ENERGY AND THE ELECTROMAGNETIC SPECTRUM

 

Environmental Geoscience (GEOL 1133), David Stahle

 

OUTLINE:

Temperature

Temperature scales (Fahrenheit, Celsius, Kelvin)

Energy

Radiant energy

Electromagnetic spectrum of radiant energy ("The Mighty Kingdom")

Electromagnetic wave length and wave frequency

Longwave vs. shortwave electromagnetic radiation (EMR)

Scientific notation and orders of magnitude

Doppler effect

Two basic laws of Radiant Energy:

            Stefan-Boltzman Law

            Wein's Displacement Law

Global energy balance

            albedo vs. greenhouse effect

Inverse Square Law of radiation intensity

Zone of possible life around our sun

Planetary distances from the sun, and the effect of atmosphere on

            planetary temperature

 

Aguado, E. and J. Burt, 2001.  Understanding Weather and Climate. 

Prentice Hall, Upper Saddle River, NJ.

Gedzelman, S.D., 1980.  The Science and Wonders of the Atmosphere. 

Wiley, NY.

Huschke, R.E., 1989.  Glossary of Meteorology. American Meteorological

Society, Boston.

Thompson, G.R., and J. Turk, 2007.  Earth Science and the Environment,

4TH edition.  Thomson, Brooks/Cole, Belmont, CA.

 

            Temperature is actually a measure of the random atomic motion in a substance.  It measures the kinetic energy of motion, the more motion, the greater the temperature.  There are three scales for measuring temperature:  Fahrenheit, Celsius, and Kelvin.  Kelvin is the temperature scale of science and zero Kelvin is the condition of no molecular motion, so-called "absolute zero", which has never been observed in nature, and in fact theoretically cannot occur [but Dr. Carl Weiman of the University of Colorado has gotten close using lasers to dampen atomic motion down to a few billionths of a degree above absolute zero! (part of their proof of Bose-Einstein condensation and the formation of blob-like ‘super-atoms’)]. 

 

 

°Fahrenheit

°Celsius

Kelvin

Boiling

212

100

373

Freezing

32

0

273

Absolute Zero

-459

-273

0

 

The Fahrenheit scale was developed over 200 years ago, and its logic is lost to modern society (0°F is the temperature achieved by mixing salt and snow, and was the lowest temperature Fahrenheit could achieve in his lab years ago).  The celsius scale was also developed about 200 years ago, but more logically scales 0 to 100°C from the freezing to the boiling points of water (‘centigrade,’ sometimes used interchangeable with celsius actually means consisting of, or divided into 100 degrees).  To convert between Fahrenheit and Celsius:

 

            °F = 1.8C + 32                                  °C = (F - 32)/1.8

 

            The theoretical upper limit of temperature is 1023Kelvin (the temperature of the Big Bang); the sun’s core is about 15 x 106 Kelvin (the solar photosphere or outer layer is about 6000°C); and the lowest theoretical limit to temperature is 0.00 Kelvin (abbreviated simply as K), or absolute zero. 

            ENERGY.  Heat is a form of energy, so what exactly is energy?  That is the $64 question of modern scientific inquiry.  Richard Feynman has explained that we really don't know what energy is.  We know what it does and how, but we do not know exactly what it is.  It was Einstein's insight, since proven dramatically and inarguably by thermonuclear explosions that:

                                                E = MC2

Energy (E) and matter (M) are related (C is the constant for the speed of light).  Matter is anything that occupies space and has mass (that is, atoms of liquid, solid, or gas).  Energy is the ability to do work, but it does not have mass and it does not occupy space.  But energy can affect matter.  A system has energy if it is capable of exerting a force over distance (is capable of doing work).  Examples of energy would include light (or radiant energy), motion (kinetic energy), potential (gravitational), and chemical energy. 

            Our principal interest here will be with radiant energy.  It is radiant energy from the sun that powers the climate system and ecosystems of planet Earth.  Nuclear reactions, like the reaction occurring in our sun, involve mass-energy conversion, and release the enormous energy stored in the atomic bonds of matter.  At high pressure and temperature, our sun fuses hydrogen to helium, releasing the energy in the atomic bond of hydrogen, and transferring that energy through space as radiant energy in the form of electromagnetic radiation (EMR).  Indeed, radiant energy is transferred by electromagnetic waves, which are oscillating electric and magnetic fields along with streams of charged particles moving at the speed of light (its believed that particles dominate at the higher frequencies or shorter wave lengths of EMR).  So light is both a wave of energy, and light is also a particle of energy (i.e., photons).

Energy is conserved, but can be transferred, and this is particularly true of heat energy, which is transferred by radiation, conduction, and convection (more on conduction and convection later).  Virtually all energy on Earth comes from the sun.  Radiant solar energy is converted to chemical energy by photosynthesis and is stored in plants (and subsequently in coal, oil, limestone).  Plants use solar energy to make carbohydrate, a form of chemical energy, which is then used to power the lives and work of animals.  So our energy to perform comes ultimately from the sun.  The energy we use becomes waste heat, and is finally returned to the environment as longwave (infrared) radiation (and matter and energy in the universe are being degraded toward a state of “inert uniformity” or entropy).

            All matter with any temperature whatever, that is >0.00 Kelvin emits radiant energy (or ElectroMagnetic Radiation, EMR).  But the type of EMR released is vastly different depending on the temperature of the object.  These vastly different types of electromagnetic radiation are described by the ELECTROMAGNETIC SPECTRUM, which defines the type of EMR according to the wavelength of the electromagnetic waves emitted (or inversely by the wave frequency, since they always travel through the vacuum of space at the same speed, that is light speed), from extremely longwave (or low frequency) radio waves to extremely shortwave (or high frequency) gamma rays.  James Clerk Maxwell first discovered electromagnetic waves, both within and beyond ordinary light.  Maxwells' equations unify electricity and magnetism, and summarize our knowledge of both (1.  unlike charges attract, like charges repel.  2.  there are no isolated magnetic poles.  3.  electrical current gives rise to magnetic poles.  4.  changing magnetic fields can cause electrical currents).

Heinrich Hertz was an important early radiation physicist, and he described the spectrum of electromagnetic radiation as "The Mighty Kingdom."  It is "Mighty" because of the incredible power provided across the spectrum, and mankind has learned to harness some of this Kingdom of energy to power civilization.

            Here are a few interesting notes about the Mighty Kingdom:

1.         Everything >0.00Kelvin emits EMR

2.         You distinguish types of EMR by wavelength (or frequency)

3.         Three broad categories of EMR are shortwave, visible, and longwave

4.         Shortwave is also referred to as ultraviolet or solar radiation; longwave is also referred to as infrared, radio, terrestrial, and even "microwave" which is an unfortunate synonym because it refers to longwave radiation.

5.         Note the vast difference in wavelengths on the electromagnetic spectrum, from 10-10 to 105 meters (or from one ten billionth of a meter to 100,000 meters from short gamma rays to long radio waves).  [This is an appropriate place to remember scientific notation, which uses exponents to represent large or small numbers.  101, 102, 103, 10n or 10-1, 10-2, 10-3, 10-n all represents powers of 10 or so-called orders of magnitude (or 10, 100, 1000, n, one tenth, one hundredth, one thousandth, -n, respectively)].

6.         Shortwave elctromagnetic radiation is dangerous.  Gamma radiation is deadly.  The heroes of Chernobyl were the firemen and helicopter pilots who took full body doses of gamma radiation when fighting to extinguish the fire and entomb the burning nuclear core of the reactor.  They died horrible lingering deaths.  Too much ultraviolet radiation (not as short as gamma) isn't good either, can lead to sun burn or even skin cancer.

7.         Visible electromagnetic radiation is actually a narrow slice out of the Mighty Kingdom between about 0.4 and 0.7 microns (a micron is one millionth of a meter).  In this portion of the spectrum are the living colors of the rainbow, and it is here that human beings have evolved the optical anatomy to see in our environment.  Why just here and not at higher or lower wavelengths on the electromagnetic spectrum?  Because our sun emits most of its energy in the visible range, so the visible range dominates the natural environment of Earth in which we have evolved.  However, not all animals on Earth restrict their vision to the visible range.  Kestrels are a small falcon of the Arctic tundra.  They hunt mice and lemmings, but their prey is sparsely distributed across the tundra (and elsewhere).  Kestrels have developed the ability to see shorter wavelengths of EMR in the ultraviolet range (just below the visible range).  Why?  because lemming and mouse urine floreses in the ultraviolet range of EMR.  So kestrels can easily locate active colonies of prey over the vast Arctic even when the prey animals are underground.

            Sir Issac Newton first discovered that white light is a mixture of the colors of the rainbow.  He used two prisms to demonstrate this fact.  The first prism bent each wavelength within white light at an angle and thus refracted the colors.  He then cast the refracted colors onto a second prism and reassembled the colors into white light coming out of the second prism.

            The colors of visible light (i.e., the component wavelengths) that are not absorbed by an object are of course reflected outward, and that is what we see, that then is the color of the object.....the wavelengths of visible light reflected.  In plants chlorophyll absorbs the red and blue portion of the visible spectrum and converts that into food (i.e., carbohydrate, thru photosynthesis).  They do not absorb at the green portion of the visible spectrum, so we see green.

            The human eye detects only visible EMR, but the body can sense infrared radiation (hold your hand over a warm oven to feel infrared radiation carrying energy away from the oven).  This infrared is just longer in wavelength and less energetic than the visible range of EMR, so cannot be seen, only sensed thermally.  We can also sense ultraviolet radiation (a wavelength just shorter than the visible range of EMR), because that is what causes sunburn.  We cannot "see" either infrared or ultraviolet EMR, but we can "feel" both.

8.         Longwave electromagnetic radiation is also referred to as the radio wave frequency, because we have technologically harnessed this sector of the spectrum for telecommunication.  We have done this by building machines that can generate electricity and transmit radio waves through the atmosphere and outer space.  Your radio actually receives and translates electromagnetic waves into sound waves.  For example:  KUAF transmits radiowaves (i.e., longwaves) at 91.3 megahertz (FM), this means that the carrier radio wave which travels at light speed from transmitter to receiver is vibrating 91.3 million times per second (that is the frequency of the electromagnetic wave, it could be expressed as wavelength also).  The music you hear is transmitted as the signal on the carrier frequency, it is a modulation of the carrier frequency (which is called "frequency modulation" or FM).  Our radio receiver then translates the carrier frequency down to the much lower soundwave frequencies.  This lower frequency then operates the membrane of the speakers which broadcast sound into the room or car at soundwave frequency, which is only about 500 hertz!  We then can sense this 500 hertz frequency with our eardrums.  (How do we generate electricity?  Through "induction."  If you wrap a shaft in electrical wire and force it to spin within a magnetic field, an electrical current will be produced.  So we use fossil fuels, for example, to make steam and force the shaft to spin, and then through induction generate electricity).

9.         Remember, most solar radiation that reaches the surface of the Earth is in the visible range of EMR.  But most Earth radiation is in the infrared range, which is longer wavelength.

10.      Doppler effect.  Light waves, which are simply electromagnetic waves in the visible wavelength range, travel at light speed, but they can be stretched or shortened (compressed) if the light emitting object is moving away from, or toward, the observer.  They same is true for sound waves (and was elegantly proven over 100 years ago by placing a band on a moving train and listening for the changing pitch of high C as the train and band approached and then moved away from the listener).  The Doppler effect and light wave stretching have proven very useful in diagnosing the relative motion of stars and galaxies.

            Two physical laws of nature describe the physics behind EMR, The Stefan-Boltzman Law and Wein's Displacement Law.  They are component to Planck's Law, which is the fundamental law of radiation.  We can use Stefan-Boltzman and Wein's Law to determine how hot the sun is, and how much radiation is emitted by the sun (or by any star or planet).

            Stefan-Boltzman Law:                                R = sT4

where R = the amount of radiation emitted by an object (measured in Langleys), s = a constant of proportionality, the so-called Stefan-Boltzman constant (5.735 x 10-5 Langleys/minute/degree4), and T = absolute temperature (Kelvin).  This laws states that the amount of radiation emitted by an object is proportional to the 4th power of its temperature (for a theoretical black body radiator, which is a perfect absorber and emitter of temperature.  Of course, this is an oversimplification for most objects in nature, but the sun comes very close to being a true black body radiator.)  Simply stated, radiation amount and temperature are related.  Hot objects emit lots of radiation, cooler objects emit much less radiation.

            Wein's Displacement Law:                       lmax = 2897/T x 10-6 meters

which states that the wavelength of maximum radiation emission (lmax) from an object is an inverse function of its temperature (T).  Wein's law is describing the type of radiation emitted as a function of the temperature of an object.  The hotter the object the shorter the wavelength of maximum emission.  Think of an iron bar placed in a blacksmith’s furnace.  As the bar is heated, it first glows red, then white, then blue.  Red light is at the longwave end of the visible spectrum and blue light is at the short end of the visible (white light integrates all visible wavelengths).  So as the bar got hotter, the wavelength of maximum emission went from red to blue, or from relatively long to short wave.  These two basic laws of radiation have never been disproved, in spite of many efforts to do so.

            Applications of Stefan-Boltzman and Wein's Law?  We can use them to determine the temperature and total radiation output of the sun, a star, a galaxy, or a planet.  So, how hot is the sun?  First take a radiometer to measure the wavelength of maximum radiation emitted from the sun to Earth (lmax).  Then solve Wein's law for temperature (T = 2897/lmax).  Then put T into the Stefan-Boltzman equation to calculate total radiation amount from the sun.  Bottom line, the sun emits lots of radiation concentrated in the short wave lengths, and the sun is HOT.  The Earth is much cooler and emits much less radiation concentrated in the long waves or ‘infrared range’ of the spectrum.  Remember, all objects at temperature above absolute zero (which is everything) emit radiation.  Hot objects emit huge amounts of shortwave radiation, cold objects emit smaller amounts of longwave radiation.

            We will compare the "clean signal" of solar radiation that hits the top of Earth's atmosphere, and the solar radiation that actually makes it down to the surface of Earth.  Most of the radiation shorter than the visible range is absorbed in, or reflected off of the atmosphere (UV = ultraviolet radiation, and it is mostly absorbed by ozone in the stratosphere).  Some visible and some longer wavelength solar radiation also fails to make it to the ground.  This is due to the albedo or reflectivity of the atmosphere and to atmospheric adsorption. 

            The Earth “thermal” radiation emission spectra is in the infrared range of EMR, mostly around wavelengths of 10 microns.  But the atmosphere is quite effective at absorbing radiation in the infrared range, especially water vapor and carbon dioxide.  And this, of course, is part of the greenhouse effect.  Without an atmosphere, the Earth would be much hotter in the day (because of the greater solar radiation load that would occur), and much colder at night (because she would lose more radiation in the absence of a greenhouse effect).  Under these 'no atmosphere' conditions, life as we know it could not exist on Earth.  There would be too much ultraviolet radiation and the diurnal temperature swings would be much too large (too hot and too cold).  Our atmosphere is a wonderful thing, it permits and protects life on Earth.

THE GLOBAL ENERGY BALANCE OF EARTH 
 This concept concerns how solar radiation is received, used, and returned to space by the Earth's atmospheric system, which is the strongly coupled air-sea-land system.  The term ‘coupled’ refers to the very strong dynamic links or interactions between the air, sea, and land.  The global energy budget is a balance between the incoming solar radiation (shortwave, SW) and the outgoing terrestrial radiation (longwave, LW).  It must be balanced or the Earth would progressively cool or warm, with potentially catastrophic consequences for life.  Consider for example the runaway greenhouse effect on Venus or the icebox on Mars.  Venus has an atmosphere of about 96.5% carbon dioxide, a runaway greenhouse effect, and surface temperatures of about 900 degrees F.  The Martian atmosphere is only about 1/150th the density of Earth’s atmosphere, but it is 95% CO2.  Mars is very cold, and is subject to 180°F day-night temperature swings.  But it would be much colder without the CO2 rich atmosphere of Mars. 

How is the global energy balance achieved?  If we represent all incoming solar radiation as 100%, we can follow these 100 units of incoming energy through the Earth atmospheric system to see what happens.  First, 31% of the incoming radiation is immediately reflected off the atmosphere and surface of Earth back to space without heating the Earth or its atmosphere at all.  This of course is the albedo effect, the reflectivity of Earth.  Dust particles, clouds, and other debris in the sky do tend to reflect some sunlight and thus contribute to the planetary albedo.  Bright surfaces on the planet itself are also reflective and contribute to albedo (notably new fallen snow on flat ground).  Notice that albedo is strongly affected by the color and texture of the surface, and by the angle of incoming sunlight (so albedo is always higher near the poles, or early in the morning or late in the evening).  Note also that there is some controversy regarding the exact albedo of Earth (I say its 31%), but there is no doubt that if albedo were to rise, the Earth would cool.  If albedo were to decrease, Earth would warm. 

Consider this albedo feedback example to see how a relatively subtle component of the coupled air-sea-land system might change, only to have the albedo effect magnify the climatic impact of that small change:  Pretend we witnessed a giant volcanic eruption which filled the polar atmosphere with dust, that would reduce solar radiation a bit by raising the albedo.  That would cool things down a bit.  Cooler temperatures would mean that the snow cover in high latitudes would not melt so early in the spring thaw.  That persistent snow cover would also raise the albedo a bit, which would enhance the cooling trend, which would mean the snow might last even longer, etc. etc.  Hopefully you get the idea that the Earth's climate system is a complicated set of interrelationships, and if you change any one part you might trigger a cascade of subsequent changes in the other parts and finally end up in a different climate. 
 

Only 24% of the incoming solar radiation is absorbed by the atmosphere to directly warm the air!  Some 3% of that absorption takes place in the stratosphere, and it is ozone, the three-atom molecule of oxygen that is doing much of this 3% absorption.  The other 21% of this direct atmospheric heating occurs mostly high above Earth's surface, and all 24% is lost back to outer space as longwave radiation from the upper atmosphere. 
 So that leaves 45% of the incoming solar radiation to actually make it down to the land or sea to warm the surface of Earth (100 - 31 – 24 = 45), and provide the heat source for the atmosphere, the heat source which in fact drives the general atmospheric circulation on this planet.  As we have said, most of the driving power behind atmospheric circulation (i.e., the wind systems of Earth) comes from the direct heating of land and water on the surface by solar radiation.  Heat stored in the ground or ocean is transferred into the air by longwave radiation, conduction, convection, and latent heat transfer. 

Longwave radiation emission from the surface to the sky is the biggest exchange, a radiation quantity equivalent to something like 110% of the solar radiation that entered the atmosphere in the first place is radiated from the surface of the planet to the sky (note that the sun can illuminate only one half of the Earth, but the Earth can radiate in 360°, day and night).  But most of that 110% is absorbed by the atmosphere, and this is one very important way that the sky acquires heat and itself begins to radiate longwave radiation in all directions, up, sideways and down.  The net result of this longwave radiation absorption is that our sky re-radiates the equivalent to 96% of the original incoming solar radiation back to the surface of Earth!  This reradiation is called "counter-radiation."  Its a recycling effect if you will, 110% radiates up, 14% of that is lost to space, but 96% is returned to Earth to further heat the planet.  So longwave radiation exchange is a big, big thing when you are talking about the global energy balance of Earth.  And the recycling of that longwave radiation is essentially the greenhouse effect.  It is the water vapor, clouds, carbon dioxide and other greenhouse gases in the sky that are crucial to the greenhouse effect because they absorb the longwave radiation to warm the atmosphere and more effectively warm the planet surface.  Alter those constituents in the atmosphere and you run the risk of altering the energy balance of Earth.  This is the fundamental reason why scientists are concerned by the rise in atmospheric carbon dioxide due to human activities (i.e, "anthropogenic" carbon dioxide).

So back to the global energy balance, we have 100% coming in, -31% due to albedo, -24% due to direct solar heating of the upper atmosphere, most of which is lost back to space, -14% due to longwave emission from the heated atmosphere itself, and now another -8% lost due to direct longwave radiation through the atmosphere into outer space (no absorption by the air).  Then we also lose another 19% of the incoming solar through latent heat transfer into the sky and then on to space.  And finally another 4% is lost due to sensible heat transfer (convection) from the surface to the sky and then to space.  So this should balance: 
  +100 -31 -24 -14 -8 -19 -4 = 0.

            The Inverse Square Law for gravity states that the gravitational attraction of an object in space declines as the inverse square of distance from that object (first articulated in Newton's universal law of gravitation).  This law also applies to solar radiation intensity, because sun beams spread out in a radial direction from the sun and diminish in intensity as the inverse square of distance.  We can use this law to determine the Zone of Possible Life around the sun.  Knowing the temperature and total radiation output of the sun, and the freezing and boiling points of water (0 and 100°C, two states which are crucial to "life as we know it" = which means carbon-based chemistry and liquid water), we can use the inverse square law and Stefan-Boltzman to calculate where these temperature conditions might exist on a planet in orbit around our sun.  It turns out that Venus, Earth, and Mars are all in the zone of possible life, but only Earth has life so far as we know.  Why?  Venus is hellishly hot due to a thick atmosphere and a runaway greenhouse effect.  Mars has a very thin and wispy atmosphere, mostly made of CO2, but it is a wispy atmosphere and it does not have a strong enough greenhouse effect to really do the job, so the place is frozen.  In other words, the nature of the atmosphere makes all the difference in the world for the actual presence of life within the Zone of Possible Life. (Some speculate that Mars might have harbored life in the remote past?).

            Earth is perfection.  Its at the proper solar distance, and has just enough atmosphere and greenhouse effect to shield us from harmful UV radiation and to hold heat with the greenhouse effect to allow liquid water on the surface and the existence of life.  But can we "terraform" Mars?  That is, could we go to Mars and "pollute" the Martian atmosphere with greenhouse gases to raise the temperature enough to consider human colonization?  We'd have to add or ‘pollute’ the Martian atmosphere with oxygen also, but is this possible or just science fiction?