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----------------- 1740 - Calculating Global Warming.
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- Think of the globe we live on as the surface of 2,000,000,000,000,000 hundred light bulbs. And, that globe in the sky that is warming us has a surface temperature of 6,000 degrees Kelvin. How do we know these things?
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- Kelvin is a temperature scale in degrees Centigrade that starts at Absolute Zero, - 273 C rather than 0 degrees C.
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- The temperature of stars is calculated from their light spectrum. The intensity of their light is plotted versus the wavelength of the light. The peak of this intensity occurs at on wavelength. The wavelength where the brightest star luminosity peaks tells us the surface temperature that is radiating that light.
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- We measure the intensity of sunlight from 250 to 3,000 nanometers wavelength. This spectrum spans from ultraviolet through blue light at 400 nanometers, to red at 700 nanometers, to infrared. The Sun’s radiation intensity reaches the peak intensity at 480 nanometers wavelength , in the blue-green region of the visible light spectrum. That peak equates to 6,000 degrees Kelvin. Here is how.
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- As a side, the sky is blue and the sun is yellow because the atmospheric atoms scatter the blue light making the sky blue. The more atmosphere the sunlight shines through the more blue is scattered unto the sky become red or orange in the late evenings when the light passes through more of the atmosphere.
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- The luminosity is the total amount of light emitted. Luminosity increases as temperature increases. In fact, luminosity increases as the 4th power of temperature.
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---------------------------------- L = T ^4
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- Luminosity is the total amount of light.
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- Flux is just that amount of light landing on one square meter of surface.
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--------------------- Flux = 5.67*10^-8 watts / ( meter^2 * Kelvin^4) * T^4
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----------------------- F = k * T^4
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---------------------- “k” is the constant called Stefan-Boltzman Constant.
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- F = k*T^4 means radiated power ( power is energy per unit time) per unit area is proportional to the forth power of the temperature.
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------------------- Luminosity = Flux * total surface area.
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--------------------- L = F * 4pi * r^2
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- Therefore if we know the temperature we can calculate the luminosity. And, if we know the peak of the luminosity we can calculate the temperature
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------------------ Peak Wavelength = 2.9*10^-3 / Temperature in Kelvin
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- This equation is called Wien’s Law:
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- The luminosity peak for the Sun’s spectrum is at 480 nanometers.
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----------------- 480 nm = 2.9 * 10^-3 / T
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---------------- T = 2.9*10^-3 / 480 * 10^-9 = 0.006042 * 10^6
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---------------- T = 6,042 Kelvin
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- The same calculation can be made from the temperature of the Earth. Any body that has a temperature , radiates heat. In fact , for any “ blackbody” of radiation there is a peak wavelength of radiation intensity. A “ blackbody” means that the radiation intensity is across’ all wavelengths”, not any particular wavelength.
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- The average temperature of the surface of the Earth is 59 F, or 15 C, or 288 Kelvin.
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------------------- Peak Wavelength = 2.9*10^-3 K / 288 K
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--------------------- Peak Wavelength = 10,100 nanometers.
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- 10,100 nanometers is in the far infrared wavelength spectrum. With that average temperature of 288 Kelvin the Flux measure over one square meter of surface is:
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------------------------ F = (5.67 *10^-8 watts / m^2*k^4) * (288 K)^4
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------------------------ F = 390 watts / m^2
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- If you are in the solar panel business this is a good number to know. Each square meter of Earth’s surface exposed to sunlight gets 390 watts of energy.
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- The surface area of the Earth is 4pi * r^2, where the radius is 6,378*10^6 meters.
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---------------------- L = F * 4pir^2
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----------------------- L = 390 watts / m^2 * 4pi * ( 6.378*10^6)^2
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------------------------ L = 200,000,000,000,000,000 watts
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- Think of the Earth as 2 * 10^15 one-hundred watt light bulbs. And, that is just the surface temperature. The Sun keeps us warm. Thank God for global warming.
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- Our Sun is among the brightest stars, most luminosity, in the Milky Way Galaxy. Of course, brightness of stars does not just depend on luminosity. The distance to the star also determines its “ Apparent Brightness”.
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- The luminosity of the star is inversely proportional to the square of the distance to it.
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- Stars range from 1/ 10,000 to 10,000,000,000 times the luminosity of the Sun. The more luminous the star the faster it burns its fuel and the shorter its lifetime.
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- The most luminous stars are blue in color. The least luminous stars are red in color. Our Sun is on the blue-green part of the color scale. Our atmosphere takes out the blue. Most of the stars in the Milky Way are cooler and redder than our Sun.
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