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Goals for Today

EOSC 112 - Radiation Balance I. Goals for Today. COMPARE infrared, ultraviolet, and visible electromagnetic radiation in terms of energy per photon, frequency, and wavelength COMPARE the amount and type of energy emitted by objects at different temperatures

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Goals for Today

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  1. EOSC 112 - Radiation Balance I Goals for Today • COMPARE infrared, ultraviolet, and visible electromagnetic radiation in terms of energy per photon, frequency, and wavelength • COMPARE the amount and type of energy emitted by objects at different temperatures • PREDICT the effect of varying the factors that determine the solar constant of a planet http://www.elearning.ubc.ca/vista

  2. Earn 1%extra credit by completing an on-line survey as part of a major initiative to improve science education at UBC • Complete the survey by Friday, September 18that http://www.eos.ubc.ca/scripts/courses/saess/survey.htmllogin: saesspassword: earth • Complete the survey again at the end of the term, dates TBA. This link is also posted on the course website

  3. RELEVANCE Mars (too cold) Venus (too hot) Earth (just right) The flux of solar radiation reaching Earth is one of the main factors dictating its mean temperature, and therefore its habitability

  4. RELEVANCE Photovoltaics Solar radiation could potentially provide an inexhaustible source of energy Artificial photosynthesis

  5. What do you need to know to figure out how much solar radiation the Earth receives, per square metre?

  6. What’s the MINIMUM information (data) you’d need to figure out how much solar radiation the Earth receives, on average, per square metre? • The Sun’s surface temperature • The Sun’s radius • The Earth’s surface temperature • The Earth’s radius • The distance from the Sun to the Earth • The Earth’s rotation rate • 1, 2, & 4 • 1, 4 & 5 • 2, 3, 4 & 5 • 1, 2, & 5 • All of them

  7. How could we figure out the temperature of the Sun? T? What can we actually measure?

  8. Properties of electromagnetic waves l = wavelength = distance between adjacent crests n= frequency = number of crests that passes a fixed point per second The speed of light (c) is constant: c = 3*108 metres/second HIGH frequency LOW frequency c = l * n (m/s = m * #/s) OR l = c / n (m = m/s / #/s) SHORT wavelength LONG wavelength HIGHER energy LOWER energy

  9. CLICKER Q: Which one of these stoves is the hottest? A B C

  10. CLICKER Q: Which one of these stoves is emitting radiation with the LONGEST wavelength? A B C D. They are all emitting at the same wavelength

  11. Wien’s law (as temperature increases, the wavelength (l) of radiation decreases) lm = w / T lm = wavelength of maximum intensity (mm) w = Wien’s constant (2897 mm K) T = absolute temperature (K) What wavelengths of radiation does the Sun emit? (What about Earth? What about you?)

  12. Emissions Spectra for Sun and Earth …Wien’s law…Tsun = 5785 K 0.5 mm

  13. Clicker question: Where would the peak wavelength of radiation occur for a human? • About halfway between the Sun and Earth peaks • Just to the left of the Earth peak • Same place as the Earth peak • Just to the right of the Earth peak • There is not enough information

  14. How is ENERGY emitted related to temperature? If you start with a cold object and add heat…  atoms vibrate faster  temperature increases  some of the kinetic energy is emitted as electromagnetic waves  electromagnetic waves propagate from the radiating object  emitted radiation increases with increasing temperature

  15. Stefan-Boltzmann’s law (very useful!) (The energy emitted by a star is proportional to its temperature to the 4th power) F = s T4 • F is the energy emitted by the Sun, per unit time, per unit area, expressed in W/m2[J/s*m2] • is a constant [5.67*10-8 W/m2K4] T is the absolute temperature (K)

  16. How much energy leaves EACH square metre of the Sun’s surface? F = s T4(Stefan-Boltzmann's law) FSun = s *(TSun)4 …calculations w/Stefan-Boltzmann… = 63,500,000 W/m2 Every single square metre of the Sun’s surface emits 63.5 million Joules every second

  17. How would you figure out the total energy emitted by the Sun? Stefan-Boltzmann tells us energy per second per square metre…

  18. Total energy emitted by the Sun Sun’s radius (rsun) = 700,000,000 m(that’s 700,000 km) rSun …a little geometry… Sun’s total surface area = 6.16*1018 m2 Total energy emitted by the Sun: = surface area * energy per m2 …multiplication… =3.91*1026 W

  19. rorb What happens to the energy after it leaves the Sun? The total amount of energy initially emitted by the Sun’s surface is spread over a larger area as it moves away from the Sun

  20. rorb How much solar energy reaches Earth? Earth-Sun distance (rorb) = 150*109 m …a little more geometry… Surface area of sphere with radius rorb = 2.83*1023 m2 …spread the total solar energy over this area… Total solar energy/area of sphere at distance rorb Forbit = 1,370 W/m2 This is the SOLAR CONSTANT

  21. Clicker question: Which planet has the smallest solar constant? • Mercury • Venus • Earth • Mars • Jupiter

  22. How much TOTAL solar energy does the Earth capture every second? 1370 W/m2 . Earth’s radius is 6371 km (6.37*106 m) Earth’s cross section is p(6.37*106m)2 = 1.28*1014 m2 The total amount of sun energy intercepted by Earth: = Ein = 1,370 (W/m2) * 1.28*1014 m2 = 1.75*1017 W

  23. How much energy does the AVERAGE square metre get?

  24. Energy received by the AVERAGE square metre • Ein = 1.75*1017 W (this is the total intercepted) • Spread this over the entire surface area of the Earth to get the AVERAGE W/m2 (Fin) • Fin = 1.75*1017 / 4p(6.37*106 m)2 • = 342 W/m2

  25. Amount of solar radiation that reaches the top of the Earth’s atmosphere (Solar Constant)/4 342 W/m2 Next…how do we use this information to figure out the mean temperature of Earth?

  26. Summary: Radiation Balance I • Objects with temperatures above absolute zero emit electromagnetic radiation • Hotter objects emit radiation with shorter wavelengths (higher frequencies & greater energy per photon) than cooler objects • The energy an object radiates is proportional to its temperature raised to the 4th power • The Earth’s SOLAR CONSTANT (1370 W/m2) depends on the energy output by the Sun, and the Earth-Sun distance • Because Earth is a spinning sphere, on average, Earth receives 342 W/m2 at the top of the atmosphere • The amount of solar energy coming in is crucial to determining Earth’s temperature Relevance: Earth’s habitability, energy resources

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