Chapter 4 Radiation
[comment: possible title, Electromagnetic Radiation’s Key Role in the Story of Energy. Keep in mind an issue driven approach, a need to know of Marty Perl - Spherical Cow view.]

 

  1. Introduction & Overview of this chapter: Why EM radiation is important, Burning Question of Global Climate Change, but also basis for all energy, food… Remember our goals of sustainability, conservation, and collaboration… Spiral approach here…

·        The context for radiation as one of three means of energy transport. √

·        Solar radiation as the principal source for almost all available energy forms, fossil fuels, wind, direct solar heating, etc. [K&R Esolar > 99.9%] √

·        Sustainable source and why that’s important √

·        Low entropy source and why that’s important [Romer] √

·        Radiation and atmosphere - weather - K­… √

·        Radiation and climate – greenhouse energy balance idea, albedo

·        Radiation and bio-systems, food (K+R), bio-molecules B&G

·        Radiation and the ocean as example [Bigg]

 

  1. The EM spectrum from hot bodies [underlying Greenhouse]

·        [Picture of solar spectrum at outer atmosphere, surface, C&N Fig 10.5 or Romer, Fig 11.15, same horizontal scale]

·        Source: Random acceleration of hot charged molecules à continuous EM radiation (compared to discrete transitions) [Romer] √

·        Eisberg text intro of blackbody idea with physics discussion, Aubrecht p. 442-443

·        Blackbody proof as most efficient radiator of radiation [Romer Ch 11]

·        Equation for radiation spectrum and discussion including description of the quantum mechanics in B&G, connection to H&R

·        Integrated à Stefan’s Law, Differentiated à Wien’s Law

·        Emissivity, blackbody, gray body, 0 < e < 1, table of surfaces [Devins, p 202, Table 6.15]

·        Emissivity = absorptivity e(l) = a(l)

·        Spectal emittance from Earth, C&N Fig 10.6

·        Example calcs: Campbell & Norman, H&R…, e.g. - clear & cloudy sky albedo, direct & diffuse radiation

·        LW vs SW and idea of selective surface [Romer, K&R, Devins, p. 204, excellent diagram, Physics Today, Feb 1972]

·        Examples: Implications of emissivity = absorptivity for radiators, hot black road, aluminum coating on insulation [K&R for two parallel surfaces], Romer Ch. 11, great problems of radiation balance,

·        How hot is planet Earth? – Spherical Cow prob 13

 

  1. The Sun and its radiation: [motivation for all sustainable energy discussions, direct solar]

·        Useful terminology: Energy, Power, Intensity in physics, E = hf, sentence

·        Irradiance, radiant emittance, radiant spectral flux density in biology [C&N – example]

·        Spectral emittance of sun, C&N Fig 10.4

·        [Picture of Sun at radius, r]

·        Discussion of Intensity [W/m2], Power from sun, I0 at upper atmosphere, units of W/m2, cal/min/cm2, inverse square law & example.

·        Constancy of I0? – Satellite measurements

·        Constancy of I0? – Summer/Winter [K&R]

·        Milankovitch cycles sentence à Chapter on Climate (spiral approach)

·        Example calcs: solar collectors at different angle, passive solar heating through window, [Hinrichs & Kleinbach practical examples of solar collection], [MHC – examples of energy balance]

 

 

  1. Greenhouse effect [Climate Change, CO2 limited society…]

·        Comment on origin of name, greenhouse [Romer – Ch 11]

·        Energy balance, Pin = Pout, Tequilibrium with no atmosphere, Spherical Cow IIIA6, Devins 460.

·        Venus example [Houghton – Ch2]

·        Earth’s albedo, table of surfaces (Devins, Table 6.14, p. 200, sea ice, cloud, leaves,…) C&N, Harte IIB18

·        Bouncing Sunbeams – Cow Prob. 18 – albedo with clouds

·        N-layered atmosphere – Cow Prob. Pr. IIIB6

·        Introduction of idea of molecular absorption of IR, re-radiation à transition to next section

 

  1. Radiation and matter [essential for energy tranfer from photons]

·        [Picture of absorption spectrum of a number of molecules, Piexoto]

·        Photoelectric effect, all or nothing [Romer – hitting bottles off  a fence with rocks, nice analogy]

·        Photons, Atomic absorption, CO2 example, E = hf [B&G]

Absorption cross sections, molar extinction coeff [B&G-Ch2]

·        Photon flux equivalent to intensity, example calc.

·        Absoption & Scattering [Devins 12.2]

·        Radiation and absorption, reflection, transmission [Houghton – Clouds, Ch6]

·        Lambert & Beer Law (B&G) – absorption of light by atmosphere à comment about GCMs and Slingo & Edwards to come.[Devins, eq. 12.2]

·        Energy loss in matter [Devins, Ch 14]

·        Ozone absorption of radiation [Houghton, Ch4]

·        Example: Vertical T profile – 2 sources of heat in Atmosphere – ir from below, uv from above - Bigg

 

  1. Radiation and biology [motivated by plant growth, food limits, biomass]

·        Terminology used by biologists and why, especially spectral densities

·        B&G biological molecules

·        C&N units

·        K&R food & sustainability

·         

  1. Photovoltaics [Motivated by huge PV potential]

·        Band gap energy, Eg

·        Photovoltaic conversion efficiency vs Eg (Fig. 6.20 K&R, Devins),

·        Technologies: crystal, amorphous silicon, etc (article from P120)

·        Paragraph from excellent P331 text of last year (Amos Kennedy)

·         

 

 


Electromagnetic Radiation: When energy travels at the speed of light

“Nature and Nature’s laws lay hid in night: God said, Let Newton be! And all was light”,

Alexander Pope (1688-1744)

 

 

A. Introduction: Why electromagnetic radiation is so important

 

Solar energy and time scales: More than 99.9% of the energy we are using today traveled from our sun as electromagnetic radiation.  For instance, fossil fuel energy sources, coal, oil, and natural gas, are the result of solar radiation over the past several hundred million years, converted through photosynthesis to plants and some on to animals and stored underground as hydrocarbons. On much shorter time scales of years (trees) or months (crops) solar energy is converted to biomass, materials containing mainly hydrogen, carbon, and oxygen such as carbohydrates.  These biomass compounds effectively store the solar energy in the form of chemical energy and can be used as a fuel.  On still shorter time scales, solar energy is converted to hydroelectric energy.  Incident visible solar radiation is absorbed by water, producing water vapor. Since this water vapor is lighter than dry air, it rises, is transported by advection to the area upstream, it condenses (releasing its stored energy) and is trapped behind a hydroelectric dam. On an even shorter time scale, the uneven absorption of the sun’s visible electromagnetic radiation heats the atmosphere starting large atmospheric convective currents.  The result is wind. Since the Sun’s electromagnetic energy travels from the sun at the speed of light, c, some 3x108 ms-1, the direct use of solar energy in photovoltaics and passive solar heating was radiated from the surface of the sun only some 8 minutes ago.   These short time scale sources are called “renewable” energy sources.

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[Question: Is there a sense in which fossil fuels are renewable?  Why do we choose not to consider this source in our long-term planning?]

 

[Question: Reed beds in wetlands form layers of biomass called peat on a scale of a few inches per hundreds years.  Is peat a renewable energy source?]

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Non-solar sources: There are, of course, energy sources that did not originate as electromagnetic energy from the Sun.  Geothermal and tidal energies are examples.  Geothermal energy, the heat energy in the Earth’s crust, comes both from the radioactive decay of unstable atomic nuclei and from residual heat from the original gravitational collapse of matter forming the earth.  Nuclear fission may also play a role [Lemley,2002]] The Moon pulls gravitationally on the Earth. It also pulls more strongly on the ocean water on the near side of the Earth and less strongly on the water on the far side of the Earth than it does on the Earth itself. Tides result, the bulging of water toward the Moon on the near side and away from the Moon on the far side.  The vast majority of this tidal motion simply heats the ocean, energy that was originally part of the total mechanical energy of the Moon in orbit about the Earth.  Electric energy is extracted from the tides by using hydroelectric dams in ocean estuaries where tides amplitudes are large.  At present we use very little energy from these sources.  These sources are often lumped into the “renewable” energy availability.

 

Lemley, B., Nuclear Plant, Discover Vol. 23, No. 8, pp. 38-42, 2002.

 

            Solar energy and sustainability: Estimates give us some 5 billion years of approximate solar stability before major changes in the output energy of the sun can be anticipated.  [Bennett et al., 1999] From the view of sustainability, a central theme of this book, depending on the sun as our primary source of energy sounds reasonable.  A valuable check would be a comparison of the size of our present energy resources, mainly fossil fuels, with the flow of energy from the sun.  If our energy use per year is already larger than the incoming energy from the sun, then we’d better look elsewhere for a sustainable source.  A back-of-the-envelope estimation in this regard is useful.

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 [Question: Table 1 in Chapter 1 gives an estimate of the world fossil fuel resource, some 200 Q = (200 Q) * (1.055x1021 Joules/Q) = 2.1x1023 Joules.  Meanwhile, some 1.73 x 1017 watts of electromagnetic energy per second strikes the top of the Earth’s atmosphere.   How many days does it take for the sun’s energy striking the top of the atmosphere to add up to our entire fossil fuel supply on Earth? Ans: 14 days.]

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Amazingly, our stored fossil fuel energy, though large, is supplied to the earth every two weeks.  Because the solar energy source is both large and steady, its detailed characteristics become very interesting from the view of energy sustainability. Electromagnetic radiation from the sun enters at several levels and places including discussions of direct solar energy use, of indirect solar energy use (biomass, wind, hydroelectric energy…), of food production, and of the critical impacts of climate change.

 

Entropy: The sun and disorder: Most importantly, the sun is a hot source with an absolute surface temperature of 5800 K.  The kinetic energy of molecules on the sun’s surface is proportional to the surface temperature. Since rapidly accelerating charged (ionized) particles produce electromagnetic radiation, the sun’s surface is an excellent radiator.  We discuss this so-called “black-body” radiation later in this chapter.  This radiation travels to earth where some of it is absorbed. However, the second law of thermodynamics requires that in any physical process the entropy of the total system must always increase, producing a less ordered system.  How, then, do we ever manage to generate nicely ordered (low entropy) energy like electricity or mechanical work for our use?  The trick is to keep the total entropy positive by dumping a small amount of heat energy into a cool system (the earth) and converting the rest of the energy from the sun into ordered low entropy energy like electricity. [ Picture here] Since the entropy change of an object is DQ/T, the hot sun decreases in entropy as it emits heat energy, DQ, but not very much because its T is large.  Heat energy absorbed by a cool (river on) earth produces a much larger increase in entropy there.  This allows us to keep the total entropy positive while running our lives with ordered energy.

 

Solar energy: the driver of weather/climate: So, what are the consequences of solar radiation hitting the earth?  To start, both the land and the sea warm as they absorb visible radiation that passes directly through the atmosphere.  The atmosphere absorbs most of the sun’s infrared radiation on its way in.  The warmed earth’s surface passes the energy along in several ways including a reflection of some of the visible radiation, the heating of the ground, the emission of infrared radiation back to the atmosphere, the evaporation of water, and convective heating of the atmosphere.  The net result is the generation of weather through the transfer of solar electromagnetic radiation to the atmosphere and ocean.  This energy drives both ocean and atmospheric circulation. Not surprisingly, the absorption of solar radiation depends on the kinds of molecules in the atmosphere.  Several molecules like H2O (water vapor), CO2 (carbon dioide), CH4 (methane) are excellent absorbers of infrared radiation.  Their concentrations in the atmosphere influence not only local weather, but also, long-term climate both regionally and globally.

 

The lumpiness of electromagnetic energy: In terms of our standard energy unit, the Joule, power is measured in watts and intensity in watts per square meter. From the view of quantum physics electromagnetic radiation comes in lumps or quanta, each with an energy determined by its frequency, f.

 

            E = hf,             E[J] = h[J sec]*f[sec-1]

 

The constant, h is Planck’s constant, h = 6.63 x 10-34 J sec and sets the scale for all of quantum mechanics.  Here, it determines the smallest energy unit allowed in a beam of light with frequency, f.  For all periodic waves the frequency and wavelength are related to the velocity of the wave by f = c/l. Thus,

 

            E = hf = h(c/l).

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Question: A 100-watt light bulb produces 5 watts of visible light (and 95 watts of heat).  How many Joules of energy does it produce per second including all wavelengths of radiation? Roughly, how many photons of visible light does it produce per second?

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            Solar energy: biomass & food: Most importantly, solar radiation is also the primary driver of photosynthesis on earth.  Solar energy converts atmospheric CO2 and H2O into molecular oxygen and a variety of hydrocarbons. Viewed from the perspective of energy, photosynthesis is a form of solar energy collection.  Though not highly efficient, the consequences for the environment are enormous.  In addition to the production of food crops, photosynthesis is responsible for the production of carbon-based fuels, both fossil and biomass.  Photosynthesis also provides a mechanism for carbon sequestration, the removal of CO2 from the atmosphere through the growing of forests or ocean phytoplankton. Even the albedo of the earth can be changed by photosynthesis in the biosphere.   Each of these processes can play an important role in producing a sustainable environment.

 

 

B. Insolation: direct radiant energy from the sun.

 

            Defining intensity:  Using solar energy directly is highly attractive because our total energy need per second is small compared to the total energy arriving at our upper atmosphere per second.  Using solar energy directly also helps to alleviate the problem of the rapid exhaustion of our finite quantities of fossil fuels. To make this discussion more quantitative, we define intensity, the amount of energy arriving each second on a square meter of surface area.  That is,

 

          P          = E/t

  power          = energy/time

P[watts]         = E[J]/t[sec]

 

             I           = P/A                       = E/(t*A)

 intensity          = power/area          = energy/(time*area)

 I[W m-2]           =  P[W]/A[m2]        = E[J]/(t[sec]*A[m2])

 

The intensity of solar radiation at the top of the atmosphere on a square meter of area directly facing the sun is called the insolation or solar constant, I0 and at present has the approximate value of 1367 Wm-2.  Relatively precise satellite measurements of the insolation have been made over the past 20 years [2].  This is a very valuable number to keep in mind even though it is not precisely constant.  With the insolation in hand, the total energy per second or power hitting the earth is just

 

            Power hitting the earth:  P = I0 * Area = I0 * pR2

 

where R is the radius of the earth.  The area we use is the cross sectional area of the earth, not the surface area of the spherical earth, 4pR2.

 

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Question: Why don’t we use the area of the earth when calculating the total solar power hitting the earth?  Hint: If you hang a sheet behind the earth, what is the area of the shadow of the earth on the sheet?

 

Question: Knowing I0, you can also calculate the total electromagnetic power radiated by the sun.  To do this you need to know the distance of the earth from the sun, R earth-sun = 1.5 x 1011 m. Hint: Assume that the radiation from the sun must pass through a sphere whose radius equals R earth-sun.  Ans: 3.9x1026 W.

 

 

 

 



 

 


                                                q

 


Sun                                                      Earth                                                    Shadow















 

 

 


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            Angles: The rays of sunlight hit the ground at an angle, q to the normal as shown in the figure.  The sun in a small area, dA^ is spread over a larger area, dA, on the surface of the earth where

 

                     dA = (dA^)/(cos q)

 

 

 

 


                                                                                    dA^             dA

 

The intensity is reduced by this same factor of cos(q) to  I = I0cos(q).  Integrating over the hemisphere, we find that, indeed, the total energy hitting the hemisphere of the earth on the sun’s side is just the cross sectional area times the insolation.

 

            dP = I*dA = I0cos(q)*2prRdq

            P = ò dP = I0 pR2 = Insolation * Cross sectional area of Earth

            [Picture of hemispherical integration]

 

            Calculating with the solar intensity, I0:  How, then, does insolation or solar intensity help to solve real problems?  Could you calculate the added energy you get from the sun in heating your apartment on a clear winter day, for example?  Assume for the moment that all of the visible radiation hitting your apartment window is transmitted through the glass and than the infrared radiation reradiated from objects inside cannot escape.  We will see below that this is not quite correct.  Being an experimental scientist, you use a pyranometer to measure the visible radiation intensity (also called radiation flux density) in units of Wm-2. Such a pyranometer gives the intensity on a horizontal plane coming from the entire hemisphere above the plane.

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Question: Suppose that your apartment has only one window, a south-facing one with vertical glass and an area of 2.0 m2. Standing outside that window at noon, you hold the pyranometer perpendicular to the window and measure a radiation flux density hitting the window of 600 Wm-2.  (You are not surprised that the intensity is less than I0 of 1367 Wm-2 at the top of the atmosphere.  The atmosphere absorbs some of the energy on its way down to the ground.  Also, the pyranometer is not facing the sun directly.)  What fraction of the 1.5 x 107 Joules/day needed to hear a typical apartment in winter could you provide from 4 hours of sunlight with an average intensity of 600 Wm-2?

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Is I0 really constant? Any long-term changes in the insolation at the top of the atmosphere, 1367 Wm-2, would have environmental consequences.  For example, an increasing I0 would add to the observed global temperature rise from greenhouse gases, aggravating the negative consequences of climate change.  Not surprisingly, I0 varies on a number of time scales.  Eight minutes after a change in sun’s power output, we will know about it on earth.  Recent precise satellite measurements taken above the atmosphere show that I0 at the top of the atmosphere varies. [Willson, 1997]  To start, the sun has an internal energy output cycle with a period of roughly 11 years.  The period of the cycle itself rises and falls with time from 9 to 13 years. In the last 11 years I0 has varied by some 0.15% from a low of 1367 to a high of 1369 Wm-2.  Interestingly, the greater the solar activity and energy output, the greater the number of sunspots. The figure from Willson combines information from three different satellite data collections. A careful measure of the minima indicates that there is…{continue here}

 

 

 

In addition to the internal variability of the sun’s energy output, the ellipticity of the earth’s orbit around the sun causes a variation in intensity at the Earth even when the sun’s power output is constant.  A bit counter intuitively, we are closest to the sun in January and farthest away in July.

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Question: The ellipticity of the orbit of the earth is defined as the ratio of the major axis to the minor axis of the ellipse minus one.  At present, the major axis is 0.6% longer than the minor axis, so the ellipticity is 0.006.  Calculate the ratio of I0 in the winter to I0 in the summer.  Hint: remember that the intensity must decrease as 1/r2.

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1500-year cycles: I0 is also found to vary on a time scale of approximate 1500 years [ref: recent Science mag].  Evidence for this variation is taken from temperature proxies such as tree-ring thickness and density (dendrochronology) [Ref: Briffa] and ice core data [Ref Mann, et al.]  Significant variability on this scale is consistent with evidence for the particularly warm “European warm period” from 900-1250 and cold “mini-ice age” from 1650-1850.

 

Milankovitch cycles: On a time scales in the range 104 – 105 years a number of patterns have emerged in the temperature proxy records.  During most of the Pleistocene period (2.5 - 0.01 Mybp) the temperature record has varied from cold glacial periods some 5-10 0C colder than present to relatively warm interglacial periods.  During the Holocene period, approximately the last 10,000 years, the earth has been in a warm interglacial period.  A Fourier analysis of the Pleistocene temperature record identifies three strong periodicities of approximately 21,000, 40,000, and 105,000 years.  For the last 800,000 years, the 105,000-year periodicity has dominated the record, producing long cold periods (ice ages) of some 100,000 years followed by shorter warm periods (interglacial periods) typically 10,000 years long.

 

            The Russian climatologist, Miltun Milankovitch, hypothesized a correspondence between long-term temperature periodicities and three periodicities in the earth-sun system.

 

1.) Precession: The earth’s rotational axis has an angle of inclination of 23.50 with respect to the normal to the plane of its revolution about the sun. It precesses about this normal with a period of 21,000 years.  At present the Northern Hemisphere is tilted toward the sun (summer) in June when we are farthest from the sun.

 

2.) Inclination: The earth’s angle of inclination, presently 23.5 degrees, changes from a minimum of 21.5 degrees to a maximum of 24.5 degrees with a period of 40,000 years. 

 

3.) Ellipticity: The ellipticity of the earth’s orbit about the sun changes from a minimum of 0.0001 to a maximum of 0.006 with a period of 105,000 years. We are presently near a minimum in ellipticity.

 

[Fig: Precession of the earth’s axis] – 21,000 yrs.

[Fig: Angle of inclination of earth’s axis] – 40,000 yrs.

[Fig: Orbital ellipticity] – 105,000 yrs.

 

Though none of these oscillations change the average insolation the earth receives from the sun, Milankovitch argued that, in combination, they do influence the conditions necessary for the establishment of an ice age and hence the global temperature.  He pointed out that there is an asymmetry in the formation and melting of ice. While local heating will melt ice, local cooling will not necessarily freeze water.  Water is mobile, and is in communication with warm water elsewhere.   In a variable climate more ice melts during the warm periods than freezes during the cold periods.  An ice age is more likely to be initiated during a period of relative temperature stability than during a period of variability.  Thus, favorable periods for entering an ice age are ones with minimum ellipticity with minimum variation in insolation. Similarly, a minimum axis of inclination makes seasons less severe.  Also, our present precession situation, where our distance from the sun is greatest in summer, leads to a smaller summer-winter difference, one that favors the formation of ice.  We will return to this discussion in the chapter on climate change.

 

C. The electromagnetic spectrum from hot bodies

 

Insolation from the sun warms the earth’s surface and as it warms, it radiates infrared radiation.  Most of that infrared radiation is absorbed by layers of atmosphere, reradiated both up and down, and effectively trapped by this greenhouse effect. All objects radiate electromagnetic radiation and the spectrum of this radiation depends primarily on the temperature of the object doing the radiating.  At this point we need to understand the radiation given off by hot objects called “black body radiation.”

 

In classical physics the acceleration of a charged particle results in the emission of electromagnetic radiation (light).  In the introduction to this chapter we introduced the notion of a photon, the smallest allowed bundle of electromagnetic energy allowed in quantum mechanics.  Electromagnetic radiation is described as the flow of photons, bundles with energy, hf.  Following the logic of classical physics, one might expect that hot objects would emit more energy (more acceleration). They could do so either by emitting more photons of low energy or by emitting higher energy photons (with higher frequency).  Looking at the spectrum of  radiation emitted by the sun, a hot object with temperature of 5800 K, we find that hotter objects do both.  They emit more photons and ones of higher frequency.  Fig ** shows the radiant spectral flux density of emitted by the sun as a function of the wavelength of the radiation emitted.

 

Fig ** [Solar spectrum at the top of the atmosphere with second line showing the spectrum, S(l) at surface, also show spectrum of an object at 2900 K, smaller by x16, and shifted.]

 

In the same figure the smaller smooth curve to the right shows the greatly reduced radiant spectral flux density emitted by an object with only ½ the temperature.  The equation that describes these shapes was derived by Max Planck.

 

S(l,T) = (2phc2)/(l5[exp(hc/klT) – 1]

 

Where k is the Boltzmann constant (1.38 x 10-23 J/K), h is Planck’s constant, c is the speed of light (3.0 x 108 m/s), and T is the temperature measured in degrees Kelvin.

 

[At this point, we need a paragraph from Eisberg describing the quantum mechanics of a black body]

 

 

 

 

 

References:

 

Willson, R. C., Total Solar Irradiance Trend During Solar Cycles 21 and 22, Science 277, 1963-1965 (1997).

 

Bennett, J., M. Donahue, N. Schneider, M. Voit, p. 525, The Cosmic Perspective, Addison-Wesley Longman, Inc., ISBN 0-201-87878-X, (1999).