increases, the maximum intensity of emitted radiation moves to lower wavelengths, which is why it is called Wiens displacement law.

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Practical Application

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Understanding Wiens displacement law has numerous practical applications. For example, consider heating an iron rod to an extremely high temperature (in the order of 1000s of Kelvin). Initially, the rod may appear red hot. This red light is due to the higher number of red photons emitted compared to other colors. The intensity of the radiation can be visualized as the number of photons emitted from a given area on the rod surface per second. At higher temperatures, the rod emits a wider range of photon wavelengths, including colors beyond the visible spectrum.

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The graph below illustrates the relationship between wavelength and emission energy intensity at a fixed body temperature of 3000K. Across different temperatures, the peak wavelength shifts, as shown in the graph below:

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Graphical Representation

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The following image represents the position of the peak emission wavelength with respect to temperature. Notice how the curve shifts to the left, indicating a decrease in wavelength with an increase in temperature:

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Graph (Image): X-axis: Wavelength, Y-axis: Emission Energy Intensity @ Fixed Body Temperature of 3000K

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Below is a series of emission vs. wavelength graphs at various temperatures of the same radiating body, showing the displacement of the peak wavelength with temperature:

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Conclusion

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Wiens displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. This fundamental law helps us understand the behavior of black bodies under varying temperature conditions and forms the foundation for studying thermal radiation.

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By comprehending Wiens displacement law, we gain deeper insights into the natural world, including the behavior of stars and the evolution of the Sun. The phenomenon of the ultraviolet catastrophe, discovered through the law, was a crucial stepping stone in the development of quantum mechanics.