10/31/2017. Calculating the temperature of earth (The greenhouse effect) IR radiation. The electromagnetic spectrum

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1 Calculating the temperature of earth (The greenhouse effect) EM radiation so far Spectrum of EM radiation emitted by many objects may be approximated by the blackbody spectrum Blackbody spectrum (plot of emitted intensity versus l)depends only on temperature Temperature determines a) Total emitted EM power S-B law: P = s a e T 4 b) Shape of spectrum range of l, l peak 1/T Today s lecture What is the greenhouse effect? Apply BB spectrum and S-B law to calculate temperature of earth s surface What determines the temperature of the earth s surface? Why do greenhouse gases in the atmosphere cause it to heat up? Lecture 19 : Understand greenhouse effect (good) Calculate current temperature of earth Understand effect of extra GH gases (bad) Reminders: HW 8 available Reading quiz in just a second The electromagnetic spectrum Your car is sitting in the bright sun. The inside of the car gets much hotter than the air next to it. Why? a. The car absorbs light energy from sun better than the pavement. b. Sunlight causes chemical reactions in car materials that give off heat. c. Electrical appliances such as clock that run all the time in car causes it to heat up. d. The windows let in energy but do not let it escape. e. None of the above make sense, must be different explanation. The greenhouse effect in your car EM energy gets into car but can t get out? How does that happen? We all know visible light travels easily through glass (windows!) But what about IR radiation? Lets try an experiment.. IR radiation This remote temperature sensor works by measuring the infrared spectrum of the thing I point it at. Try it out. Now we put a piece of glass in the way. What will temperature sensor read? a. Same temperature, b. Slightly less, c. Much less, d. Absolute zero 1

2 power 10/31/017 The greenhouse effect in your car BB spectra of emitted EM radiation from sun and car UV Visible sun 40 C inside car IR wavelength Remember effect of T on shape of BB spectrum Sun is very hot (5800K) and emits most power as visible light, which goes through the car window. The interior of the car absorbs this energy and heats up. Inside of car is less hot than sun (310 K) so emits most power in the IR, which cannot go out through the glass. Extra energy is trapped inside car making it hotter than the surrounding environment The greenhouse effect (not a bad thing). What are green house gases? CO, H O and others Why does the temperature of the earth s surface depend on the presence of green house gases in the atmosphere? Greenhouse gases insulate the earth, increase its temperature (Without them, life would not survive.) Exactly how does the temperature change now we are adding more CO? Details of this get complicated But the temperature at the surface can be understood by considering a power balance and using just the BB spectrum and SB law. Once we understand what determines the temperature, we can see why extra greenhouse gases are gradually causing it to heat up. How can we calculate the temperature of the earth (T E )? Consider a power balance: 1) Power in: Visible light energy from hot sun hits the earth and is absorbed ) Power out: The cool earth (at temp. T E ) radiates power out mainly as IR radiation 3) If earth remains at a constant temperature (ignoring the v.v.v. slow temperature increase due to global warming), it must have constant thermal energy: Depends on T E, so we can calculate temperature of earth! First lets calculate the power arriving at the earth from the sun: If R e is the radius of the earth, what is the area of the earth absorbing sunlight? a) pr e b) pr e c) 4pR e d) 4/3 p R e 3 P in = 1380 W/m x pr e x 0.7 = 1. x W solar power/m at earth area of earth absorbing sunlight fraction of sunlight absorbed by earth Now lets calculate the power radiated from earth at temperature T E : Use S-B law for a black body: P = s x T E 4 x a If R e is the radius of the earth, what is the area of the earth that emits EM radiation (mainly IR)? a) pr e b) pr e c) 4pR e d) 4/3 p R 3 e

3 From Stefan Boltzman law: P space = s x T E 4 x surface area of Earth X f Fraction of radiation that actually makes it through atmosphere to space W/m x pr e x 0.7 = s X T E4 X 4pR e X f Can we rearrange this to find a value for T E? 1380 x 0.7 = 4 x (5.67 x 10-8 ) x T E4 x f 4.6 x 10 9 = T E4 x f T E4 = 4.6 x 10 9 / f T E = sqrt (sqrt (4.6 x 10 9 / f )) Power balance equation If there are no greenhouse gases in the atmosphere, f = 1. As GH gases increase, f decreases. More greenhouse gases: Smaller fraction of earth s IR radiation gets through atmosphere f decreases T E increases Earth is warmer! First consider a world with NO GH gases. T E = sqrt (sqrt (4.6 x 10 9 / f )) Lets try some numbers! First assume that we have NO GH gases around the earth f=1 T E = sqrt (sqrt (4.6 x 10 9 / 1 )) = Why doesn t all of the radiated IR go directly into space? Certain types of molecules in the atmosphere called greenhouse gases absorb IR and send it back towards earth. Carbon dioxide, H O, but not oxygen or nitrogen. Because of GH gases (mostly naturally occurring) only about 61% of IR radiated from surface of earth actually makes it to space (f = 0.61) No GH gases Water would freeze! Life would be impossible! The surface of the earth is not this cold, because the atmosphere naturally contains GH gases. Naturally occuring GH gases are good for us! Why doesn t all of the radiated IR go directly into space? Certain types of molecules in the atmosphere called greenhouse gases absorb IR and send it back towards earth. Carbon dioxide, H O, but not oxygen or nitrogen. Because of GH gases (mostly naturally occurring) only about 61% of IR radiated from surface of earth actually makes it to space (f = 0.61) So what T E does f = 0.61 imply? T E = sqrt (sqrt (4.6 x 10 9 / f )) = sqrt (sqrt (4.6 x 10 9 / 0.61 )) = 89 K = 16 C ~ 61 F With GH gases With GH gases So what T E does f = 0.61 imply? Very close to actual value of 87 K Naturally occurring greenhouse gases keep the planet habitable. 3

4 What is the current state of global warming? Temperature of earth has risen 1 F (~0.5 C) in the 0 th century..5 to 10 F rise predicted for the next century. Is that significant? - At peak of last ice age (0,000 years ago), global temp was only 10 F colder and most of North America was under 3000 feet of ice. Lets process all that with some clicker questions.. When we increase the concentration of GH gases in the atmosphere by burning fossil fuels etc, what happens? a. Less IR reflected back to earth, (lower f value) b. Less IR reflected back to earth, (higher f value) c. More IR reflected back to earth, (lower f value) d. More IR reflected back to earth, (higher f value) e. None of the above After the concentration of greenhouse gases has gone up due to burning fossil fuels (assume the temperature of the earth has stabilized), the total power emitted by earth and making it through the atmosphere to space, a. goes up b. goes down c. stays the same To maintain the SAME amount of EM power reaching outer space (still balancing power in from the sun), what changes must occur at the surface of the earth? a. More EM power must be emitted higher surface temperature b. More EM power must be emitted lower surface temperature c. Less EM power must be emitted lower surface temperature d. Less EM power must be emitted lower surface temperature e. Neither emitted power or surface temperature changes If we look at Earth from outer space with remote temperature probe (measures the amount of IR radiation arriving at the probe from earth to determine temperature), what temperature do we measure? a. 55K b. 87 K c. 95 K d. 000 K Now add clouds to the simulation. What is their effect? a. Clouds decrease temperature because they reflect part of sunlight back to space. b. Clouds increase temperature because they absorb IR radiation from earth. c. Clouds increase temperature because the sunlight is reflected then absorbed by the greenhouse gases in the atmosphere. d. a or b, e. a or c GH gas summary: - Transmit all EM power from sun at visible l - Partially reflect EM power from surface of earth at IR l - Surface temperature must rise in presence of GH gases to maintain power balance No GH gases: T E = 55 K With GH gases: T E = 87 K 4

5 Why is earth surface hotter in presence of GH gases? Thickness of arrows represents amount of power Color of arrows represents wavelength NO GH GASES WITH GH GASES 1. In both cases, the earth is at a stable T (constant thermal energy). For stable T, P in (from sun) = P space (lost to space) 3. Since P in never changes (is same in both cases), P space is the same in both cases 4. No GH gases: P earth (power radiated from surface of earth) = P space 5. With GH gases: P earth = P space + P reflected P earth is BIGGER in presence of GH gases Temp of surface higher in presence of GH gases (from SB law) 5