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Planck's Law of Black-Body Radiation

Planck's Law of Black-Body Radiation
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2013-12-31 12:53
FunctionTrigonometryCalculus
This example illustrates Planck's law, which describes the spectral distribution of an ideal black body at thermal equilibrium. Key mathematical concepts include functions, trigonometry, and limits. Using GeoGebra commands such as PolyLine, Point, Max, and Distance, the relationship between temperature and spectral radiance is constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. PolyLine(A, B, C, D, E, F, G) → Path1
  2. Point(Path1, Path1_%) → P_{ColorPath}
  3. Max(B_{λ-log}, -10, 10) → Max_λ
  4. Max(B_{flog}, 0, 20) → Max_f
  5. Distance(P_{ColorPath}, (0, 0)) → S_{Color Sat}
  6. Circle(P_{ColorPath}, 0.5) → Test_{Circle}
  7. OrthogonalLine(V_{vis-λ-max}, xAxis) → sichtbaresSpektrum_2
  8. OrthogonalLine(V_{vis-λ-min}, xAxis) → sichtbaresSpektrum_1
  9. OrthogonalLine(V_{vis-f-max}, xAxis) → sichtbaresSpektrum_4
  10. OrthogonalLine(V_{vis-f-min}, xAxis) → sichtbaresSpektrum_3

AI Drawing Prompt Reference

Draw the spectral radiation distribution of an ideal black body, showing the relationship between temperature and spectral radiation intensity. Start by drawing a polyline, then place a point on the path. Find the maximum value of spectral radiation intensity and draw a circle with a radius of 0.5 centered at this point. Define the range of visible spectrum and draw two vertical lines to indicate the minimum and maximum wavelengths. Finally, draw two more vertical lines to indicate the minimum and maximum frequencies.
The prompt above was compiled from the original drawing commands and is for reference only.