INTR EXISTENTIALISM Philos 7
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Date Created: 09/12/15
LECTURE 7 6 Improper OneSided Limits 20 min A onesided limit of a function at a point a can fail to exist in different ways77 depending on the structure of f As I approaches a from the right the values may 0 move around77 Without getting and staying near any speci c value example a 0fz sin1z for z gt 0 0 decrease Without bound 0 increase Without bound The latter case7as 1 tends to a from the right the values increase Without bound7can be characterized precisely as follows For every real number R gt 0 there exists rightsided neighborhood la a 6 such that gt R on laa 6 Example 1 0 The above characterization is equivalent to saying that 1 l39 7 0 152 m 7 and in this case it is often more convenient though less appropriate to Write lirn oo 18 z a and f is then said to have an improper limit as I approaches a from the right CAUTION Notations similar to 18 are used for improper leftsided limitsi These notations although con venient are risky since they seem to indicate a limit Where none existsi Thus in the above example although one Writes 18 the answer to the question Does the limit exist77 is Not Note Improper onesided limit relations for the other case7fz decreasing wthout bound7are de ned similarlyi Summary f considered on interval sign of f proper limit corresponding improper limit laa 6 limiEaJr 0 limiEaJr 00 l1 Ml limz7a 0 limzar fr 00 19 w 61 7 1mm 7 0 11mm fltzgt 700 la 7 6a 7 liminai 0 liminai 700 7 Limits of Ratios of Functions Guidelines for Practical Computation 25 min Suppose two functions f g are given Whose domains include an interval a 7 R1a and an interval la a R2 We assume that f and g are nonzero on these intervals In the problem of analyzing im La 91 20 different scenarios are possible We examine several of them here Fossil Fuel Use Resources and Global Warming Dennis Silverman Physics and Astronomy U C Irvine wwwohvsicsuciedusilvermaresources0Iot October 7 2005 Our Energy Future Future of Fossil Fuels Use and Resources ll Global Warming Future of Fossil Fuels Petroleum Natural Gas Coal Oil Shale and Tar Sands 002 Emissions US 20 Year Projections of Energy Use in Quads US Uses 100 Quadsyear m lHlllnnr PraiaImam g g m l anlaum xquot a If f f at vr aquot P39 fquot quoth r l K F H mtgE l lsfga i li 3 J at in I r if a 5 mmmm 39i a a an 2393 Kl II quot139Iquot H39Ila iiquot ii l 1iquot39 l allyquot Narimm Myth lm rmwabms m s V quotquot1 levngW E r lia lug ittinmt39TFquotM lrquoti m ailIF a 47 L 19m 1933 199039 2036 211m 2025 Petroleum Fuel Future US oil production peaked around 1970 US energy consumption is increasing at 15 a year The US currently imports 60 of its oil Proven total world oil resources was about 2000 billion About 800 billion of this has already been used More discovery and increasing recovery to 50 from 30 may boost this to 3000 billion barrels total At the peak the price rises steeply and consumption must level off perhaps leading to recession However we may see a very flat long peak where prices rise bringing in new oil resources to keep production flat with efficiency and conservation setting in to hold demand flat to a fixed supply It is unlikely that major investment in refineries and tankers would be made only a decade before a sharp decline again leading to a plateau The year of a peak is then irrelevant but the production level is important Different Interpretations of a Hypothetical EJJW Billinn lElarrel Worlrl Original 39Dil iini Place Resource Base 0000 I Unrecmerat la 5000 I Reserves Ernwth I Lnciseovered 4000 E E I roved 50 esewes 5 3000 E Fact ur Cumulath E Reserves Produeticn 1139 2000 00 Recurrent 1000 Reserves Growth LISGE Approach 1995 Eampbelli Laherrere Approach Figure Different Interpretations of a Hypnthetical 6 0 Billion World Original DiIin Place Resource Base 33 Peaking of World Oil Production Hirsch Report Feb 2005 Table I 1 Predictions nit Ward Di l Production Peaking Preiected Date 2006 2007 EUU T EDUQ After 200 Befere EDUQ Befere 1201 iii Armand 2WD After 2m 1 2i 391 UEDED 20 1 I33 After 212120 2025 or later We wieible Peatt Sean rce uf Prniectien Bekwh iteri Sim mans Shreb ewski Deffeyes Seed stein Cempbeii World Energyr Ceuncii Laherrere EI A Nominal CERA She Lynch World Oil Growth and Decline Pessimistic 2000 Bbl resources 1000 Bbl reserve Prqductiun Gblyearl 16 0039 lab ia Hisrow QgtampI 20 FEE 3200 1999 I World Oil 1 Forecast 199 r Ws x V 1m IEEWEM 1 20002343 39 Iquot quot I 39 DPEDfnnn OPED 1 Crossover event OPEC quotLL f V dominance 139 Nunopen 0 U0 a I I J 1960 1930 2000 2020 2043 Optimistic 3000 Bbls of oil total resources US Geological Survey Annual Production Scenarios with 2 Percent Growth Rates and Different Decline Methods Mezn w 2 Grnwlh and 2 Decline Uiiimaie RemEN EEis 195a 1975 zum 2u25 zusu 2u75 21m 2125 ml usuulunsvzrenumtumeuscsfmugnmunstuminivan1mm Figure A1 Two EIA oil productloll scenarios uaseu an expected ultimate 00 mm on demand escalatmn U S Oil Sources US 35 65 imported including 33 from OPEC Map shows percent of imports m 1 5 A quot A ECUADOR GABON w A O l 5 no ads IMPORYS or quot DATA FROM 51 CRUD OIL ETROLEUM PRODUCTS 2m MAP av m mason US and World Natural Gas US demand growth is 3 per year A shortage now exists in the US and plans for Liquid Natural Gas LNG terminals for imports exist around the country Ventura Long Beach Baja California and up to 40 sites nationwide The Federal Government wants the final say on allowing siting of these terminals LNG could grow from 1 now to 20 by 2020 The graphs are for the time the supply will last The lighter color is less likely than the darker part S WORLD Punen 3 EEunmLs 25 gmth W 14110 quads 23W 97th m 183 quads No wuwih NAT TRAL 3A5 IESUI I I T T T T I T r I 1 l 10 2 EU 1quot GO 70 an m 100 1391 M b 39 V Lear I I I I F 05 10 TIME Iltfespaul V l Resourceful N I Largest proved oil and gas reserves lt Barrels of oilaqui39a39alent tin F il39 Gas 3923 13922quot ESII 331 wt Total reserves I I with natural gas reserves RUSS in equivalent Eaud Nama billion barrels of Iran 0 bb39 United Arab 39i World Oil consumption Emirates is 30 bblyear Iraq Left out Canadian tar sands at 179 bbl oil US has 22 bbl oil and WWIIJew Kuwait produces 20 bblyear Menm and would last only 11 United years Statea Qatar Nigeria Sirunit FIL39 nal35 quotrnllrlc395 crulltlr39rlttl39llrs US Coal Supply The total US coal reserve is 5700 Quads The current rate of use is about 20 Quads per yeah Population growth will reduce its longevity of 250 years with no growth Conversion to motor fuel uses 2 Quads of coal to generate 1 Quad of fuel plus the additional 002 emission Conversion to hydrogen fuel uses even more The graph assumes 54 of underground coal is recoverable Estimates are for various growth rates of use L39U J AL E LEEEJ LE39E US Coal Lifetime CURRENT USE 1 l quot391 quot grer l1 211 3 g lm 39h AFTER EUNVEHEIQN I 139 I L quot15 gl wwth 21 Li mnw n 1 I 1W MI W M I are L Nu i gl39h39MiM 1 E39Lllij39 25H I I 39l l 233239 quotJ IME I li piam World Coal Reserves Smaldng Eual FESEWES end BEIGE tanner MI 393 5391 1W 15B 200 EEG United States 39 Russia China India Australia Eerma ny Eanuth Af ta Strum EP Fossil Fuel Future Summary Oil Natural Gas Shale Oil and Coal produce COZ Carbon sequestration requires an extra 30 of power and needs research FutureGen 1 billion research plant Oil is needed for transportation fuel Too expensive for electricity generation Total world reserve of oil is a large question uses politically motivated estimates of individual countries and industry secrets Reserves About 50 years with growth in use 23 is in the Middle East Coal may last 100 years with growth in usage but only 70 years if partly converted to replace oil Current rate of use of fossil fuels will increase worldwide U 8 proposed climate technoloqv proqram Short Term Optimum The best way to hold down COZ increases is to remove fossil fuels from electricity generation but just use gasoline for transportation and natural gas for heating Since 12 of US electricity comes from coal which generates twice as much COZ per energy unit as does natural gas we should switch to natural gas This however involves massive imports We need increases in alternate energy sources such as hydro nuclear wind and solar However coal and LNG will be cheaperthan nuclear so a sacrifice is required here Solar cells are very expensive Direct solar water heating is much more efficient We also need increases in energy efficiency and conservation This especially includes high mileage vehicles Comparative Projected Vehicle Fuel Economies I Guzzlirlg Fuel econumyquot miles per US gallun ED EIJI Jal an 13quotquot 5393 Eh 4 7 4m mj tralia tllgr quot39Iquot39Eanadal n II39quot39 EU J I l l 4 I I 439 2m M GS 133 W 1 Ir39l lugl cars mintutility w 139i lti nd ruinl39vana HieHenri Linn3 mprmur pm pcxsm39l 2313 x I arda 50mm Na tlmml Ilh m l39i i n I n Ermr39gy P li g PmCer utre rm Glam3 Elima u Change ll Global Warming Effects Predicted Global Warming of 5 F will affect everyone in most structural aspects of society and in their costs We don t realize how our present housing business and supply nets are closely adapted to our current climates The major increase in temperature and climate effects such as rainfall drought floods storms and water supply will affect household and business insulation heating and cooling energy and farming These may require large and costly modifications Some present cold areas may benefit and some hot areas will become unfarmable and costly to inhabit It is very misleading to portray the problem as a purely environmentalist issue which affects only polar bears a few Pacific islanders and butterflies Global Temperature Record Unusual 1 F Rise in the Last Century 5 5 lt Northern Mexmsphere a Global 4 l l r r 0 rrerrr the 1961 1990 average J l l l l l l l 5 ln lemperahjres l l l l l l l l l l as l l l l l l l l l l Departure r r r r r r r r r r l run 1109 200 ram Mao mm 1500 run mm 1900 2m 2m Year CO2 in 2100 The laST wiTh business as usual 600 years from ice Double preindusTrial CO2 cores and The 500 nex r 100 years LowesT possible CO2 Temperature red sTabilisaTion level by 2100 400 Tracks 602 green cog now 300 10 TemperaTure difference 0 200 from now C 10 I u I 1 100 160 120 80 40 NOW Time Thousands of years CO2 concenTraTion ppm 002 Production Rate Preindustrial 275 ppm 002 will be doubled to 550 ppm by adding 200 ppm to the present 350 ppm Present burning of 360 Quads of fossil fuel per year can increase 002 by 34 ppm per year Thus 200 ppm will be added by 60 years or sooner if fuel use increases Climate models have a mean prediction of an increased temperature of 5 F for this doubling of 002 Comparison of CO2 Doubling to Fossil Fuel Reserves 360 Quads over 60 years is 22000 Quads which would double preindustrial C02 Tripling CO2 will require another 30000 Quads Summary of estimated fossil fuels 23000 Quads world coal 10000 Quads natural gas 6000 12000 Quads oil 6000 possible tar sands oil shale depending on cost Total 40000 50000 Quads of fossil fuel available Ignoring Carbon absorption burning all fossil fuel can lead to tripling preindustrial CO2 To stop at doubled CO2 we must use no more than half of available fossil fuels Allocating Carbon Use Fees Just as we have a gas tax to pay for roads carbon taxes should be applied to pay for the total cost of fossil fuels This is one main way to limit carbon production below the consumption of all fossil fuels The costs include that of securing energy sources or energy wars that may get more severe as the value and competition for energy increases So far the Iraq war has been allocated 200 billion There was also the 903 retaking of Kuwait The costs should also include US and foreign damages from global warming Whereas the New Orleans and Gulf Coast flooding may not be due to global warming this time there may be similar damages in the future from global warming There is also the moving of the Inuit villages from sea level rise And we expect future environmental and crop damage and relocations We pay for the energy security costs and massive damages anyway By using carbon fees we discourage wasteful uses of fossil fuel and encourage conservation while calling attention to the full cost of these fuels compared to renewable resources which must replace them Comparative World 002 Emissions The US emits 25 of World 002 CG EMIESDDHS 1mm IMILLIGM IGHHES ChiIa l s Russia 7 Jam1r 1 j W I 93D 39ii ElliSE lil39Gi l E Q cn 5quot CI 1 93 I 2033 3303 EJI I EIZICIIZI Ei IZIIZI iiii Z n EL quot W Eliiiifli iina39i i 1 him 0 397 wires inlin2 I39niquot i Huzrgi pshi Ly Li 3 L332 17391 L i 1 1 iv i miquot L51 Global Warming Scenario Greenhouse gases 002 methane and nitrous oxide Already heat world to average 60 F rather than 0 F without an atmosphere The present radiation imbalance will cause another 1 F heating by 2050 even without more greenhouse gas emissions Recent cleaning of air is causing the earth s surface to be hotter and brighter Stabilizing the amount of 002 would require a reduction to only 5 to 10 of present fossil fuel emissions Effects of the Doubling of CO2 Doubling of C02 projected by end of century causing approximately a 5 F increase in average temperature most rapid change in over 10000 years 2 3 foot sea level rise More storms and fiercer ones as illustrated by Atlantic hurricanes this past year with 5 F hotter Caribbean sea temperatures Loss of coral reefs Increase in tropical diseases since no winter coolness to kill insects 25 decline in species that cannot shift living ranges Possible removal of Gulf Stream causing ice age in Northern Europe Warming expected to be greater over land Hot areas expect greater evaporation from hotter winds thereby causing drought Lower heating costs in winter more air conditioning costs in summer Global Warming Effects Global Warming is an average measure Local warming or climate fluctuations can be very significant Arctic is 5 warmer Ice cap is 12 the thickness of 30 years ago Antarctic is 5 warmer Ice shelves over the sea are melting and breaking off and may allow the 10000 foot thick ice sheet over Antarctica to slide off the continent faster This would cause a sea level rise An analogous local effect is that while ozone is affected everywherethere IS a more severe seasonal ozone hole over Antarctica Rainfall is hard to predict It could be increased or decreased Drought can partly be caused by increased evaporation at the higher temperature C02 Effects to Increase Ove r Ce ntu ri es 002 concentration temperature and sea level continue to riselong after emissions are reduced Magiiilude oi response Time km to reach equilibrium w gt1 uw iiu i u u ui iuuu MW cevelal Illillenllla Cogemissinns peak M0100 years riw i Hwquot iiHlv iii Hi rm ii auwiu celilulies lo millennia T iaiiire statihzutioii a few centuries co siabihzaiian 100m 300 years C02 emissions I I I T diy 100 years mun years Global Warming effects in California Summer temperatures rise by 48 F by 2100 for low emission scenario 8 15 F for higher emissions Heat waves will be more common more intense and last longer Spring snow packs in the Sierra could decline by 7090 as winters will be warmer Agriculture including wine and dairy could be affected by water shortages and higher temperatures More forest fires Tree rings show that in eras of global warming mega droughts of decades hit the southwest US Fliger 1 Ealliifrma CD81 Emissiims 1999 Indu rial 39 11 Heslggbntlal 3quot Emmmerzial A 3 MID Incluma 39 l f from Inuitrm li l39ll Eurm Cumml Emrgjl Comni n 25111 Irmatow li l39 calfEmu nhmm E Bum11 and 5m lam ms IjT39g III qun US Carbon emission sources Emissions Allocated t0 Essnsmic Sector Elamn39n39ny Ganaraljun Indusirg gn39nuhurs Burrrnarcial Hasijenljal 25ch 203 quot 153 39 LEI D I I l I I I I l l I l I I 1943 1a91 1992 1933 193 1935 1995 159 1931 1933 mm 2031 51m 3113 Tam Conclusions on Energy and GW At current or increased rates of production oil and natural gas will be gone in 50 years or so and will be expensive long before that Production of oil from coal and tar sands could be somewhat expensive Use of coal for electricity would highly pollute smog prone areas With the high costs of fuel and of fuel conversion or substitution the costs of global warming should be added in to promote alternate energy sources including nuclear power Global warming will continue until we drop fossil fuel use to a small fraction of its present rate The costs of relocation substitution extreme weather increased deaths and diminishing fuel will soon exceed the costs of developing alternate energy sources The sooner we act in research and development and conservation and conversion the easier and less costly the transition will be Cost of Conversion to Industry and Consumers Order of magnitude At 60barrel for oil we are currently sending 220 billion per year to foreign oil sources The 1St gulf war required our presence to retake Kuwait and defend Saudi Arabia for their oil resources The 2ncl gulf war Iraq may be costing us 100 billion per year at present to some day make available more oil resources Even if nuclear reactors cost as much as 5 billion each we could build 40 nuclear plants a year with this money Since nuclear is 20 of our electricity with 100 plants in 10 years of such payments we could produce 400 more plants and have 100 of our electricity nuclear Use plants at night to charge up electric car batteries The economics is similar to the question of renting versus owning The costs of building and operating US plants also go to American workers not overseas So we are already spending the magnitude of funds necessary to convert but not accomplishing it What can California Do California is the world s fifth largest economy and has led the way on reducing vehicle pollution before State law for utilities to increase renewable electricity to 20 by 2017 Can increase and extend to city power BEWARE Million solar roof initiative will spend 23 billion to create the power of only half a nuclear reactor Use combined heat and electricity systems in large plants Clean up older high polluting plants Mass transit and growth planning Removing firewood in forests and increasing them as a carbon storage component See Union of Concerned Scientists wwwcllmatechanqeorq Lower greenhouse emissions from cars by 30 by 2017 The Invisibility of Modern Energy and Global Warming In ancient times we gathered firewood and watched it burn With steam powered transportation we saw the coal loaded and burned and the steam go off Today we pump gas invisibly and burn it with no visible emission We don t see the oil being pumped from the ground although we can see tankers in the harbor and refineries We don t see it flowing through pipelines We don t see the electricity powering our houses except through light and don t monitor its usage We usually don t see the power plants We often don t even see power lines to our houses In natural gas heating we don t see the gas burn or the heater and we don t monitor it The greenhouse gases are invisible to us so we can t see their emission or buildup Their effects on temperature show up globally with careful averaging and often in subtle effects Any particular warming area or period is hard to precisely attribute to global warming Eventually global warming effects will be more prevalent after much of its prevention period is gone Signs of Progress Globally The Kyoto Treaty went into effect in Feb 2005 with signers reducing emissions to 5 below 1990 levels except for developing countries which includes China China however with many smoggy cities is planning 30 nuclear reactors by 2020 and considering 200300 by 2050 including breeder and pebble bed reactors Nationally Western governors committing to 20 renewable energy sources by 2020 New mileage limits on SUVs and light trucks by 2011 GM Gen IV V8 with cylinder shutdown technology to 4 cylinders to give 620 better fuel economy Honda will apply this to V6 also including hybrids Renewable energy sources Hydroelectric very useful At 30 50 of maximum use Effects of dams Variable with season and climate Wind power Need high wind areas 13 mph on cheap land 6002000 large turbines the equivalent of a nuclear reactor Would need 30 linear miles of turbines Already scenic protests in Nantucket Many areas far from the power grid Can be as cheap as natural gas If the wind dies down or is too high have to have a full backup in fossil fuel plants to avoid outages Waiting for Tax Credit law renewal 3040 average delivery of maximum rating more in summer San Gorgonio area averages about 110 of a nuclear reactor California wind contribution is 127 from three areas Solar Power Solar power 80 efficient for water heating on roofs Only 10 efficient for rooftop electricity Solar cell electricity more costly by a factor of 10 40 square miles equivalent to one nuclear reactor The sun doesn t shine at night If cloudy need full backup with fossil fuel plants to avoid power outages Need more research to improve efficiency and to lower manufacturing costs Biomass Ethanol and Geothermal Biomass Competes with farm use forfood Insufficient for total power by a factor of 40 2000 square miles equivalent of one nuclear reactor Burns to methane and nitrous oxide both greenhouse gases Sea growing possibilities being researched Ethanol Political Issue for Rural Red States and areas May be forced to include in gasoline as antiknock preventer but no pipelines or ships so truck transportation costly and not needed by the Blue States or cities Again generates CO2 Geothermal Few sites mostly in the west Produces Sulfur and heavy element pollution Drilled holes cool after sufficient water is heated Conservation Populations of largest 002 producing countries are stabilizing Mass transit car pooling cash for not parking Transit Villages built around transportation lines Fuel economy improvements Hybrid and electric cars cylinder shut down engines Transportation replaced by communications Energy smart offices houses and buildings Energy cost increases will drive conservation COZ production taxes and increased fuel taxes Signs of Progress Nationally US reducing offroad vehicle diesel emission 90 by Cities Mayors of 130 cities have pledged to follow Kyoto formula including Seattle and New York City California Committing to lower greenhouse emission fuel in new autos by 30 by 2016 Seven northeastern states likely to follow this NY NJ Canada demanding 25 reduction in new cars by end of this decade CA estimates cost of 1000 per vehicle with continuously variable transmission alternative AC coolant and engines that shut off cylinders A 20 reduction in GW gasses with existing technology would pay off in fuel cost savings in three years of driving Zero Emission Vehicle regulation will generate 200000 hybrids per year by 2015 Q What is today39s anthropogenic Radiative Forcing The radlallve forclng of cllmale slnce 1750 by gases pamcles land use and solar varlallon 3 Regionally dlsm buled 2 0 m E E g1 M l E Tropospherlc FOSS mere g Home carbon dur51 3 0 1 ll I 5 Slralospherlc Land a ozone use Sultale Elomass L 3 carbon a 71 I E m I E I 6 39 Dlrecl effect 8 72 on clouds I Globally well mlxed Aerosols Q Why worry about climate change 1 1 NORTHERN HEMJSPHERE Deparlures in lemperalure 70 1r0m1he1961 I01990 average 710 Dam 1mm thermometers red and from tree n ng cora s1ce Cores and hvsmrvca records We 1 1 1 1 1 1 00 1200 1400 1600 1800 20 o Q Why worry about climate change Global costs of extreme weather events inflationadjusted Annual Insses in houszu miHmn v5 duUzrs m 195 u Lllkgj elgpddljkn 1 1m 1992 I u L0 Q o m amp 05 e T 5f 00 g 00gt cu m 03 05 r J J 10 I I I I 1000 1200 1400 year 1600 1800 2000 4 2 Projected Temperature increase 00 Q Where will energy002 emissions come from Carbon in fossil fuel reserves and resources compared with historical fossil luel r n emissions and w h cumulative carbon emissions from arange of SRES scenario and TAR stabilization scenarios up until 2100 m A mm m 3 m m mm 3 um I we 25w 2 mm M WNElnnn 1 5m 92 mm Br 1 Duo mm emissluns man1m 0 Reserves and resources Emissions SRES scenarios Q What are the range of projections Emissions and quot g to different stabilization levels for CO1 concentrations ta 01 emissions Gt a 2n is b m2 concentration mun Hun mu 22m man man WRE plumes wag mu 0 RE 75a i RE ssu wRE ssu i wag 450 5 pro les SRES scenarios Global Ammunic Calhoun Diand Emissims GE Scenarios of C production with different economies gray and with mitigation goals imposed red 4 m 4 15241 mm 5355 ME mum TSEh ch SEES A1 Samaria man was sues A1FI scenarios Hi 3339 243 2d 113 1 to 39 77 fr1 quot n o DJ 4 1991 mm mm mm mm was 1990 mm 20m mm mm ma 1993 mm man mm mm mm 4 40 0 15211 mm GEES A2 Scenarios ITS239s was 5153 B1 Sonatina i TSIf wot axis a seamring 34 33 30 an 2DJ w 101 p quot i III a ll 1m 2WD 203E 24150 244MB 209 mo 213139 mm 21153 mm mm HIM 2134i 2030 2135 20m M30 Details of Economic Scenarios Scene Emmmy Emiranmnt 39 39 39 39 39 A2 a 2
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