1. Energy Balance

2. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer

3. Electromagnetic Spectrum (  m) 10001001010.10.01 visible light 0.7 to 0.4  m

4. Electromagnetic Spectrum (  m) 10001001010.10.01 ultraviolet visible light

5. Electromagnetic Spectrum (  m) 10001001010.10.01 ultraviolet visible light infrared

6. Electromagnetic Spectrum (  m) 10001001010.10.01 ultraviolet visible light infrared microwaves x-rays

7. Electromagnetic Spectrum (  m) 10001001010.10.01 ultraviolet visible light infrared microwaves x-rays High Energy Low Energy

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

9. Basic Laws of Radiation 1)All objects emit radiant energy.

10. Basic Laws of Radiation 1)All objects emit radiant energy. 2)Hotter objects emit more energy than colder objects.

11. Basic Laws of Radiation 1)All objects emit radiant energy. 2)Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object.

12. Basic Laws of Radiation 1)All objects emit radiant energy. 2)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 E =  T 4 E = total radiant energy emitted per unit time per unit surface area(W/m 2 ) T = temperature (K)  = 5.67 x 10 -8 W/m 2 K 4 (a constant)

13. Basic Laws of Radiation 1)All objects emit radiant energy. 2)Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. 3)The hotter the object, the shorter the wavelength ( ) of emitted energy.

14. Basic Laws of Radiation 1)All objects emit radiant energy. 2)Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. 3)The hotter the object, the shorter the wavelength ( ) of emitted energy.  This is Wien’s Law max  2828  m T(K)

15.  Stefan Boltzmann Law. F =  T 4 F = flux of energy (W/m 2 ) T = temperature (K)  = 5.67 x 10 -8 W/m 2 K 4 (a constant)  Wien’s Law max  2828  m T(K)

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

17. Solar Radiation and Earth’s Energy Balance

18. Planetary Energy Balance We can use the concepts learned so far to calculate the radiation balance of the Earth

19. Some Basic Information: Area of a circle =  r 2 Area of a sphere = 4  r 2

20. 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).

21. Energy Balance: Incoming energy = outgoing energy E in = E out E in E out

22. How much solar energy reaches the Earth?

23. As energy moves away from the sun, it is spread over a greater and greater area.

24. 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

25. S o = L / area of sphere

26. S o = L / (4  r s-e 2 ) = 3.9 x 10 26 W = 1370 W/m 2 4 x  x (1.5 x 10 11 m) 2 S o is the solar constant for Earth

27. S o = L / (4  r s-e 2 ) = 3.9 x 10 26 W = 1370 W/m 2 4 x  x (1.5 x 10 11 m) 2 S o is the solar constant for Earth It is determined by the distance between Earth (r s-e ) and the Sun and the Sun’ luminosity.

28. Each planet has its own solar constant…

29. How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (r e ) E in rere

30. How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (r e ) E in = S o (W/m 2 ) x  r e 2 (m 2 ) E in rere

31. How much energy does the Earth emit? 300 K

32. How much energy does the Earth emit? E out = E x (area of the Earth)

33. How much energy does the Earth emit? E out = E x (area of the Earth) E =  T 4 Area = 4  r e 2

34. How much energy does the Earth emit? E out = E x (area of the Earth) E =  T 4 Area = 4  r e 2 E out = (  T 4 ) x (4  r e 2 )

35. (  m) 10001001010.10.01 Earth Sun Hotter objects emit more energy than colder objects

36. (  m) 10001001010.10.01 Earth Sun Hotter objects emit more energy than colder objects E =  T 4

37. (  m) 10001001010.10.01 Earth Sun Hotter objects emit at shorter wavelengths. max = 2828/T Hotter objects emit more energy than colder objects E =  T 4

38. How much energy does the Earth emit? E out = E x (area of the Earth) E out

39. How much energy does the Earth emit? E out = E x (area of the Earth) E =  T 4 Area = 4  r e 2 E out = (  T 4 ) x (4  r e 2 ) E out

40. How much solar energy reaches the Earth? E in

41. 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 (r e ). E in rere

42. 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 (r e ). E in = S o x (area of circle) E in rere

43. S o = L / (4  r s-e 2 ) = 3.9 x 10 26 W = 1370 W/m 2 4 x  x (1.5 x 10 11 m) 2 S o is the solar constant for Earth It is determined by the distance between Earth (r s-e ) and the Sun and the Sun’s luminosity. Remember…

44. 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 (r e ). E in = S o x (area of circle) E in = S o (W/m 2 ) x  r e 2 (m 2 ) E in rere

45. How much solar energy reaches the Earth? E in = S o  r e 2 BUT THIS IS NOT QUITE CORRECT! **Some energy is reflected away** E in rere

46. How much solar energy reaches the Earth? Albedo (A) = % energy reflected away E in = S o  r e 2 (1-A) E in rere

47. How much solar energy reaches the Earth? Albedo (A) = % energy reflected away A= 0.31 today E in = S o  r e 2 (1-A) E in = S o  r e 2 (0.69) rere E in

48. Energy Balance: Incoming energy = outgoing energy E in = E out E out E in

49. Energy Balance: E in = E out E in = S o  r e 2 (1-A) E out E in

50. Energy Balance: E in = E out E in = S o  r e 2 (1-A) E out =  T 4 (4  r e 2 ) E out E in

51. Energy Balance: E in = E out S o  r e 2 (1-A) =  T 4 (4  r e 2 ) E out E in

52. Energy Balance: E in = E out S o  r e 2 (1-A) =  T 4 (4  r e 2 ) E out E in

53. Energy Balance: E in = E out S o (1-A) =  T 4 (4) E out E in

54. Energy Balance: E in = E out S o (1-A) =  T 4 (4) T 4 = S o (1-A) 4  E out E in

55. T 4 = S o (1-A) 4  If we know S o and A, we can calculate the temperature of the Earth. We call this the expected temperature (T exp ). It is the temperature we would expect if Earth behaves like a blackbody. This calculation can be done for any planet, provided we know its solar constant and albedo.

56. T 4 = S o (1-A) 4  For Earth: S o = 1370 W/m 2 A = 0.31  = 5.67 x 10 -8 W/m 2 K 4

57. T 4 = S o (1-A) 4  For Earth: So = 1370 W/m 2 A = 0.31  = 5.67 x 10 -8 T 4 = (1370 W/m 2 )(1-0.31) 4 (5.67 x 10 -8 W/m 2 K 4 )

58. T 4 = S o (1-A) 4  For Earth: So = 1370 W/m 2 A = 0.31  = 5.67 x 10 -8 T 4 = (1370 W/m 2 )(1-0.31) 4 (5.67 x 10 -8 W/m 2 K 4 ) T 4 = 4.23 x 10 9 (K 4 ) T = 254 K

59. Expected Temperature: T exp = 254 K ( o C) = (K) - 273

60. Expected Temperature: T exp = 254 K ( o C) = (K) - 273 So…. T exp = (254 - 273) = -19 o C

61. Is the Earth’s surface really -19 o C?

62. NO. The actual temperature is warmer! The observed temperature (T obs ) is 15 o C

63. Calculate the average temperatures of Mars and Venus applying the Simple Global Temperature Model: PlanetVenusEarthMars Distance from Sun(10 6 km 108150218 Solar Constant (W/m 2 ) 26201370589 Albedo (%) 763125 Atmospheric Pressure (atm) 9010.006 Effective Temperature(K) Surface Temperature(K)

64. PlanetVenusEarthMars Distance from Sun(10 6 km 108150218 Solar Constant (W/m 2 ) 26201370589 Albedo (%) 763125 Atmospheric Pressure (atm) 9010.006 Effective Temperature(K) 229254210 Surface Temperature(K) 750288218

65. Is the Earth’s surface really -19 o C? NO. The actual temperature is warmer! The observed temperature (T obs ) is 15 o C The difference between observed and expected temperatures (  T):  T = T obs - T exp  T = 15 - (-19)  T = + 34 o C

66. In other words, the Earth is 34 o C warmer than expected based on black body calculations and the known input of solar energy.

67.  T = + 34 o C In other words, the Earth is 34 o C warmer than expected based on black body calculations and the known input of solar energy. This extra warmth is what we call the GREENHOUSE EFFECT.