Lecture 5 Blackbody Radiation Energy Balance

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Lecture 5 -- Blackbody Radiation/ Planetary Energy Balance: 

Lecture 5 -- Blackbody Radiation/ Planetary Energy Balance Abiol 574

Slide2: 

Electromagnetic Spectrum  (m) visible light 0.7 to 0.4 m

Slide3: 

Electromagnetic Spectrum  (m) ultraviolet visible light

Slide4: 

Electromagnetic Spectrum  (m) ultraviolet visible light infrared

Slide5: 

Electromagnetic Spectrum  (m) ultraviolet visible light infrared microwaves x-rays

Slide6: 

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

Blackbody Radiation: 

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

The Planck Function: 

The Planck Function Blackbody radiation follows the Planck function

Slide9: 

Basic Laws of Radiation All objects emit radiant energy.

Slide10: 

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

Slide11: 

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.

Slide12: 

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)

Slide13: 

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.

Slide14: 

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)

Slide15: 

 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)

Slide16: 

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

Slide19: 

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

Slide21: 

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

Slide23: 

 Stefan Boltzman Law. F =  T4 F = flux of energy (W/m2) T = temperature (K)  = 5.67 x 10-8 W/m2K4 (a constant)

Slide25: 

Solar Radiation and Earth’s Energy Balance

Planetary Energy Balance: 

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

Slide27: 

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

Slide28: 

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).

Slide29: 

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

Slide30: 

(The rest of this derivation will be done on the board. However, I will leave these slides in here in case anyone wants to look at them.)

Slide31: 

How much solar energy reaches the Earth?

Slide32: 

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

Slide33: 

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

Slide34: 

So = L / area of sphere

Slide35: 

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

Slide36: 

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’ luminosity.

Slide37: 

Each planet has its own solar constant…

Slide38: 

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

Slide39: 

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

Slide40: 

How much energy does the Earth emit? 300 K

Slide41: 

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

Slide42: 

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

Slide43: 

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

Slide44: 

 (m) Earth Sun Hotter objects emit more energy than colder objects

Slide45: 

 (m) Earth Sun Hotter objects emit more energy than colder objects F =  T4

Slide46: 

 (m) Earth Sun Hotter objects emit at shorter wavelengths. max = 3000/T Hotter objects emit more energy than colder objects F =  T4

Slide47: 

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

Slide48: 

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

Slide49: 

How much solar energy reaches the Earth? Ein

Slide50: 

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

Slide51: 

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

Slide52: 

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. Remember…

Slide53: 

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

Slide54: 

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

Slide55: 

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

Slide56: 

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

Slide57: 

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

Slide58: 

Energy Balance: Ein = Eout Ein = So  re2 (1-A) Ein

Slide59: 

Energy Balance: Ein = Eout Ein = So  re2 (1-A) Eout =  T4(4  re2) Ein

Slide60: 

Energy Balance: Ein = Eout So  re2 (1-A) =  T4 (4  re2) Ein

Slide61: 

Energy Balance: Ein = Eout So  re2 (1-A) =  T4 (4  re2) Ein

Slide62: 

Energy Balance: Ein = Eout So (1-A) =  T4 (4) Ein

Slide63: 

Energy Balance: Ein = Eout So (1-A) =  T4 (4) T4 = So(1-A) 4 Ein

Slide64: 

T4 = So(1-A) 4 If we know So and A, we can calculate the temperature of the Earth. We call this the expected temperature (Texp). 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.

Slide65: 

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 W/m2K4

Slide66: 

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 T4 = (1370 W/m2)(1-0.3) 4 (5.67 x 10-8 W/m2K4)

Slide67: 

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 T4 = (1370 W/m2)(1-0.3) 4 (5.67 x 10-8 W/m2K4) T4 = 4.23 x 109 (K4) T = 255 K

Slide68: 

Expected Temperature: Texp = 255 K (oC) = (K) - 273

Slide69: 

Expected Temperature: Texp = 255 K (oC) = (K) - 273 So…. Texp = (255 - 273) = -18 oC (which is about 0 oF)

Slide70: 

Is the Earth’s surface really -18 oC?

Slide71: 

Is the Earth’s surface really -18 oC? NO. The actual temperature is warmer! The observed temperature (Tobs) is 15 oC, or about 59 oF.

Slide72: 

Is the Earth’s surface really -18 oC? NO. The actual temperature is warmer! The observed temperature (Tobs) is 15 oC, or about 59 oF. The difference between observed and expected temperatures (T): T = Tobs - Texp T = 15 - (-18) T = + 33 oC

Slide73: 

T = + 33 oC In other words, the Earth is 33 oC warmer than expected based on black body calculations and the known input of solar energy.

Slide74: 

T = + 33 oC In other words, the Earth is 33 oC 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.

Slide75: 

T = + 33 oC In other words, the Earth is 33 oC 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. It is a result of warming of the Earth’s surface by the absorption of radiation by molecules in the atmosphere.

Slide76: 

The greenhouse effect: Heat is absorbed or “trapped” by gases in the atmosphere. Earth naturally has a greenhouse effect of +33 oC.

Slide77: 

The concern is that the amount of greenhouse warming will increase with the rise of CO2 due to human activity.

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