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Lecture 5 -- Blackbody Radiation/ Planetary

Energy Balance

- Abiol 574

Electromagnetic Spectrum

visible light

0.7 to 0.4 ?m

? (?m)

Electromagnetic Spectrum

visible light

ultraviolet

? (?m)

Electromagnetic Spectrum

visible light

ultraviolet

infrared

? (?m)

Electromagnetic Spectrum

visible light

ultraviolet

infrared

x-rays

microwaves

? (?m)

Electromagnetic Spectrum

visible light

ultraviolet

infrared

x-rays

microwaves

High Energy

Low Energy

? (?m)

Blackbody Radiation

Blackbody radiationradiation emitted by a body

that emits (or absorbs) equally well at all

wavelengths

The Planck Function

- Blackbody radiation follows the Planck function

- Basic Laws of Radiation
- All objects emit radiant energy.

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

objects.

- 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.

- 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)

- 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.

- 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 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

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Electromagnetic Spectrum

visible light

ultraviolet

infrared

x-rays

microwaves

High Energy

Low Energy

? (?m)

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- 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

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? Stefan Boltzman Law. F ? T4 F flux

of energy (W/m2) T temperature (K) ? 5.67

x 10-8 W/m2K4 (a constant)

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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

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

(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.)

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

W/m2 4 x ? x (1.5 x 1011m)2

So is the solar constant for Earth

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.

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

(re)

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

(re) 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

Hotter objects emit more energy than colder

objects

? (?m)

Sun

Earth

Hotter objects emit more energy than colder

objects F ? T4

? (?m)

Hotter objects emit at shorter wavelengths. ?max

3000/T

Sun

Earth

Hotter objects emit more energy than colder

objects F ? T4

? (?m)

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

Eout (? T4) x (4 ? re2)

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 (rs-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)

re

Ein

Energy Balance Incoming energy outgoing

energy Ein Eout

Eout

Ein

Energy Balance Ein Eout Ein So ? re2 (1-A)

Ein

Energy Balance Ein Eout Ein So ? re2

(1-A) Eout ? T4(4 ? re2)

Ein

Energy Balance Ein Eout So ? re2 (1-A) ?

T4 (4 ? re2)

Ein

Energy Balance Ein Eout So ? re2 (1-A) ?

T4 (4 ? re2)

Ein

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

Ein

Energy Balance Ein Eout So (1-A) ? T4

(4) T4 So(1-A) 4?

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.