Solar Radiation Emission and Absorption

					Solar Radiation: Emission and Absorption

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V1003 - Science and Society

Take away concepts
1. 2. 3. 4. 5. 6. 7. Conservation of energy. Black body radiation principle Emission wavelength and temperature (Wein’s Law). Radiation vs. distance relation Black body energy flux (Stefan-Boltzmann Law) Effective temperature calculation, differences from actual temperature. Why there are seasons.

What is Energy?
Energy is an abstract quantity that matter or a waves possess. “The ability to do work”. Energy measured in Joules (1 J = 0.24 calories). Power measured in Watts (1 J/s)
(what’s a “kilowatt hour”?)

Energy is always conserved (1st law of TD). Energy can be changed from one form to another, but it cannot be created or destroyed.

Types of Energy
・Kinetic Energy ・Chemical energy ・Gravitational energy ・Electrical energy ・Mass energy ・Thermal energy ・Elastic energy ・Nuclear energy ・Radiant energy

Solar Energy
Nuclear fusion: H to He Emits Electromagnetic radiation (radiant E) EM waves behave like particles and waves
EM travels at c (3 x 108 m/s)

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EM Radiation

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Since c is constant, frequency of EM wave emission related to electron vibration Warm things have more energy than cold things, so ….?

Properties of waves
Amplitude (A) Wavelength (µm) Period (sec) Frequency (1/sec) c is constant

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Blackbody Radiation
A “blackbody” absorbs and emits radiation at 100% efficiency.
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energy in = energy out Across all wavelengths

Wein’s Law
emission wavelength and temperature

max = a / T
Where:

max a T

is wavelength of emitted

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radiation (in µm) = 2898, constant emitter temperature (in K)

Recall that K = T°C - 273.15 Sun’s temperature is 5800K What’s its wavelength?

What’s your wavelength? max = a / T
(a = 2898)

Your body is 37°C or 37+273 = 310K

max = ?
9.4 µm (far infrared)

Earth’s Infrared “Glow”: 15µm

Electromagnetic spectrum

9 µm “hot” “cold”

0.5 µm

1 µm = 1000 nm

Visualizing emission temperatures

Sunny day: 6000K Sunset: 3200K Candlelight: 1500K

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Blackbody applet: http://qsad.bu.edu/applets/blackbody/applet.html

The effect of distance on radiation
“the 1 / r2 rule”

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Sun emission decreases in proportion to 1 / r2 of the Sun-Planet distance

Mars is 1.52 AU
(1 AU = earth-sun distance = 1.5 x 1011 m)

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Using 1/

r2 rule…

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1 / (1.5*1.5) = 0.44 Mars receives ~44% of the Earth’s solar radiation.

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Summary so far…
Wein’s Law (emission freq. and temperature)
The “1 / r2” law (radiation amt and distance) Now let’s calculate the total radiative energy flux into or out of a planet using the: Stefan - Boltzmann Law

Stefan - Boltzmann Law
Energy emitted by a black body is greatly dependent on its temperature:

I =  T4
Where: I = Black body energy radiation  = (Constant) 5.67x10-8 Watts/m2/K4 T = temperature in Kelvin

Example: Sun surface is 5800K, so I = 6.4 x 107 W/m2

Calculating the Earth’s “Effective Temperature”
Easy as 1-2-3…
1. Calculate solar output. 2. Calculate solar energy reaching the Earth. 3. Calculate the temperature the Earth should be with this energy receipt.

1. Calculate solar output.
Calculate Sun temperature assuming it behaves as a blackbody (knowing that sun= 0.5µm).
From S-B law: Isun = 6.4 x 10 7 W/m2 We need surface area of sun: Area = 4r2 = 4(6.96x108 m) = 6.2 x 10 18 m2

Total Sun emission: 3.86 x
Solar Emission Power

1026

Watts (!)

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2. Calculate solar energy reaching the Earth.

Simple Geometry.
(recall the inverse square law..)

Earth-Sun distance (D): 1.5 x 1011 m Earth radius (r): 6.7 x 108 m So, 3.86 x 10 26 Watts / (4 (1.5 x 1011 m)2 )

Earth’s incoming solar radiation: 1365 W/m2

3. Earth energy in = energy out
You have Iearth, solve for Tearth Stefan - Boltzmann law: Iearth =  Tearth4
Incoming solar radiation: 1365 W/m2 About 30% is reflected away by ice, clouds, etc.: reduced to 955 W/m2 Incoming on dayside only (DISK), but outgoing everywhere (SPHERE), so outgoing is 1/4 of incoming, or 239 W/m2
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239 W/m2 =  T4

Teffective = 255K
Earth Effective temp: 255 K, or -18°C Earth Actual temp: 288K, or +15°C
… the difference of +33°C is due to the greenhouse effect!
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So what Earth’s radiation wavelength?

max = a / T
Where:

max a T

is wavelength of emitted
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radiation (in µm)
= 2898, constant emitter temperature (in K)

If Earth effective temperature is 255K What’s the wavelength?

Emission Spectra: Sun and Earth

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0.5 µm

9 µm 15 µm

Radiation and Matter

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Also dependent upon the frequency of radiation! (next lecture)


				
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Lingjuan Ma Lingjuan Ma
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