Goals for Today 1.COMPARE infrared, ultraviolet, and visible electromagnetic radiation in terms of energy per photon, frequency, and wavelength 2.COMPARE the amount and type of energy emitted by objects at different temperatures 3.PREDICT the effect of varying the factors that determine the solar constant of a planet EOSC Radiation Balance I

Earn 1% extra credit by completing an on-line survey as part of a major initiative to improve science education at UBC 1.Complete the survey by Friday, September 18 th at login: saess password: earth 2.Complete the survey again at the end of the term, dates TBA. This link is also posted on the course website

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

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

Key units for Today’s Goals (International System; SI) Force (Newton; N) = mass x acceleration A force of 1N accelerates a mass of 1kg at a rate of 1m/sec 2 Energy or work (Joule; J) = Force x distance 1 J is the energy produced (or work done) by a force of 1N moving an object by 1 m Power (Watt; W) = Energy / time Amount of energy that is emitted, absorbed or reflected per unit time (1J/sec) Energy flux or intensity (Watt per m 2 ; W/m 2 ) = Power / area Amount of energy that is emitted, absorbed or reflected per unit area per unit time (J/m 2 *sec) notes

Scientific Notation Example: Write a really big number in scientific notation: 63,500,000,000 is more easily written as: 6.35*10 10 which means 6.35 x 10,000,000,000 (10 zeros) Example: Write a really small number in scientific notation: is more easily written as: 6.35* which means 6.35/10,000,000,000, i.e.6.35/10 10 (which is the same thing as 6.35* ) notes

Absolute temperature and the Kelvin scale As heat is applied:  atoms vibrate faster  temperature increases Absolute temperature (°K) = Temperature in °C Absolute zero = temperature at which atoms are not vibrating (-273°C) notes

Useful Geometry notes Surface area of a CIRCLE =  *r 2 r Surface area of a SPHERE = 4  *r 2 r Surface area of sphere/surface area of circle = 4

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

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

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

LOW frequency LONG wavelength Properties of electromagnetic waves The speed of light (c) is constant: c = 3*10 8 metres/second = wavelength = distance between adjacent crests = frequency = number of crests that passes a fixed point per second c = * (m/s = m * #/s) OR = c / (m = m/s / #/s) HIGH frequency SHORT wavelength LOWER energy HIGHER energy

CLICKER Q: Which one of these stoves is the hottest? ABC

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

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

…Wien’s law…T sun = 5785 K Emissions Spectra for Sun and Earth 0.5  m

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

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

F is the energy emitted by the Sun, per unit time, per unit area, expressed in W/m 2 [J/s*m 2 ]  is a constant [ 5.67*10 -8 W/m 2 K 4 ] T is the absolute temperature (K) Stefan-Boltzmann’s law (very useful!) F =  T 4 (The energy emitted by a star is proportional to its temperature to the 4 th power)

F =  T 4 (Stefan-Boltzmann's law) F Sun = (5.67*10 -8 W/m 2 K 4 )*(5785 K) 4 = 6.35*10 7 (W/m 2 ) = 63,500,000 W/m 2 How much energy leaves EACH square metre of the Sun’s surface? Every single square metre of the Sun’s surface emits 63.5 million Joules every second

F =  T 4 (Stefan-Boltzmann's law) F Sun =  *(T Sun ) 4 …calculations w/Stefan-Boltzmann… = 63,500,000 W/m 2 How much energy leaves EACH square metre of the Sun’s surface? Every single square metre of the Sun’s surface emits 63.5 million Joules every second

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

Sun’s radius (r sun ) = 7*10 8 m (that’s 700,000 km) r Sun Total energy emitted by the Sun Sun’s total surface area = 4  (r sun ) 2 = 6.16*10 18 m 2 Total energy emitted by the Sun: = surface area * energy per m 2 = 6.16*10 18 m 2 * 6.35*10 7 (W/m 2 ) = 3.91*10 26 W

Sun’s radius (r sun ) = 700,000,000 m (that’s 700,000 km) r Sun Total energy emitted by the Sun …a little geometry… Sun’s total surface area = 6.16*10 18 m 2 Total energy emitted by the Sun: = surface area * energy per m 2 …multiplication… = 3.91*10 26 W

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 r orb What happens to the energy after it leaves the Sun?

r orb Radius of Earth’s orbit (r orb ) = 150*10 9 m Surface area of sphere with radius r orb : = 4  (150*10 9 m) 2 = 2.83*10 23 m 2 Solar energy received per unit area at the distance of the earth’s orbit: = F orbit = 3.91*10 26 W / 2.83*10 23 m 2 = 1,370 W/m 2 How much solar energy reaches Earth? This is the SOLAR CONSTANT

r orb Earth-Sun distance (r orb ) = 150*10 9 m …a little more geometry… Surface area of sphere with radius r orb = 2.83*10 23 m 2 …spread the total solar energy over this area… Total solar energy/area of sphere at distance r orb F orbit = 1,370 W/m 2 How much solar energy reaches Earth? This is the SOLAR CONSTANT

Clicker question: Which planet has the smallest solar constant? A.Mercury B.Venus C.Earth D.Mars E.Jupiter

How much TOTAL solar energy does the Earth capture every second? W/m 2 Earth’s radius is 6371 km (6.37*10 6 m) Earth’s cross section is  (6.37*10 6 m) 2 = 1.28*10 14 m 2 The total amount of sun energy intercepted by Earth: = E in = 1,370 (W/m 2 ) * 1.28*10 14 m 2 = 1.75*10 17 W

How much energy does the AVERAGE square metre get?

E in = 1.75*10 17 W (this is the total intercepted) Spread this over the entire surface area of the Earth to get the AVERAGE W/m 2 (F in ) F in = 1.75*10 17 / 4  (6.37*10 6 m) 2 = 342 W/m 2 Energy received by the AVERAGE square metre

Amount of solar radiation that reaches the top of the Earth’s atmosphere Next…how do we use this information to figure out the mean temperature of Earth? (Solar Constant)/4 342 W/m 2

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 4 th power The Earth’s SOLAR CONSTANT (1370 W/m 2 ) 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/m 2 at the top of the atmosphere The amount of solar energy coming in is crucial to determining Earth’s temperature Summary: Radiation Balance I Relevance: Earth’s habitability, energy resources