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Thread: Wien's Formula: LT = 3E6 (nm*K)

  1. #1 Wien's Formula: LT = 3E6 (nm*K) 
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    What is the formula used to determine the temperature and wavelength of sunlight entering the atmosphere? I tried Wien's formula (LT = 3E6 nm * K), but I get skewed results.

    When I plug in the wavelength for yellow light (570 nm), I get the sun's surface temperature. When I plug in an earth temperature, I get an extremely long wavelength. It is my understanding that sunlight that enters the atmosphere has shorter waves and cooler temperatures.

    Please assist. Thanks in advance.
    :-D


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  3. #2 Wien's Formula: LT = 3E6 (nm*K) 
    Forum Sophomore Vaedrah's Avatar
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    Perhaps you are mixing up optical light and black body radiation. Materials emit radiation and hot materials have a broad spectral peak that have a lower wavelength (higher frequency) than colder material. Hence we can associate a "temperature" with a wavelength. The sun has a high surface temperature and therefore emits short wavelength radiation that we see as yellow light. The same is true for incandescent light bulbs. The tungsten filament heats up due to the current flowing through it that it glows yellow-white. However you will notice that a torch will shine yellow-white on good batteries but as these run down the light will shift towards orange and red. (I haven't seem them glow green though )

    The light we see is not the same as temperature; instead its temperature is associated with a broad spectral peak based on the mechanism of production. Fluorescent lamps, for example produce white light but not from "black body radiation". Temperature can be used to "describe" their subjective color without suggesting that the lamp operates at this temperature.

    The earth's temperature is low relative to solar temperatures and so it will have a low black body peak emission in the infra-red long wavelength region.

    Light per se does not have a temperature in an explicit sense but its radiation can be absorbed by a material and cause a temperature rise. Sunlight is no different. A visibly black material will absorb light of any visible wavelength whilst a colored material will be selective, absorbing one or more wavelengths and reflecting others.


    "The sky cannot speak of the ocean, the ocean cannot speak of the land, the land cannot speak of the stars, the stars cannot speak of the sky"
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  4. #3 Thanks! 
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    I'm still confused but I get the impression that Wien's formula is limited to measuring surface temperatures of stars and planets. Anyway, I was able to find sunlight's intital temperature when it enters the atmosphere. One web site claimed it is around 2000 to 3000 degrees Kelvin. Does that sound right? Apparently, the atmosphere filters out a lot of that heat or we would fry. LOL! :-D
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  5. #4 Wien's Formula: LT = 3E6 (nm*K) 
    Forum Sophomore Vaedrah's Avatar
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    williampinn, you may want to check out Wikipedia on Wien's Law

    http://en.wikipedia.org/wiki/Wien%27s_displacement_law

    Starting for the prediction for a "spectral peak" based on the temperature of the black body source



    and the associated spectrum, showing a broad distribution with an energy peak at the predicted wavelength



    This does not imply that light "has a temperature". The temperature is just that required by an object to emit light of a particular wavelength profile with a spectral peak as described by Wien's formula.

    The "black body" just refers to a black object heated up until it glows. A black object presumably emits more energy than a shiny one (reciprocal theorem of radiation and absorption efficiency being equal), but the energy versus wavelength profile (shape) stays the same.
    "The sky cannot speak of the ocean, the ocean cannot speak of the land, the land cannot speak of the stars, the stars cannot speak of the sky"
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  6. #5  
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    There's an eaiser way to find the answer.

    When you know what the status is when the cup is half empty (no sunlight, night), you can calculate the cup half full (day). You can also calculate the background radiation using the "night" scenario.

    But, the wording of your question is quite strange. The wavelength of sunlight entering the atmosphere: exactly where? As it hits like it hasn;t hit yet, or on the surface of the soil, like there is no more atmosphere to go through? And the "heat" of that wavelength, well, you're measuring how much quite a body of mass is heated up during daylight. That can be caculated compared to night.

    Ask any astronaught how cold it is in space. That's your answer to the moment when light hits the atmosphere. But are you not assuming sunlight has heat? The heat generated is a result, in the atmopshere, it would seem by a general large reaction that something HAS to the sunlight itself that APPEARS to heat everything, to release energy. Now, on that point, one considers "photosynthesis", the surface of the soil, that chemical reaction, the energy released, and how the sun offers the quantum ingredient to power that heat release. Because as any greenhouse scientist knows, compared to photosynthesis, the gaseous ingredients of our atmopshere ain't that special in terms of a chemical reaction, otherwise our skin would boil.This is why the forrestry commision of your local power base needs to pay very close attention to what is considered as "viable human-compatible, not-2-sudden-development, confined-only-to-this-planet........shiiiiiiiiiiit". Because, basically, if we do things too fast in kettle called earth wihtout using outside sources of information with the aim of living out there in space, we could cook ourselves. We work on a heat that works for us, which is why I think if we take away the trees, we are going to freeze, like MARS might be a tad cold, like the only thing you will find when you drill is ICE, not gold, depending on your equipment, of courze.

    Do that math, you might win a nobel prize. You will have explained to everyone the equation of the greenhouse effect. For me, well, I don't want a reward for any equation, I want to make policy POLICY.
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  7. #6 Thanks for your replies. 
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    Thank you both for the input. I think for now I am going to go with the Solar Constant which is 1370 Watts per square meter or 1370 J/s/meter squared.
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