Chapter 3Part 2 Blackbody Radiation/ Planetary Energy Balance

Chapter 3Part 2 Blackbody Radiation/ Planetary Energy Balance

Chapter 3Part 2 Blackbody Radiation/ Planetary Energy Balance Blackbody Radiation Planck function Blackbody radiationradiation emitted by a body that

emits (or absorbs) equally well at all wavelengths Basic Laws of Radiation 1) All objects emit radiant energy. Basic Laws of Radiation 1) All objects emit radiant energy. 2) Hotter objects emit more energy than colder objects.

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

Scientific Notation 10 = 101 100 = 102 1,000 = 103 1,000,000 = 106 1,000,000,000,000 = 1012 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. 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 Wiens Law max 3000 m T(K) Stefan-Boltzmann law

F = T4 F = flux of energy (W/m2) T = temperature (K) = 5.67 x 10-8 W/m2K4 (a constant) Wiens law max 3000 m T(K)

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

Sun 6000 Earth 300 max (m)

region in spectrum F (W/m2) T (K)

(m) Sun 6000 0.5 Earth

300 10 Wiens law: max region in spectrum

max 3000 m T(K) F (W/m2) Electromagnetic Spectrum infrared

microwaves 1000 Low Energy visible light ultraviolet

100 10 (m) 1 0.1

x-rays 0.01 High Energy Sun

T (K) (m) 6000 0.5 max

region in spectrum Visible (yellow?) Earth 300

10 infrared F (W/m2) Blue light from the Sun is removed from the beam by Rayleigh scattering, so the Sun appears yellow

when viewed from Earths surface even though its radiation peaks in the green Sun T (K) (m)

6000 0.5 max region in spectrum Visible

(green) Earth 300 10 infrared

F (W/m2) Sun T (K) (m)

6000 0.5 max region in spectrum F

(W/m2) Visible 7 x 107 (green) Earth

300 10 Stefan-Boltzmann law: infrared 460

F = T4 Solar Radiation and Earths Energy Balance 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.) Some Basic Information: Area of a circle = r2 Area of a sphere = 4 r2 Energy Balance: The amount of energy delivered to the Earth is equal to the energy lost from the Earth.

Otherwise, the Earths temperature would continually rise (or fall). Energy Balance: Incoming energy = outgoing energy Ein = Eout Eout

Ein How much solar energy reaches the Earth? How much solar energy reaches the Earth? As energy moves away from the sun, it is spread over a greater and greater area. 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 So = L / area of sphere So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 4 x x (1.5 x 1011m)2

So is the solar constant for Earth W/m2 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 (r s-e) and the Sun and the Suns luminosity. Each planet has its own solar constant 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) Ein re 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)

Ein = So (W/m2) x re2 (m2) Ein re How much energy does the Earth emit? 300 K

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

F = T4 Area = 4 re2 Eout = ( T4) x (4 re2) Sun Earth 1000

100 10 (m) 1 0.1

0.01 Hotter objects emit more energy than colder objects Sun Earth

1000 100 10 (m) 1

0.1 0.01 Hotter objects emit more energy than colder objects F = T4 Hotter objects emit at

shorter wavelengths. max = 3000/T 1000 100 Sun Earth

10 (m) 1 0.1 0.01

Hotter objects emit more energy than colder objects F = T4 How much energy does the Earth emit? Eout = F x (area of the Earth) 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) Eout How much solar energy reaches the Earth?

Ein 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

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

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 (r s-e) and the Sun and the Suns luminosity. 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 How much solar energy reaches the Earth? Ein = So re2 BUT THIS IS NOT QUITE CORRECT! **Some energy is reflected away** Ein

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

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) Ein re

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

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

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

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

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

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

Eout Ein 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. T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3

= 5.67 x 10-8 W/m2K4 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 = 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 Expected Temperature: Texp = 255 K (oC) = (K) - 273

Expected Temperature: Texp = 255 K (oC) = (K) - 273 So. Texp = (255 - 273) = -18 oC (which is about 0 oF) Is the Earths surface really -18 oC?

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

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. 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 Earths surface by the absorption of radiation by molecules in the atmosphere. The greenhouse effect: Heat is absorbed or trapped by gases in the atmosphere.

Earth naturally has a greenhouse effect of +33 oC. The concern is that the amount of greenhouse warming will increase with the rise of CO2 due to human activity.

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