This Week (3) Concepts: Light and Earth’s Energy Balance Electromagnetic Radiation Blackbody Radiation and Temperature Earth’s Energy Balance w/out atmosphere.

This Week (3)Concepts: Light and Earth’s Energy

Balance•Electromagnetic Radiation

•Blackbody Radiation and Temperature

•Earth’s Energy Balance w/out atmosphere

Read chapter 3 (34 – 41.5) of your textKeep up by working on assignment 1

Today—Light

•What is light?

•How much energy does light have?

•Emission and Absorption Spectra

Oscillators

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Oscillators-

+

Oscillators

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Oscillators

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As charged particles oscillate, their motion causes the electric force field to oscillate.

Oscillations in the electric and magnetic fields (caused by one another) can propagate (move) through space.

Such oscillations are known as electromagnetic radiation (which encompasses light)

Electromagnetic Radiation

Electric and magnetic fields oscillate perpendicular to each other and to direction of propagation (travel).

Wavelength (): distance between peaks (1 full cycle)—m,cm,nmFrequency (): # of full cycles passing a point per second – Hz

and related to each other by speed of light (c): = c/

Electromagnetic RadiationLight acts both like a wave and as a stream of particles

We call these packets of light photons

A photon is the smallest packet of energy that can be transported by an EM wave of a given frequency.

The energy a photon carries is directly proportional to its frequencyEphoton = h h is Plank’s constant

6.636x10-34 Js

The intensity (brightness) of radiation is related to the number of photons of a particular frequency

Questions1. List in order of increasing energy: green light (530

nm), blue light (420 nm), infrared (~10,000 nm).

2. Consider a 1 Watt green laser (532 nm). How many photons are being emitted from the laser per second?

3. Suppose the green laser above is a spot with 1 cm diameter. What is the photon flux in units of W/m2?

Electromagnetic SpectrumEnergy increases this way Wavelength increases

this way

Solar Emission Flux The sun emits about 6.3 X 107 W/m2 of radiant energy

How are we still here?

Radiant Energy FluxRecall FLUX: amount of energy (or mass) passing through an area oriented perpendicular to the flow per unit time.

Except for lasers, most objects, such as the sun, radiate in all directions –flux decreases with distance from source.

vsrobj

d1 d2

2 1

21

2*d d

dF Fd

Flux decreases as inverse square of distance from source

**this picture is a bit misleading

**

Inverse Square Law

The reason flux from a “point” source decreases as the inverse square due to the geometry of spheres.

The surface area of a sphere is 4r2

The further from the initial sphere of radiation, the larger the sphere over which the same total amount of radiation is spread.

ro

r1

r2

Spectrum of Solar Radiation Flux

“Flu

x”

Shows how the total flux is distributed among different wavelengths.

(measured at Earth)





Read chapter 3 (34 – 41.5) of your textKeep up by working on assignment 1

Today—Radiation & Temperature

•Light and matter

•The perfect emitter (or absorber)

•Solar Emission

A Brief ReviewYesterday’s key concepts (which will come up again):

1. Light carries energy: E = hv = hc/

2. The intensity of light is related to the total number of photons (emitted) per time

3. Radiation flux is the amount of light energy passing perpendicularly through a unit area in a second. (J/s/m2 = W/m2)

4. The radiation flux from a single source decreases by the inverse square of the distance from the source

Oscillators

-light

- light

The blue spring is being forced with a frequency it “likes” to oscillate at and thus it absorbs the energy and converts it into vibrational motion

Light and Matter

Four possible results of light and matter interaction:

1. Absorption—causes matter to warm2. Emission – causes matter to cool3. Transmission – “no interaction”4. Scattering – like reflection but more

generalIn the end, which of these actually occurs depends on the wavelength (frequency) of light and the type of matter.

All processes happen on Earth and are important in considering the energy balance of the planet.

Questions

1. Based on what we’ve learned so far, why would absorption of light cause a temperature increase in some object, and why would emission of light by an object cause a decrease in its temperature?

2. Give a real world example for each of the possible results of light interacting with matter.

Blackbody Radiation A blackbody is a perfect emitter and absorber of radiation. It’s emission spectrum is a function of its temperature only. the peak

wavelength...

…is inversely proportional to the temperature of the objectHotter objects emit more at shorter wavelengths

Radi

atio

n Fl

ux

(W/m

2 )

Blackbody Radiation A blackbody is a perfect emitter and absorber of radiation. It’s emission spectrum is a function of its temperature only.

Radi

atio

n Fl

ux

(W/m

2 )

Area under curve proportional to total amount of radiation

Total amount of radiation emitted is larger for hotter objects.

Blackbody Radiation—So What

If I know the emission spectrum of an object, then I know its temperature! (or vice versa)

Satellites have used this to measure Earth’s temperature and confirm the increase in T over the past two decades.

The hotter an object the more radiation it emits. That is, the more energy it gives off thereby cooling itself faster.

This is a negative feedback!

Questions

1. The peak in the sun’s emission spectrum occurs at about 500 nm or 0.5 micrometers. What is the temperature of the sun?

2. How much “brighter” is the sun compared to the Earth?

Imperfect Absorbers/Emitters

Kirchoff’s Law: A body can/will only emit the same wavelengths it absorbs.

If (0-1) is the fraction of light absorbed at some wavelength, then only that fraction (of blackbody radiation) will be emitted at that wavelength. Ra

diat

ion

Flux

Dist

ribut

ion

Ideal Blackbody distribution

True distribution

is known as the emissivity





Read chapter 3 (34 – 41.5) of your textSee “Closer Look” on page 42 of your textKeep up by working on assignment 1 (due tomorrow!)

Today—Earth’s Energy Balance Part 1

•Setting up the problem (goals and assumptions)

•How much solar radiation does Earth actually receive?

•How much of this radiation does Earth absorb?

•If Energy Flow Rate In = Energy Flow Rate Out, what’s the T?

A Brief ReviewYesterday’s key concepts (which will come up again):

1. The total amount of radiant energy emitted by a blackbody is proportional to its T4 (Stefan-

Boltzmann)

2. The hotter the object the more radiation it emits as shorter wavelengths (Wien’s Law)

3. An object which is not a blackbody can be treated as a blackbody as long as its emissivity is known (a result of Kirchoff’s Law)

Solar and Terrestrial Emission Fluxes

max ~ 0.5 microns

max ~ 10 microns

(if they were blackbodies…not so pretty in reality!)

Earth’s Energy Balance

To calculate Earth’s equilibrium temperature knowing only: the solar energy flux and how to calculate the terrestrial energy flux to space at a given temperature.

Goal

Assumptions and Simplifications1. Energy in = Energy out at all times and locations2. Solar radiation flux constant in time3. Everywhere on Earth receives same average solar

energy flux4. Earth is a blackbody (absorbs what it gets w/100%

efficiency and thus emits at 100% efficiency)


Fin = FoutWhat is Fin?Need to account for a) Earth-Sun distance, b) Earth intercepts fraction of total solar flux, and c) Earth “reflects” some of the intercepted radiation

DSERS

Earth’s Energy BalanceIncoming solar flux at Earth Iin = 1370 W/m2 (solar constant)

Earth intercepts an area of this incoming solar radiation equal to a flat disc with R = Rearth (Area = pi*RE

2)

~ 28% of this intercepted radiation is reflected. This fraction is known as Earth’s albedo.planet

Iin/4 (Iin /4)A TE4


Iin (1-A) / 4 = TE4

Fin = Fout

This energy balance is good for ANY planet!

Though it is always subject to the same assumptions we made.

Earth’s Energy Balance--Summary

Iin (1-A) / 4 = TE4

Fin = Fout

•Earth absorbs FIN = 240 W/m2 of energy (averaged over whole earth surface, day and night)

•If the earth system radiates like a blackbody then TE = 255 K = -18 C

•The actual average surface temperature of Earth is about 288 K = 15 C!

Where did we mess up???

This Week (3) Concepts: Light and Earth’s Energy Balance Electromagnetic Radiation Blackbody Radiation and Temperature Earth’s Energy Balance w/out atmosphere.

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