Lecture Notes on The Changing Earth Module | PHYS 2028, Study notes of Physics

Download Lecture Notes on The Changing Earth Module | PHYS 2028 and more Study notes Physics in PDF only on Docsity! Physics 2028: Great Ideas in Science II: The Changing Earth Module Notes Dr. Donald G. Luttermoser East Tennessee State University Edition 2.0 Abstract These class notes are designed for use of the instructor and students of the course Physics 2028: Great Ideas in Science II. This edition was last modified for the Spring 2009 semester. v) The troposphere is the lowest layer of the atmo- sphere; it begins at the surface and extends to be- tween 7 km (23,000 ft) at the poles and 17 km (56,000 ft) at the equator, with some variation due to weather factors. vi) The troposphere has a great deal of vertical mix- ing due to solar heating. This heating makes air masses less dense so they rise. When an air mass rises, the pressure upon it decreases so it expands, doing work against the opposing pressure of the surrounding air. vii) As the temperature decreases with height, wa- ter vapor in the air mass may condense or solid- ify, releasing latent heat that further uplifts the air mass. This process determines the maximum rate of decline of temperature with height, called the adiabatic lapse rate. viii) The troposphere contains roughly 80% of the total mass of the atmosphere. Fifty percent of the total mass of the atmosphere is located in the lower 5.6 km (18,000 ft) of the troposphere. b) Stratosphere: Temperature increases with height due to ozone (O3) absorption of solar UV light. i) The boundary between the stratosphere and tro- posphere is called the tropopause. ii) The origin of this word is from the Latin word “stratus” meaning spreading out. III–3 iii) The stratosphere extends from the troposphere’s 7–17 km (4.3–11 mi; 23,000–56,000 ft) range to about 51 km (32 mi; 170,000 ft). iv) The stratosphere contains the ozone layer, the part of the Earth’s atmosphere which contains rel- atively high concentrations of ozone. “Relatively high” means a few parts per million =⇒ much higher than the concentrations in the lower atmosphere but still small compared to the main components of the atmosphere. v) The ozone layer is mainly located in the lower portion of the stratosphere from approximately 15– 35 km (9.3–22 mi; 49,000–110,000 ft) above Earth’s surface, though the thickness varies seasonally and geographically. c) Mesosphere: Temperature decreases again due to a sharp decrease in air density and heat capacity. i) The boundary between the mesosphere and the stratosphere is called the stratopause. It lies typi- cally 50–55 km (31–34 mi; 160,000–180,000 ft) above the ground. The pressure here is 1/1000th sea level. ii) The origin of this word is from a Greek word meaning middle. iii) The mesosphere extends from about 50 km (31 mi; 160,000 ft) to the range of 80–85 km (50–53 mi; 260,000–280,000 ft). III–4 iv) Temperature decreases with height, reaching –100◦C (–148.0◦F; 173.1 K) in the upper meso- sphere. v) This layer is also where most meteors burn up when entering the atmosphere. d) Thermosphere: Sharp increase in temperature due to X-rays from the Sun being absorbed by nitrogen and oxy- gen. i) The temperature minimum at the boundary be- tween the thermosphere and the mesosphere is called the mesopause. It is the coldest place on Earth, with a temperature of –100◦C (–148.0◦F; 173.1 K). ii) X-rays cause these 2 atoms/molecules to ionize. iii) From 80–85 km (50–53 mi; 260,000–280,000 ft) to over 640 km (400 mi; 2,100,000 ft), temperature increasing with height. Although temperatures are high (T > 1000◦C), air density is very low so total heat content is low. iv) The International Space Station orbits in this layer, between 320 and 380 km (200 and 240 mi). v) Higher levels called the ionosphere =⇒ atoms completely ionized. The aurorae are located in the ionosphere. The ionosphere marks the inner edge of the magnetosphere where charged parti- cles trapped from the solar wind are located. III–5 • If it moves in the x, y, and z directions, it has 3 degrees of freedom. • So, we can write three separate energy equations: Ex = 1 2 mv2x = 1 2 kBT Ey = 1 2 mv2y = 1 2 kBT Ez = 1 2 mv2z = 1 2 kBT and the average kinetic energy is then the sum of the energies in these three different directions: E = Ex + Ey + Ez = 1 2 m ( v2x + v 2 y + v 2 z ) = 1 2 m ( v2 ) = 1 2 kBT + 1 2 kBT + 1 2 kBT = 3 2 kBT , or v2 = 3kBT m . (III-7) f) The square root of v2 is called the root-mean-square (rms) velocity: vrms ≡ √ v2 = √√√√3kBT m (III-8) =⇒ when we talk about velocity of gas particles, we will always mean vrms. In this equation, kB is Boltzmann’s constant, T is temperature measured in Kelvin, and m is the mass of a given gas particle. As can be seen by this equation, the lower the mass of a gas particle the higher the thermal velocity of the particle. g) The temperature of a planetary depends upon a variety of factors, including the amount of greenhouse gases (see III–8 below) contained in the atmosphere. However the most important factor is the distance that a planet is from its star, in our case, the Sun. h) As such, if vrms > vesc, a planet will gradually lose such a gas over time. This is why the abundance of He and H2 is so low in the Earth’s atmosphere and why the Moon has no atmosphere. 4. Ozone depletion. a) Ozone (O3) in the stratosphere absorbs solar UV light. b) UV light has higher energy than visible light =⇒ enough energy to break apart complex molecule chains. i) UV light can alter the structure of the DNA molecule =⇒ gives rise to mutations. ii) Most mutations are bad (i.e., harmful) to living organisms =⇒ cancer results. c) Ozone reacts with hydrofluorocarbons (a common refrig- erant): i) CH3CHF2 + O3 → CO2 + H2O + CH2F2 (ethylidene fluoride) + (ozone) → (carbon dioxide) + (water) + (a hydrofluorocarbon radical). ii) The ozone disappears! The resulting molecules have no absorption lines in the UV → the solar UV radiation is able to reach the ground. III–9 5. The Greenhouse Effect. a) How a greenhouse works. i) Visible light from the Sun is able to pass through the glass of a greenhouse and heats the inside of the greenhouse. ii) The insides warms to a temperature which emits IR light =⇒ radiates like a blackbody. iii) The glass is opaque to IR light =⇒ the IR pho- tons cannot escape into the outside environment — the greenhouse heats up! b) CO2 and H2O gas in the Earth’s atmosphere works the same way as the glass in a greenhouse. i) Solar visible light passes through the atmosphere unimpeded. ii) Heats the ground so that it radiates IR light. iii) IR light then radiates outward back into space, however, the CO2 and H2O absorb this light which heats the atmosphere. c) If it wasn’t for CO2 and H2O, the Earth’s atmosphere (and surface) would be too cold for liquid water to exist early in the history of the planet =⇒ life would not have formed or evolved. d) The burning of fossil fuels releases tremendous amounts of gaseous CO2 into the atmosphere. i) CO2 abundance has increased by over 20% over the past 100 years due to the industrial revolution. III–10 f) Opacities : Bound-bound, bound-free, and free-free tran- sitions for atoms and molecules are needed; electron scat- tering is needed for ionospheres; Rayleigh (molecule) and Mie (dust) scattering are needed. g) Precipitation and the water cycle are needed for those planets where liquid water can exist (i.e., those planets in a habital (life) zone around a star). h) Finally, static vs. dynamic atmospheres: the difference be- tween these two is whether winds exist in an atmosphere. Initial models usually assume a static atmosphere where the hydrostatic equilibrium is used to determine how pressure changes with height. 3. The physics and chemistry of a planetary atmosphere is driven by the radiation falling upon the atmosphere. As such, stellar evolution must be taken into account when modeling planetary atmospheric structure and evolution. a) Ninety percent of the thermonuclear life of a star is spent on the main sequence. The main sequence lifetime is de- termined via tMS = 1.1 × 1011 f XH M?/M L?/L years , (III-11) where f is the fraction of the star’s mass involved in nu- clear fusion, XH is the abundance of hydrogen, M? is the mass of the star, and M and L are the Sun’s mass and luminosity, respectively. b) While on the main sequence, the temperature and lumi- nosity of a star will slowly increase over time changing less than 10% during the main sequence lifetime. III–13 c) The ultraviolet and X-ray flux of solar-like stars primarily arises from chromospheric and coronal regions of a stellar atmosphere. These 2 regions are hotter than the underly- ing photosphere where the bulk of the energy flux is emit- ted. This heating primarily arises from magnetic fields on the surface of a star which diminish over time due to the slowing of the rotation of stars due to magnetic breaking with the magnetic field of the interstellar medium. As such, the UV and X-ray flux diminishes over the course of a star’s main sequence lifetime. d) Once the evolutionary time exceeds the main sequence lifetime, it follows evolutionary tracks on the HR Dia- gram where the star expands and its surface cools =⇒ it becomes a red giant. The large increase in size causes a large increase in luminosity. 4. The basic modeling technique. a) The pressure scale height is determined from the hydro- static equilibrium (HSE) equation: dP dz = −g ρ (III-12) for a plane-parallel atmosphere or dP dr = −G M ρ r2 (III-13) for a spherically-symmetric atmosphere, where P is the total pressure, z is the height in the atmosphere, g is the surface gravity, ρ is the gas density, and r is the distance from the planet’s center, and M is the mass of material in a shell of thickness dr. III–14 b) In addition to this equation, we also need an equation of state for the gas. As mentioned we use the ideal gas law: PV = nRT (III-14) or P = NkBT , (III-15) where V is the volume of gas, n is the number of gas particles in moles, R is the universal gas constant, T is temperature, N is the particle density, and kB is Boltz- mann’s constant. c) The assumption of HSE along with the ideal gas law is used to calculate P , T , and ρ as a function of height (or radius). From this, the thickness τ of the atmosphere is calculated under the condition that z = τ when P = 0.001 P◦, where P◦ is the surface atmospheric pressure. d) With this structure in place the chemical composition is determined by initially assuming chemical equilibrium us- ing the partition functions of atomic and molecular species of importance. The condensation and freezing points of the gases are included, which also will affect the atmo- spheric gas composition. We will not describe non-equilibrium calculations due to their difficulty. e) Once the chemical composition is determined, this data to determine the opacity of the gas as a function of wave- length. f) The equations of radiative transfer and convection are then solved. i) The mixing-length theory is typically assumed to accurately describes convection. III–15 addition to the radiative heating) and driving off mass. vi) Energy conservation thus demands the following: 1 2 ∆MP v 2 P = 1 2 ∆M∗ ∆ΩP 4π v2w , (III-17) where ∆MP is the total mass lost by the planet, vP is the speed at which it is lost, ∆M∗ is the to- tal mass lost by the star, ∆ΩP is the fraction of the wind that is intercepted by the planet, and vw is the total speed of the impinging stellar flow. The equa- tion can be re-expressed as fractional mass lost, with ∆MP MP = ∆ΩP ∆M∗ 4πMP v2w v2P . (III-18) vii) The curves of Figure 1 closely follow a power- law trend of r−2 (the plotted curves are slightly steeper than this), implying that the factor ∆ΩP dominates the variation with radius. This trend results because the wind speed term v2∞ is consid- erably larger than either the orbital motion term v2orb or the planetary escape speed term v 2 esc. C. Evolution of the Earth’s Atmosphere 1. The early Earth atmosphere. a) At the Earth’s formation, light elements such as hydro- gen and helium exist in large quantities near the Earth’s surface. b) After loss of the hydrogen, helium and other hydrogen- containing gases from early Earth due to the Sun’s radia- tion, primitive Earth was devoid of an atmosphere. III–18 Figure III–1: A plot of the BHL capture radius rcap relative to the planetary radius as a function of planetary escape speed. The solid curves are for different relative velocities of incoming flow v◦ from 15 to 105 km/s in intervals of 15 km/s. The condition of BHL accretion requires that rcap exceeds RP. Note that even if the Earth were motionless, it would still fail to accrete the slowest AGB winds beyond its own geometric cross-section. c) The first atmosphere was formed by outgassing of gases trapped in the interior of the early Earth, which still goes on today in volcanoes. d) For the Early Earth, extreme volcanism occurred during differentiation, when massive heating and fluid-like mo- tion in the mantle occurred. It is likely that the bulk of the atmosphere was derived from degassing early in the Earth’s history. The gases emitted by volcanoes today are in the following table. Composition of volcanic gases for three recent volcanoes H2O CO2 SO2 H2S HCl 95 1.1 1.5 0.07 0.006 96 1.9 2.3 0.08 0.004 97 1.1 1.5 0.07 0.006 III–19 e) Life started to have a major impact on the environment once photosynthetic organisms evolved. These organisms, blue-green algae, fed off atmospheric carbon dioxide and converted much of it into marine sediments consisting of the shells of sea creatures. f) While photosynthetic life reduced the carbon dioxide con- tent of the atmosphere, it also started to produce oxygen. i) For a long time, the oxygen produced did not build up in the atmosphere, since it was taken up by rocks, as recorded in banded iron formations and continental red beds. ii) To this day, the majority of oxygen produced over time is locked up in the ancient “banded rock” and “red bed” formations. iii) It was not until probably only 1 billion years ago that the reservoirs of oxidizable rock became satu- rated and the free oxygen stayed in the air. g) Once oxygen had been produced, ultraviolet light split the molecules, producing the ozone UV shield as a by- product. Only at this point did life move out of the oceans and respiration evolved. h) Oxygen became a key atmospheric constituent due en- tirely to life processes. It built up slowly over time, first oxidizing materials in the oceans and then on land. i) Sometime just before the Cambrian, atmospheric oxygen reached levels close enough to today’s level (20%) to allow for the rapid evolution of the higher life forms. For the rest III–20