Great Ideas in Science II
Great Ideas in Science II PHYS 2028
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This 24 page Class Notes was uploaded by Iva Cormier on Sunday October 11, 2015. The Class Notes belongs to PHYS 2028 at East Tennessee State University taught by Donald Luttermoser in Fall. Since its upload, it has received 17 views. For similar materials see /class/221407/phys-2028-east-tennessee-state-university in Physics 2 at East Tennessee State University.
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Date Created: 10/11/15
Physics 2028 Great Ideas in Science II The Changing Earth Module Notes Dr Donald G Luttermoser East Tennessee State University Edition 20 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 modi ed for the Spring 2009 semester III The Changing Earth Atmosphere A The Current Earth s Atmosphere 1 Composition of the Atmosphere a The Earth s atmosphere is simply called air It is primar ily composed of many discrete gases each with its own physical properties in which varying quantities of tiny solid and liquid particles are suspended b The composition of the air is not constant it varies from time to time and from place to place i However if the suspended particles water vapor and other variable traces gases were removed from the atmosphere its makeup is very stable over all of the Earth up to an altitude of about 80 km ii As can be seen by Table 111 1 two elements ni trogen and oxygen in molecular form make up 99 of the volume of clean dry air iii Most of the remaining 1 is the inert element argon iv The carbon dioxide abundance has been increas ing since the dawn of the industrial age v Water vapor is one of the most variable gases in the atmosphere In the warm and wet tropics it may account for up to 4 of the atmosphere by volume while in the air of deserts and polar regions it may compromise only a tiny fraction of 1 c Table III 1 Principal Cases of Dry Air Symbal Canstituent Percent by Valume N2 Nitrogen 78084 02 Oxygen 20946 A Argon 0934 002 Carbon Dioxide 00325 Ne Neon 000182 He Helium 0000524 CH4 Methane 000015 Kr Krypton 0000114 H2 Hydrogen 000005 Also water is the only substance in the atmosphere that can exist in all three states gas liquid and solid It is the source of all clouds in the atmosphere and for precip itation 2 Four distinct layers of the atmosphere exist 3 Troposphere weather sphere Temperature decreases with height due to a density hence heat capacity de crease i Heat capacity is a measure of the ability of a material to absorb heat ii It is de ned as the constant of proportionality be tween the amount of heat and the change in tem perature that the heat produces in the material change in heat energy 111 C heat capaclty c ange in temperature iv The word troposphere is based on a Greek word meaning to change 111 2 b v The troposphere is the lowest layer of the atmo sphere it begins at the surface and extends to be tween 7 km 23000 ft at the poles and 17 km 56000 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 56 km 18000 ft of the troposphere Stratosphere Temperature increases with height due to ozone 03 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 111 3 C iii The stratosphere extends from the troposphere s 7 17 km 43 11 mi 23000 56000 ft range to about 51 km 32 mi 170000 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 gt 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 93 22 mi 49000 110000 ft above Earth s surface though the thickness varies seasonally and geographically 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 160000 180000 ft above the ground The pressure here is 11000th 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 160000 ft to the range of 80 85 km 50 53 mi 260000 280000 ft 111 4 01 iv Temperature decreases with height reaching 1000C 1480 F 1731 K in the upper meso sphere v This layer is also where most meteors burn up when entering the atmosphere 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 1000C 1480 F 1731 ii X rays cause these 2 atoms molecules to ionize iii From 80 85 km 50 53 mi 260000 280000 ft to over 640 km 400 mi 2100000 ft temperature increasing with height Although temperatures are high T gt 10000C 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 gt 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 111 5 3 Retention of atmospheric gases a b The ability of a planet to hold onto gases in a plane tary atmosphere depends upon two competing processes the planet s gravitational eld and the temperature of the planet s atmosphere For an object to just overcome any gravitating body s like the Earth s potential eld an object has to be launched with w total energy that is PE to escape the primary body s 69 Earth s gravitational eld gt the escape velocity i Hence to calculate the escape velocity from the surface of a large body of mass M and radius R we just have to set the initial kinetic and potential energy sum to zero and solve for the velocity 1 2 GM m i Etot Emvesc R 0 Ill 1 ii This gives the equation for the escape velocity or escape speed 111 2 iii As can be seen from Eq Ill 2 the escape veloc ity does Lot depend upon the mass of the escaping body or particle Using the values for Earth in Eq Ill 2 we get 2GM Re 7 Uesc 111 3 or vase 112 kms to leave the Earth s gravita tional eld 111 6 iv For an object to escape the gravitational eld of a primary body it must achieve a velocity greater than or equal to the escape velocity v 2 vase c The kinetic theory of gases describes the microscopic motion of gas particles It assumes that the gas behaves ideally e their equation of state obeys the ideal gas law 1 At the heart of this theory The temperature of the gas is related to the average velocity of a gas par ticle i Thermal energy average kinetic energy of parti cles in the gas TE 3 1 7 i T 7 2 Ill 4 where the overline indicates average 01quot ii The average velocity of a gas particle is v2EF 111 5 0 The average component velocities are equal to each other for random motion 0 So Eq Ill 5 can be rewritten as W 3E HI6 e A degree of freedom in a gas refers to the number of independent means by which a gas particle can possess energy 111 7 f g o If it moves in the x y and 2 directions it has 3 degrees of freedom 0 So we can write three separate energy equations 1 7 1 E1 l 7 l Ey l 7 1 E2 and the average kinetic energy is then the sum of the energies in these three different directions 1 7 7 7 E EIEyEZ mltvgUZUZgt l l l l 3 01quot 17 BkBT 111 7 m The square root of U72 is called the rootmean square rms velocity f7 BkBT 2 7 Um U m Ill 8 gt when we talk about velocity of gas particles we will always mean Um In this equation ICE 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 The temperature of a planetary depends upon a variety of factors including the amount of greenhouse gases see 111 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 vms gt vase 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 03 in the stratosphere absorbs solar UV light b UV light has higher energy than Visible light gt enough energy to break apart complex molecule chains i UV light can alter the structure of the DNA molecule gt gives rise to mutations ii Most mutations are bad e harmful to liVing organisms gt cancer results c Ozone reacts with hydro uorocarbons a common refrig erant i OH3OHF2 03 gt C02 H20 OHgFg ethylidene uoride ozone gt carbon dioxide water a hydro uorocarbon radical ii The ozone disappears The resulting molecules have no absorption lines in the UV gt the solar UV radiation is able to reach the ground Ill 9 5 The Greenhouse Effect 3 b c d 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 gt radiates like a blackbody iii The glass is opaque to IR light gt the IR pho tons cannot escape into the outside environment the greenhouse heats upl C02 and H20 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 C02 and H20 absorb this light which heats the atmosphere If it wasn t for C02 and H20 the Earth s atmosphere and surface would be too cold for liquid water to exist early in the history of the planet gt life would not have formed or evolved The burning of fossil fuels releases tremendous amounts of gaseous C02 into the atmosphere i C02 abundance has increased by over 20 over the past 100 years due to the industrial revolution Ill 10 e 0 ii The average temperature of the Earth also has increased by about 3 K 30C over this same time period iii The hypothesis has been made that the increased C02 abundance has caused this temperature in crease Venus has experienced a runaway greenhouse effect We will have further details of the greenhouse effect in the atmospheric modeling section later in this section of the notes B Atmospheric Modeling 1 There are two main conditions which dictate how the atmosphere of a planet is structured and how it evolves over time a b The rst is the size and mass of the planet which deter mines the escape velocity vesc from the planet via ZGMP RP where Mp is the mass of the planet R10 is the radius of the 111 9 Uesc planet and G is Newton s universal constant of gravity The second is the stellar energy lnput which is a function of the distance the planet is from the star 7 and the luminosity of the star 1 i If blackbody radiation is assumed a the stellar luminosity is a function of temperature TN and radius Pd ii These stellar parameters determine the surface temperature of the planetary atmosphere T in 111 11 conjunction with the albedo A of the planet atmosphere R T 1 A 4 11 P Initially in modeling it is assumed that the frac via 111 10 111 tion of energy that is not re ected back into space is completely absorbed and not scattered ie ther mal equilibrium However once initial models are conserved scattering is included in the calculations iv Heat retention due to the greenhouse effect also needs to be included 2 Assumptions used in atmospheric modeling a b C d 8 Geometry of the atmosphere typically either the assump tions of plane parallel or spherically symmetric are used Transport of energy usually only radiation transport and convective transport are important Equation of state of the gas usually the ideal gas law is assumed Equilibrium vs non equilibrium chemistry initial models usually assume equilibrium conditions exist in an atmo sphere and once these models are converged non equilibrium equations are used These calculations also need to in clude dust formation Local thermodynamic equilibrium LTE vs non local ther modynamic equilibrium NLTE radiation transport once again initial models assume LTE then NLTE equations are brought into the calculations Ill 12 f g h Opacitics 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 Precipitation and the water cycle are needed for those planets where liquid water can exist ic those planets in a habital life zone around a star Finally static vs dynamic atmospheres the difference be tween these two is whether winds exist in an atmosphere lnitial models usually assume a static atmosphere where the hydrostatic equilibrium is used to determine how pressure changes with height 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 tMg 11 x 1011fXH MM 81quot L L yas Ill 11 where f is the fraction of the star s mass involved in nu clear fusion X H is the abundance of hydrogen M is the mass of the star and MG and LG 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 Ill 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 elds 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 eld of the interstellar medium As such the UV and X ray flux diminishes over the course of a star s main sequence lifetime 1 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 gt 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 E i gp Ill 12 for a plane parallel atmosphere or E i G M p d T 7 2 for a spherically symmetric atmosphere where P is the Ill 13 total pressure 2 is the height in the atmosphere 9 is the surface graVity p is the gas density and 7 is the distance from the planet s center and M is the mass of material in a shell of thickness d7 Ill 14 b c d e f 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 111 14 01quot P NkBT 111 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 ICE is Boltz mann s constant The assumption of HSE along with the ideal gas law is used to calculate P T and p as a function of height or radius From this the thickness 739 of the atmosphere is calculated under the condition that z 739 when P 0001 Po where PO is the surface atmospheric pressure 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 dif culty Once the chemical composition is determined this data to determine the opacity of the gas as a function of wave length The equations of radiative transfer and convection are then solved i The mixing length theory is typically assumed to accurately describes convection Ill 15 g ii lnitial atmosphere models assume local thermo dynamic equilibrium LTE in the solution of the transfer equation Since the densities in a plane tary atmosphere are typically large the LTE as sumption should be valid iii Published stellar spectra is typically used as in put of the stellar radiation eld for the radiative transfer calculations iv These calculations will then result in a temperature density strati cation for a given evolutionary time As a planet evolves a modeling code must determine whether conditions are appropriate for life to form If so non equilibrium chemistry must be introduced in the form of life affecting the composition of an atmosphere The physics of retention of a planetary atmosphere 3 b C A variety of processes are important to the ability of a planet to hang on to an atmosphere The rst as stated in the last section depends upon the amount of energy falling onto a planetary atmosphere from the star or stars in the system versus the strength of the gravitational eld of a given planet The loss of at mospheric gas from this processes is known as radiative ablation Beside this process a planetary atmosphere can either gain mass or lose mass through momentum exchange sometimes called momentum ablation with a stellar Wind Ill 16 i This change of the mass of a planetary atmosphere will depend upon the strength of a stellar or in the case of the Solar System solar wind ii Many cool giant stars have rather massive winds which makes this process important in the distant future of the evolution of the Solar System when the Sun becomes a red giant star iii For this process we need to de ne the accretion radius of a planet RBHL relative to the planet s size which is given by RBHL Wimp III16 RP vim where Urel is the relative speed between the accreted matter and the planet in this expression gas pres sure effects are assumed negligible and RF is the radius of the planet in question The approach de scribes how streamline ow is gravitationally fo cused downstream of the planet Crossing wind streams lead to a shock and a some fraction of this gas falls back onto the planet iv One considers accretion to be important only if RBHL gt RP e when the gravitational potential at the planet is deeper than the kinetic energy of the incoming matter v To estimate how much mass is lost by a planet via a stellar wind it is assumed that the deposi tion of kinetic energy by the giant star wind goes into heating the outer atmosphere of the planet in 111 17 addition to the radiative heating and driving off mass vi Energy conservation thus demands the following AQP 2 47F UW where AMP is the total mass lost by the planet Up is the speed at which it is lost AM is the to tal mass lost by the star ADP is the fraction of the wind that is intercepted by the planet and UW is the 1 1 E AMP v12 E AM 111 17 total speed of the impinging stellar flow The equa tion can be re expressed as fractional mass lost with AMP AQP AM 1 MP AIpr 17 III18 vii The curves of Figure l closely follow a power law trend of 7 the plotted curves are slightly steeper than this implying that the factor ADP This trend is consid dominates the variation with radius 2 results because the wind speed term v00 erably larger than either the orbital motion term Ugrb or the planetary escape speed term v2 esc 39 C Evolution of the Earth s Atmosphere 1 The early Earth atmosphere a At the Earth s formation light elements such as hydro b gen and helium exist in large quantities near the Earth s surface 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 Ill 18 2 l I I I I I I I I I I I I I I I I I I I I v0 15 kms Accretion No Accretion v0 105 kms O 05 1 log vm kms Eigure lll 1 A plot of the BllL capture radius reap relative to the planetary radius as a function of planetary escape speed The solid curves are for different relative velocities of incoming flow no from 15 to 105 kms in intervals of 15 kms The condition of BllL accretion requires that reap exceeds Rp Note that even if the Earth were motionless it would still fail to accrete the slowest AGB winds beyond its own geometric crosssection c The rst 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 uidlike mo tion in the mantle occurred lt 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 H20 C02 802 H28 HCl 95 11 15 007 0006 96 19 23 008 0004 97 11 15 007 0006 e f g h 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 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 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 Oxygen became a key atmospheric constituent due en tirely to life processes It built up slowly over time rst oxidizing materials in the oceans and then on land 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 Ill 20 of geologic time the oxygen in the atmosphere has been maintained by the photosynthesis of the green plants of the world much of it by green algae in the surface waters of the ocean 2 The distant future of the Solar System and Planetary Atmo spheres 3 b lmportant questions that need to be asked about the Earth and the other planets in the Solar System and planets in other stellar systems when a star nears the end of its thermonuclear life include i Can Earth like planets retain an atmosphere at late stellar phases ii Will gas giants like Jupiter experience substantial mass loss or accretion of stellar wind gas iii What effect do the strong ultraviolet UV emis sion lines from the thick chromospheres and out ward propagating shocks of red giant branch RGB and asymptotic giant branch AGB stars have on the structure of their planetary companions For planets in orbits around red giant stars object like Jupiter can suffer evaporative mass loss due to radiative and momentum ablation of up to about 30 for quite small orbits of 03 AU above a solar stellar photosphere and Saturn like objects can lose more than 10 of their mass out to modest sized orbits of order 1 AU above the photosphere Ill 21 C d e f A body like Uranus might evaporate entirely at an orbit of 1 AU whereas an Earth like body will lose its atmo sphere at an orbit as large as 5 AU The major conclusion is that atmospheric losses because of red giant winds might be signi cant depending pri marily on the mass of the planet the speed of the stellar wind and the orbital distance of the planet from the star Over the course of time the radius of the planet s orbit will begin to drift either outward because of mass lost by the star or potentially inward because of drag with the solar wind Modeling has shown that this rst effect dominates the later for the inner planets at least until the future Sun engulfs them If a planet experiences signi cant mass loss during the late stages of the Sun s evolution then its escape speed will decrease and mass loss will become even easier due to radiation and momentum ablation i For Jovian planets their size will change as a re sult of this mass loss reducing its wind intercepting cross section which will have a compensating effect for the reduced escape speed vase ii For terrestrial planets the solid planet should re main of constant radius throughout the loss of its atmosphere note that the mass of a terrestrial at mosphere is small fraction of a planet s total mass 111 22
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