Announcements. Homework 6 due Thursday

Transcription

1 Tuesday, October 23rd. Announcements. Homework 6 due Thursday Lecture #13-1

2 Lecture #13-2

3 Highlights that although natural gas is less bad for the environment than coal, it is much more expensive. (Although perhaps the power companies were overstating the price difference) In the absence of government regulations on CO 2 emissions, it seems likely that many new coal plants will be built in the coming years Lecture #13-3

4 Highlights the influence of the recent Supreme Court decision in Massachusetts v. Environmental Protection Agency. Judges and regulators are pointing to it to justify decisions limiting greenhouse gas emissions. What was the Massachusetts v. EPA case? From Wikipedia - Massachusetts v. Environmental Protection Agency is a U.S. Supreme Court case decided 5-4 on April 2, 2007 in which twelve states and several cities of the United States brought suit against the United States Environmental Protection Agency (EPA) to force that federal agency to regulate carbon dioxide and other greenhouse gases as pollutants. The Administrator of the Environmental Protection Agency determined in 2003, first, that the EPA lacked authority under the Clean Air Act to regulate carbon dioxide and other greenhouse gases (GHGs), second, that even if the EPA did have such authority the EPA declined to regulate carbon dioxide and other GHGs. The petitioners asserted that the EPA does have authority over global warming and greenhouse gases because of the broad wording of the statute, and that the EPA's decision not to regulate greenhouse gases exceeded the scope of its discretion under the law. Majority opinion - The petitioners were found to have standing, the Clean Air Act does give EPA the authority to regulate tailpipe emissions of greenhouse gases, and the EPA is required to review its contention that it has discretion in regulating carbon dioxide and other greenhouse gas emissions - specifically, its current rationale for not regulating was found to be inadequate, and a scientific basis is now required. In addition, the majority report commented that "greenhouse gases fit well within the Clean Air Act!s capacious definition of air Lecture #13-4 pollutant.

5 Last time we started into the greenhouse effect. We want to understand what it is, how it works and the role played by CO 2 and other greenhouse gasses? Why does a real greenhouse stay warm inside? The glass lets in the sun s rays, warming up the plants, soil and air inside, but then blocks the warm air from escaping. The greenhouse effect for our planet makes the near Earth atmosphere warmer than it would otherwise be without the presence of heat trapping gasses. The Royal Greenhouses of Laeken in Brussels. The greenhouse effect is very well established scientifically. Without it, as we ll see, Earth s surface would be much colder, below the freezing point of water & life as we know it would not have evolved. Lecture #13-5

6 Before we try to understand how the greenhouse effect works, we ll calculate what Earth s temperature would be without it. This requires some physics! Roughly speaking, Earth s temperature is set by an energy balance with the Sun. Every day the Earth absorbs energy in the form of light from the sun. Every day the Earth must radiate away this same amount of energy. If it doesn t, it will either heat up, or cool down. How much the Earth radiates depends on its temperature. If its temperature increases, it radiates more and viceversa. This is a very important point. It is what it means for Earth to be in thermal equilibrium with the Sun. Let s look at all the pieces of this process, starting with the Sun. Where does the Sun s energy come from? Lecture #13-6

7 The Sun is made of hydrogen (74%) and helium (25%) and is powered primarily by the nuclear fusion of hydrogen into helium. The key ingredient to understanding nuclear fusion is Einstein s famous equation E = m c 2 which says that mass is another form of energy. How much energy does 1 kg of mass represent? Let s work this out as an inclass assignment c is the speed of light c = 3 x 10 8 m/s Lecture #13-7

8 The key ingredient to understanding nuclear fusion is Einstein s famous equation E = m c 2 which says that mass is another form of energy. How much energy does 1 kg of mass represent? E = (1 kg) x (3 x 10 8 m/s) 2 = 9 x J c is the speed of light c = 3 x 10 8 m/s Lecture #13-8

9 Part 2.. The world used 447 Quads of energy in If all this energy was in the form of mass, how many kilograms would this be? Recall. 1 Quad = 1 quadrillion BTU = BTU 1 BTU = 1050 Joules Lecture #13-9

10 In class assignment.. The world used 447 Quads of energy in If all this energy was in the form of mass, how many kilograms would this be? Recall. 1 Quad = 1 quadrillion BTU = BTU 1 BTU = 1050 Joules First convert 447 Quads into Joules E = 447 Quads = (447 x BTU)(1050 J/BTU) = 4.7 x J Solving E = mc 2 for m gives m = E / c 2 = (4.7 x J)/(3 x 10 8 m/s) 2 = 5200 kg Lecture #13-10

11 Solving E = mc 2 for m gives m = E / c 2 = (4.7 x J)/(3 x 10 8 m/s) 2 = 5200 kg This is an amazing result, that all the energy we burn in a year is equivalent to about 10,000 pounds of mass energy! This is why nuclear power is so attractive. But neither fusion, nor fission convert all the mass energy that one starts with into useful energy, only a tiny bit. This is about 14 kg s worth of energy per day to supply the world Lecture #13-11

12 Back to fusion energy & the Sun.. In nuclear fusion, two light nuclei combine to produce a heavier nuclei. However, the mass of the heavier nucleus is slightly less than the sum of the masses of the original two lighter nuclei. The difference in mass energy comes out of the reaction in some other form, e.g. light. The main fusion reaction in the Sun involves the merger of two hydrogen nuclei into a helium nucleus. Although the amount of energy released by each nuclear fusion reaction is small, the Sun is huge. Overall, some 4 billion kilograms of matter are converted into energy every second in the Sun. The Sun is about 1.3 million times Earth s size. Its total mass is 2 x kg. The Earth absorbs some tiny fraction of this energy. Lecture #13-12

13 How much energy does the Earth receive from the Sun each day? As the light from the sun spreads out, it gets weaker. At the radius of Earth s orbit, the sunlight has power density of 1.35 kilowatts/(meter) 2 This is known as the solar constant, even though it is not precisely constant. It varies by a few percent over the year, as Earth s slightly elliptical orbit moves our planet a little closer, or farther from the Sun. Lecture #13-13

14 How much of the Sun s power is the Earth absorbing on average? From the Sun s perspective, the Earth appears as a disk with radius R earth = 6400 km 30% of the 1.35 kilowatts/(meter) 2 that hits the Earth is reflected back into space, by clouds, interactions with the air and the Earth s surface. This figure is called Earth s albedo. The total solar power absorbed by Earth and the atmosphere is then 2 Area =! R earth P absorbed = (solar constant)(1-albedo)(area of Earth s disk) = (1.35 kw/m 2 )(1-0.30)(3.14)(6,400,000 m) 2 = 1.2 x kilowatts = 120,000 Gigawatts A truly huge number.. Lecture #13-14

15 In order for Earth s temperature to remain constant on average, it must be re-emitting this same amount of power back into space. How does this work? All hot objects radiate energy in a way that is characteristic of their temperature.. We are familiar with this from thermal imaging. For warm blooded animals, such as humans, the energy radiated is in the infrared range, outside of the range of our vision. Thermal imaging devices detect this and convert it to images we can see. This has many applications, from military ones to detecting heat leaks from buildings. Note: this doesn t mean we can t make use of the incoming solar power! False color thermal image of a dog Lecture #13-15

16 It s helpful to have an overview of the properties of light.. Light is a type of wave built out of electric and magnetic fields We ll talk more about these later on when we talk about electricity Light waves travel at the speed of light, c = 3 x 10 8 m/s. Like other kinds of waves, light waves have an amplitude (strength) and a wavelength. The energy carried by the light depends both on the strength of the wave and its wavelength. Lecture #13-16

17 Visible light has a range of wavelengths between nm, 1 nm = 1 nanometer = 10-9 meters At longer wavelengths, there are infrared radiation, microwaves and radio waves. At shorter wavelengths, there are ultraviolet rays, X-rays and gamma rays. Lightwaves come quantized in packets called photons. The energy of a photon is inversely proportional to wavelength. So, a short wavelength photon has higher energy than a long wavelength photon, gamma rays being the most energetic of all. Lecture #13-17

18 Sunlight is a mixture of different wavelengths of light. A prism refracts (changes the angle of) light of different wavelengths and separates the different colors. A hot object radiates light with a mixture of wavelengths characteristic of its temperature. For a sort of perfect thermal emitter known as a blackbody, the spectrum of emitted light can be calculated and has a fairly simple form known as the blackbody spectrum. A blackbody is both a perfect emitter and a perfect absorber - hence the name blackbody. Physicists often make the approximation that an object - like the Earth or the Sun - is a blackbody, even if it is not a perfect absorber at all wavelengths. Lecture #13-18 Blackbody spectrum graphs power emitted vs. wavelength

19 We see that the peak in the blackbody spectrum moves to shorter wavelength - higher energy - as the temperature is increased. This effect has a simple mathematical description known as Wien s displacement law! peak = b T Wavelength of peak Temperature Blackbody spectrum graphs power emitted vs. wavelength b = 2.9 x 10-3 m K Wien s displacement constant Lecture #13-19

20 ! peak = b T b = 2.9 x 10-3 m K What is the peak wavelength for human body temperature? In Celsius, body temperature is 37C, which is ( )K = 310K.! peak = 2.9 " 10#3 mk 310K = 9.3 " 10 #6 m = 9300nm Recall that visible light is in the range nm in wavelength. The peak wavelength we ve found is in the infrared range. Blackbodies below about 700K emit very little visible radiation and appear black. This is why we can t see each other at night with our eyes. Lecture #13-20

21 What about the Sun? T sun = 5780 K This is the temperature at the Sun s surface. The temperature at the Sun s core is thousands of times higher, T core =13,600,000 K.! peak = 2.9 " 10#3 mk 5780K = 5.0 " 10 #7 m = 500nm Right in the middle of the visible range. An object at this temperature looks white to us. Lecture #13-21

22 When we look at the Sun through the atmosphere, it appears yellow because the blue light has been preferentially scattered out. This effect is most pronounced at sunset, when the sun looks red. At this time of day, sunlight is passing through the greatest length of atmosphere to reach us. We see the blue light in the color of the sky. Lecture #13-22

23 To figure out what the temperature of the Earth would be without the greenhouse effect, we need one more physics input The Stefan-Boltzmann law for the power emitted by a blackbody. P =! AT 4 P = power emitted, A = surface area, T= temperature! = 5.7 " 10 #8 Watts m 2 K 4 Stefan-Boltzmann constant We know that the Earth has to be emitting as much power as it absorbs from the Sun P = 1.2 x watts. The surface area of the Earth is A = 5.1 x m 2 Lecture #13-23

24 P =! AT 4 P = power emitted, A = surface area, T= temperature! = 5.7 " 10 #8 Watts m 2 K 4 We know that the Earth has to be emitting as much power as we receive from the Sun, P = 1.2 x watts. The surface area of the Earth is A = 5.1 x m 2 T = ( P 1.2 " W! A )1/4 = ( (5.7 " 10 #8 Wm #2 K #4 )(5.1" m 2 ) )1/4 = 253K Lecture #13-24

25 T = ( P 1.2 " W! A )1/4 = ( (5.7 " 10 #8 Wm #2 K #4 )(5.1" m 2 ) )1/4 = 253K This gives T = -4F, well below the freezing point of water. This is very close to the temperature at the top of Earth s atmosphere (255K). The average temperature at Earth s surface is 288K = 15C = 59F. The difference is due to the greenhouse effect - the heat trapping properties of certain atmospheric gasses. Lecture #13-25