Energy and the Environment Lecture 3 PHYS/ENVS 3070 Professor Dmitri Uzdensky Aug. 29, 2014 PHYS/ENVS 3070 1REMINDERS: • Read Chapter 1 of E&E textbook. • CAPA Homework #1 due next Friday 11 PM. • Pick up your paper copy of CAPA (with this week’s PIN) in Duane 2B hallway. If you don’t have one, do CAPA Late Enrollment. • No lecture on Monday (Labor Day). • Email: - best way to contact me for non-physics questions; - please include “PHYS-3070” in the Subject line. • Course webpage: http://www.colorado.edu/physics/phys3070/ Aug. 29, 2014 PHYS/ENVS 3070 2YES! Is Calculus necessary? NO! Aug. 29, 2014 PHYS/ENVS 3070 3 The math skills in this class span a large range. Do not fear the math you do not know, just resolve to put in the effort to learn it during this course. Math%Requirements%Brief%Math%Review:%Powers%of%Ten%1,000$=$103$=$1E3$=$1e3$=$10^3$=$1$kilo.$or$1$k$1,000,000$=$106$=$1E6$=$1$Mega.$or$1$M$(1$million)$1,000,000,000$=$109$=$1$Giga.$or$1$G$(billion)$1012$=$1$Tera.$or$1$T$(trillion)$1015$=$1$Peta.$or$1$P$or$1$Q$(quadrillion)$So$1$QBtu$=$1,000,000,000,000,000$Btu$=$1015$Btu$Aug.$29,$2014$ PHYS/ENVS$3070$ 4$Million$Billion$Trillion$Quadrillion$Aug.$29,$2014$ PHYS/ENVS$3070$ 5$Clicker%Ques<on%?101010100723=×××−A)$108$B)$10$C)$109$D)$103270$E)$None$of$the$above$answers$8)0723(1010 =++−Note$that$100$=$1.$$Makes$sense$since$102$x$10.2$$=$100/100$=$100$$=$1$Aug.$29,$2014$ PHYS/ENVS$3070$ 6$Room Frequency DCMath%Review:%Logarithms%and%Exponen<als%logm$(Xn)$=$n$logm$X$$Example:$?)000,100(log10=5)10(log5)10(log)000,100(log1051010===Note$that$we$usually$do$not$say$log10,$$just$log.$Aug.$29,$2014$ PHYS/ENVS$3070$ 7$logm$m$=$$1$$ logm$1$=$$0$$log10(10)$=$1.$Natural Logarithm & Exponential ex$=$(2.718…)x$=$exp(x)$$Exponential Function: ex$=$10(x/2.303…)$=$10(x/ln(10))$$$Aug.$29,$2014$ PHYS/ENVS$3070$ 8$y$=$ex$$à$$x$=$ln$y$=$loge$y$Natural$Logarithm:$$Relaaonship$between$ex$and$10x:$10$=$eln$10$à$$10x$=$(eln$10)x$=$e(x$$ln$10)$=$e(2.303$x)$.$Why do exponential functions often occur? What are they? NtN∝ΔΔOften the rate of change of some quantity N is proportional to the quantity N itself. Can you think of some examples? If you turn this into a differential equation and solve it, the solution is an exponential ! cNdtdN=cdtNdN=)exp()( cttN +=If you have never seen a differential equation, do not worry. Just know that exponentials occur all the time. Aug.$29,$2014$ PHYS/ENVS$3070$ 9$Amoeba%popula<on%growth%1=∝ΔΔNtN2=∝ΔΔNtN4=∝ΔΔNtNLots$of$other$examples$(compound$interest$on$money,$virus,$nuclear$decay$ΔN/Δt$<$0).$$$Note$that$ocen$there$are$correcaons$$(e.g.$amoeba$also$die$at$some$rate…)$$Aug.$29,$2014$ PHYS/ENVS$3070$ 10$)exp()( cttN +=There is a very nice “pocket formula” to remember. The time for something to double (“Doubling Time”) is given: Doubling Time = 70 Percent Increase Per Year If inflation is 3.5%, how many years will it take for prices to double? A) 3.5 years D) 70 years B) 10 years E) 200 years C) 20 years Aug.$29,$2014$ PHYS/ENVS$3070$ 11$Clicker Question Room Frequency DCExponen<al%Growth%Example:%C om pound%Inte r est%Aug.$29,$2014$ PHYS/ENVS$3070$ 12$Why%Logarithmic%Scale%is%Useful?%The$two$graphs$below$are$plodng$the$same$funcaon$[y"=$exp(x)]$On$a$linear$scale,$because$the$y$values$span$such$a$large$range$much$of$it$looks$like$zero.$$On$a$logarithmic$y.axis$scale,$each$factor$of$ten$is$evenly$spaced$out.$Note$that$the$right$graph,$the$relaaonship$between$y$and$x"looks$linear,$but$it$is$not$!$Linear$Scale$Logarithmic$Scale$Aug.$29,$2014$ PHYS/ENVS$3070$ 13$Annual Energy Consumption (QBtu) Which does the graph above show for the total energy usage? A) Linear growth (E ~ t) B) Exponential growth (E ~ et) C) Power law growth (E ~ tx) D) Not really sure (?) Aug.$29,$2014$ PHYS/ENVS$3070$ 14$Clicker Question Room Frequency DCAnnual Energy Consumption (QBtu) From 1850 to 2000, the annual energy consumption has increased by a factor of ? A) 10 B) 20 C) 50 D) 100 E) 200 100 10 1 Aug.$29,$2014$ PHYS/ENVS$3070$ 15$Clicker Question Room Frequency DCReal%World%Limita<ons%on%Exponen<al%Growth%%%• In$real$natural$and$human$systems$exponenaal$growth$does$not$conanue$indefinitely…$$• Real$systems$are$subject$to$finite$resource$constraints$that$limit$unchecked$growth:$$– resource$depleaon$for$non.renewable$sources$$(e.g.,$fossil$fuels,$fossil$aquifers);$$– finite$replenishment$rate$for$renewable$sources$(e.g.,$ocean$fisheries,$hydro.electric$power,$etc.);$– external$factors$(predators,$wars,$asteroids,$etc.).$$Aug.$29,$2014$ PHYS/ENVS$3070$ 16$What is this graph telling us? How can we verify that it is reasonable? Limita<ons%on%Growth%Example%1:%Fossil%Fuel%Deple<on%Aug.$29,$2014$ PHYS/ENVS$3070$
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