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# Chapter 3—Part 2

Chapter 3—Part 2. Blackbody Radiation/ Planetary Energy Balance. Blackbody Radiation. Planck function. Blackbody radiation —radiation emitted by a body that emits (or absorbs) equally well at all wavelengths. Basic Laws of Radiation All objects emit radiant energy.

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## Chapter 3—Part 2

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1. Chapter 3—Part 2 Blackbody Radiation/ Planetary Energy Balance

2. Blackbody Radiation Planck function Blackbody radiation—radiation emitted by a body that emits (or absorbs) equally well at all wavelengths

4. Basic Laws of Radiation • All objects emit radiant energy. • Hotter objects emit more energy than colder objects.

5. Basic Laws of Radiation • All objects emit radiant energy. • Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.

6. Basic Laws of Radiation • All objects emit radiant energy. • Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power. •  This is the Stefan Boltzmann Law • F =  T4 • F = flux of energy (W/m2) • T = temperature (K) •  = 5.67 x 10-8 W/m2K4 (a constant)

7. Scientific Notation 10 = 101 100 = 102 1,000 = 103 1,000,000 = 106 1,000,000,000,000 = 1012

8. Basic Laws of Radiation • All objects emit radiant energy. • Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. • The hotter the object, the shorter the wavelength () of emitted energy.

9. Basic Laws of Radiation • All objects emit radiant energy. • Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. • The hotter the object, the shorter the wavelength () of emitted energy. • This is Wien’s Law • max  3000 m • T(K)

10. Stefan-Boltzmann law F =  T4 F = flux of energy (W/m2) T = temperature (K)  = 5.67 x 10-8 W/m2K4 (a constant) Wien’s law max  3000 m T(K)

11. We can use these equations to calculate properties of energy radiating from the Sun and the Earth. 6,000 K 300 K

12. 1000 100 10 1 0.1 0.01 Electromagnetic Spectrum visible light infrared ultraviolet x-rays microwaves Low Energy High Energy  (m)

13. Blue light from the Sun is removed from the beam • by Rayleigh scattering, so the Sun appears yellow • when viewed from Earth’s surface even though its • radiation peaks in the green

14. Stefan-Boltzmann law:F =  T4

15. Solar Radiation and Earth’s Energy Balance

16. Planetary Energy Balance • We can use the concepts learned so far to calculate the radiation balance of the Earth (The rest of this lecture will be done on the blackboard. The slides are included, though, for people who want to study them.)

17. Some Basic Information: Area of a circle =  r2 Area of a sphere = 4  r2

18. Energy Balance: The amount of energy delivered to the Earth is equal to the energy lost from the Earth. Otherwise, the Earth’s temperature would continually rise (or fall).

19. Energy Balance: Incoming energy = outgoing energy Ein = Eout Eout Ein

20. How much solar energy reaches the Earth?

21. How much solar energy reaches the Earth? As energy moves away from the sun, it is spread over a greater and greater area.

22. How much solar energy reaches the Earth? As energy moves away from the sun, it is spread over a greater and greater area.  This is the Inverse Square Law

23. So = L / area of sphere

24. So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth

25. So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

26. Each planet has its own solar constant…

27. How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re) Ein re

28. How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re) Ein = So (W/m2) x  re2 (m2) Ein re

29. How much energy does the Earth emit? Eout = F x (area of the Earth)

30. How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2

31. How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2 Eout = ( T4) x (4  re2)

32. 1000 100 10 1 0.1 0.01 Sun Earth Hotter objects emit more energy than colder objects  (m)

33. 1000 100 10 1 0.1 0.01 Sun Earth Hotter objects emit more energy than colder objects F =  T4  (m)

34. 1000 100 10 1 0.1 0.01 Hotter objects emit at shorter wavelengths. max = 3000/T Sun Earth Hotter objects emit more energy than colder objects F =  T4  (m)

35. Eout How much energy does the Earth emit? Eout = F x (area of the Earth)

36. Eout How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2 Eout = ( T4) x (4  re2)

37. How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein re

38. How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein = So x (area of circle) Ein re

39. Remember… So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

40. How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein = So x (area of circle) Ein = So (W/m2) x  re2 (m2) Ein re

41. How much solar energy reaches the Earth? Ein = So re2 BUT THIS IS NOT QUITE CORRECT! **Some energy is reflected away** Ein re

42. How much solar energy reaches the Earth? Albedo (A) = % energy reflected away Ein = So re2 (1-A) Ein re

43. How much solar energy reaches the Earth? Albedo (A) = % energy reflected away A= 0.3 today Ein = So re2 (1-A) Ein = So re2 (0.7) re Ein

44. Energy Balance: Incoming energy = outgoing energy Ein = Eout Eout Ein

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