Planck's law, Stefan-Boltzmann law, Wien's law
<Text-field style="Heading 1" layout="Heading 1">Problem</Text-field> Based on Planck's law for radiance, calculate (A) the Stefan-Boltzmann law for flux, (B) Wien's displacement law and (C) the colour index for the following ranges of two colour filters: blue: 400-500 nm; red: 600-700 nm. Hints: Integrate Planck's law to find the Stefan-Boltzmann law. Make substitutions to simplify the calculation. To find Wien's displacement law, find the maximum value of Planck's law. Use the colour-index formula, below, to find an approximate colour index for the filters listed in the problem, above.
<Text-field style="Heading 1" layout="Heading 1">Useful Equations</Text-field> Planck's Law 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 Colour Index 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Planck's Formula for the Radiance as a Function of Wavelength and Temperature 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 LCQqLiIiIyIiIkkjUGlHJSpwcm90ZWN0ZWRHRiVJImhHNiJGJSlJImNHRilGJEYlKUknbGFtYmRhR0YpIiImISIiLCYtSSRleHBHNiRGJ0koX3N5c2xpYkdGKTYjKixGKEYlRitGJUYtRi9JImtHRilGL0kiVEdGKUYvRiVGJUYvRi9GJQ==
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution (A) Stefan Boltzmann Law</Text-field> Find the flux by integrating Planck's law. It is necessary to reassign some variables so that Maple can solve the problem. 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 KixJImhHNiIiIiJJImNHRiRGJUknbGFtYmRhR0YkISIiSSJrR0YkRihJIlRHRiRGKA== 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 KixJImhHNiIiIiJJImNHRiRGJSlJJ2xhbWJkYUdGJCIiIyEiIkkia0dGJEYqSSJUR0YkRio= 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 LCQqMiIiIyIiIkkjUGlHJSpwcm90ZWN0ZWRHRiUpSSJjRzYiRiQhIiIpSSJoR0YqIiIkRispSSJ4R0YqRi5GJSlJImtHRioiIiVGJSlJIlRHRipGM0YlLCYtSSRleHBHNiRGJ0koX3N5c2xpYkdGKjYjRjBGJUYlRitGK0Yl JSFH Integrate Rx from zero to infinity to find the flux. 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 LCQqLiMiIiMiIzoiIiIpSSNQaUclKnByb3RlY3RlZEciIiZGJylJImNHNiJGJSEiIilJImhHRi4iIiRGLylJImtHRi4iIiVGJylJIlRHRi5GNUYnRic= JSFH Calculate the constants to find F = 5.6761 * 10-8 T4. More accurately, the Stefan-Bolzmann law states: F = 5.6704 * 10-8 T4, where 5.6704 * 10-8 W m-2 K-4 is known as the Stefan-Boltzmann constant, symbolized by \317\203. The flux (F) is in W/m2. To obtain the total flux, multiply this by the surface area of the radiating object: F = 4 * \317\200 * radius2 * 5.6704 * 10-8 T4.
<Text-field style="Heading 1" layout="Heading 1">Solution (B) Wien's Displacement Law</Text-field> Now derive Wien's law by finding the value of the wavelength, lambda, which maximizes the radiance R. Set the derivative equal to zero. JSFH 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 Warning, solutions may have been lost LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi5RJyZyYXJyO0YnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkmbXRleHRHRiQ2JVEsYXR+NX5kaWdpdHNGJ0YvRjJGQw== 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 LCQqLCQiJlQsIyEiJiIiIkkiaEc2IkYnSSJjR0YpRidJImtHRikhIiJJIlRHRilGLEYn Define the constants. 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The general form of Wien's law is \316\273max T = 2.8978 * 10-3 (Karttunen et al., 2014, p. 105).
<Text-field style="Heading 1" layout="Heading 1">Solution (C) Colour Index</Text-field> Colour is related to temperature. Consider filters that have the following colour ranges: blue: 400-500 nm; red: 600-700 nm. 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 JCIkKyUhIio= JSFH Use the colour index formula. JSFH 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 JCIrMVQhKUc9ISM1 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= (A correction constant of integration must be added to this value.) Usually, actual measurements are made using blue and visual filters. In the standard Johnson and Morgan system, the blue (B) filter is centred at 436 nm and has a spread of 94 nm. The visual (V) filter is centred at 545 nm and has a spread of 88 nm. A star is viewed through each filter, and a photometer measures the flux. The ratio of the fluxes is then used to determine the colour index (Karttunen et al. 2007, p. 87). 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 :
<Text-field style="Heading 1" layout="Heading 1">References</Text-field> _______________________________________________ Karttunen, H. et al. (2007). Fundamental Astronomy (5th ed.). Berlin: Springer.
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