Deriving the Wein displacement law

Thread starter Fluxthroughme
Start date Mar 6, 2013
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deriving Displacement Law

In summary, the Wein displacement law, also known as Wien's law, states that the peak wavelength of a black body radiation curve is inversely proportional to the temperature of the object emitting the radiation. It was discovered by German physicist Wilhelm Wien in 1893 and can be derived using Planck's law of black body radiation and principles of thermodynamics. The law has various applications in astronomy, thermography, and materials science, and is applicable to ideal black body radiators and as an approximation for real objects with high emissivity values.

Mar 6, 2013

Fluxthroughme

I am not really sure where to go from here, since T varies. I am guessing this means I am approaching the problem incorrectly, but in that case, I have no idea how to do it. Any help/guidance would be appreciated.

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Mar 6, 2013

rude man

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Looks like an error in computing dI/dλ.

d/dx e^u = e^u du/dx.

If u = a/x, d/dx e^u = (-a/x²)e^a/x, not (a)e^a/x..

1. What is the Wein displacement law?

The Wein displacement law, also known as Wien's law, is a principle in physics that describes the relationship between the wavelength of the peak of the black body radiation curve and the temperature of the object emitting the radiation. It states that the peak wavelength is inversely proportional to the temperature, with hotter objects emitting shorter wavelengths of radiation.

2. Who discovered the Wein displacement law?

The Wein displacement law was discovered by German physicist Wilhelm Wien in 1893. He observed that the peak wavelength of a black body radiation curve shifted to shorter wavelengths as the temperature of the object increased.

3. How is the Wein displacement law derived?

The Wein displacement law can be derived using Planck's law of black body radiation and the principles of thermodynamics. It involves calculating the maximum energy distribution of a black body at different temperatures and finding the wavelength at which the energy is the highest. This can be done using mathematical equations and concepts such as the Stefan-Boltzmann law and the Boltzmann distribution.

4. What are the applications of the Wein displacement law?

The Wein displacement law has various applications in different fields, including astronomy, thermography, and materials science. It is used to determine the temperature of stars and galaxies, to improve the accuracy of infrared cameras, and to understand the thermal properties of materials. It also has implications in the development of technologies such as solar cells and LED lights.

5. Is the Wein displacement law applicable to all objects?

The Wein displacement law is only applicable to ideal black body radiators, which absorb and emit all incident radiation. However, it can also be used as an approximation for real objects, as long as their emissivity is close to 1. Objects with different emissivity values will have slightly different peak wavelengths, but the overall relationship between peak wavelength and temperature still holds true.