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Find the limits in Exercises 4163

Thomas' Calculus Early Transcendentals | 12th Edition | ISBN: 9780321588760 | Authors: George B. Thomas ISBN: 9780321588760 156

Solution for problem 50 Chapter 2

Thomas' Calculus Early Transcendentals | 12th Edition

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Thomas' Calculus Early Transcendentals | 12th Edition | ISBN: 9780321588760 | Authors: George B. Thomas

Thomas' Calculus Early Transcendentals | 12th Edition

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Problem 50

Find the limits in Exercises 4163

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The Future Climate Introduction:  The IPCC stated in 2013: "Warming of the climate system is unequivocal, and since the 1950s, many of the observed changes are unprecedented over decades to millennia." So what will happen in the future  Predicting the future for our climate is more difficult to guess  Knowing the composition of the atmosphere, the solar constant, the albedo of the earth helps understand what the future temperature will be There are three key factors that control greenhouse gas emissions 1 Population 1 Affluence (How rich individual people are) 1 Technology  Together, these make up the formula I=PAT , which can be used to predict the impacts of energy consumption o (Impact = Population x Affluence x Technology) What exactly causes emissions  Population: o the more people, the more consumption o People consume goods and services  Affluence: o How rich individual people are o The richer you are, the more you consume o GDP has a positive correlation with per capita energy consumption o Affluence has changed over time o Example: average homes in the 60s were much smaller than they are today  Technology o Energy Intensity is how much energy is being used, i.e. how efficient the energy is being used.  If you replace incandescent light bulbs in classrooms, you change the energy intensity  Measured in J/$ o Carbon Intensity is how much carbon is being used and put into the environment  If you switch from coal power to wind, you change the carbon intensity  Measured in C/J o Total Technology Intensity is made up of the energy intensity and carbon intensity together  Measured in GtC/$ Types of Generation Technology Type of Source of Carbon Power Energy Intensity Fossil Fuels Coal Highest Oil Middle Natural Gas Lowest Renewable Wind* 0 s Solar* 0 Biomass* 0 Hydro* 0 Other Nuclear* 0 *Are these "renewable" energies really green Here are the major criticisms of these energy sources:  Wind power can affect the migratory patterns of birds  Solar technology production of "green" products takes a lot of manufacturing energy  Biomass and deforestation can take decades to regrow completely, and affects the environment and organisms that live in it  Hydro power changes the flow of rivers, which affects the ecosystem and marine organisms  Nuclear fuel made of plutonium becomes radioactive, and the radioactive waste can destroy the environment, or if disposed of, takes up space and energy to safely secure Global Scale  Economics affects emissions o Example: What happened in 2009  From 2008-2009, the IPAT trend that normally is increasing suddenly dropped and declined for a little  This was because of affluence: During the economic crisis, the housing market declined and people were poorer, so they consumed less stuff  Countries all over the world are increasing in their I=PAT scale due to increases in population, affluence and technology o Example: Why is China's impact increasing rapidly  China's new technology has made their economy grow, which leads to more technology and the ability to use more carbon and energy per person  Their technology is largely based on coal, so it isn't very energy efficient, and this is why their impact accounts for about 1/5 of the world's impact  Also keep in mind, a global temperature increase of 2-4 degrees Celsius will mean different things for each part of the world. So we can expect to see more warming on land than in the oceans, and the most extreme warming will be around in the artic regions. Artic regions may increase 6-7 degrees Celsius, while other continents increase 3 degrees Celsius. Areas over the ocean may only increase 1 degree Celsius. Also, land that is inland will increase more than the coasts.  To Summarize Important Points: 1. There will be more warming on land than ocean 2. There will be more warming in artic  This is because of the ice-albedo feedback, i.e. as more ice melts, the less albedo and the more heat that is absorbed by the landscape 3. There will be more warming inland than coastal regions 4. There will be more warming in the night than in the day  Because at night, the warming is all coming from the atmosphere (not the sun) so the temperature is more reflective of the greenhouse gases in the atmosphere. Only 8% change in warming during the day, and a 25% change in warming during the night 5. There will be more warming in the winter than the summer Predicting the future  Population is expected to increase to at least 9 billion by 2050  Developing countries means that people are expected to become richer  If population, affluence and technology increase as expected, then our future impact now depends on two factors 1. The amount of social-economic challenges for adaptation 2. The socio-economic challenges for mitigation  Over the next century, our warming could be between 1.8 and 2.8 degrees Celsius  This increase does not represent equilibrium temperature because it is only for one moment in time, and we will still most likely increase the temperature after  Even if our CO2 emissions peak in the next century, the atmospheric CO2 levels and temperature increase will remain elevated for more than a thousand years  Problems with predictions 1. Initial value problem: Predicting weather is an initial value problem because in order to predict the weather, you need to know what it was the day before. In other words, we can only predict weather about 5-10 days before it happens, so it is difficult to predict long term future weather 2. Boundary Value problem: Predicting climate is a boundary value problem, because in order to predict the climate, you have to know the values of , , and o Short Term Variability: +/- 1 degree Celsius over 10 years o Long Term Variability: +3 degrees Celsius over 100 years, or . 3 degrees Celsius over 10 years Why is the warming so alarming 1 Historic Variation o Over human history, climate temperature has only varied about 1 degree Celsius. This means that the 2-4 degree Celsius prediction increase in the future is well outside the historical range. Even though temperatures have been warmer since the last ice age, humanity was not industrialized as we are now. 2 Glacial and Interglacial Comparisons o The warming we are causing now is comparable to the change between glacial and interglacial periods, which were very extreme temperature changes 3 Changes are Large and Rapid o The glacial to interglacial warming took 10,000 years to warm, when today, the warming has only taken 100 years. So we are experiencing immense amount's of warming very rapidly. This doesn’t allow communities of plants and animals enough time to evolve and adapt to the warming, and so many are at risk of extinction Conclusion:  Climate change scientists are very confident (90%)with the predicted temperature increases

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Chapter 2, Problem 50 is Solved
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Textbook: Thomas' Calculus Early Transcendentals
Edition: 12
Author: George B. Thomas
ISBN: 9780321588760

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Find the limits in Exercises 4163