Lecture 5 -- Blackbody Radiation/ Planetary

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


                             visible
                              light




1000     100    10       1             0.1   0.01

                         0.7 to 0.4 m

                 (m)
       Electromagnetic Spectrum


                             visible
                              light ultraviolet




1000     100    10       1           0.1          0.01




                 (m)
       Electromagnetic Spectrum


                                   visible
               infrared             light ultraviolet




1000     100          10       1           0.1          0.01




                       (m)
              Electromagnetic Spectrum


                                          visible
microwaves            infrared             light ultraviolet      x-rays




       1000     100          10       1           0.1          0.01




                              (m)
                Electromagnetic Spectrum


                                            visible
microwaves              infrared             light ultraviolet      x-rays




         1000     100          10       1           0.1          0.01


 Low                                                          High
Energy                                                       Energy
                                (m)
        Blackbody Radiation




Blackbody radiation—radiation 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

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.
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)
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 Wien’s 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)



 Wien’s 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     max   region in     F
                      spectrum
        (K)    (m)               (W/m2)


Sun     6000



Earth   300
         T     max   region in     F
                      spectrum
        (K)    (m)               (W/m2)


Sun     6000   0.5



Earth   300    10
                Electromagnetic Spectrum


                                            visible
microwaves              infrared             light ultraviolet      x-rays




         1000     100          10       1           0.1          0.01


 Low                                                          High
Energy                                                       Energy
                                (m)
         T     max   region in     F
                      spectrum
        (K)    (m)               (W/m2)


Sun     6000   0.5    Visible
                      (yellow?)


Earth   300    10     infrared
• 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
         T     max   region in     F
                      spectrum
        (K)    (m)               (W/m2)


Sun     6000   0.5    Visible
                      (green)


Earth   300    10     infrared
 Stefan Boltzman Law.

                  F =  T4

            F = flux of energy (W/m2)
            T = temperature (K)
             = 5.67 x 10-8 W/m2K4 (a constant)
         T     max   region in     F
                      spectrum
        (K)    (m)               (W/m2)


Sun     6000   0.5    Visible 7 x 107
                      (green)


Earth   300    10     infrared     460
Solar Radiation and Earth’s 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 Earth’s 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)
             Earth         Sun




1000   100    10       1         0.1     0.01


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




1000   100    10       1         0.1     0.01


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

                            F =  T4
Hotter objects emit at
shorter wavelengths.

   max = 3000/T         Earth         Sun




     1000      100        10       1         0.1     0.01


                                        Hotter objects emit
                                        more energy than
                           (m)        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 (rs-e)
       and the Sun and the Sun’s 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 Earth’s surface really -18 oC?
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.
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
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 Earth’s 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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posted:12/3/2011
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