Radiation from the Sun

Black-body radiation spectrum/blackbody-spectrum_en.html spectrum/blackbody-spectrum_en.html

Wien’s law λ max T = constant (2.9 x mK)

Example The sun has an approximate black-body spectrum and most of its energy is radiated at a wavelength of 5.0 x m. Find the surface temperature of the sun. From Wien’s law 5.0 x x T = 2.9 x T = 5800 K

Spectral ClassColourTemperature/K OBlue – BBlue - white – AWhite7 500 – FYellow - white6 000 – GYellow4 500 – KYellow - red3 000 – MRed2 000 – In the astrophysics option you need to remember the classes and their order. How will you do this?

Spectral classes Oh be a fine girl….kiss me!

Stefan-Boltzmann law The amount of energy per second (power) radiated from a body depends on its surface area and absolute temperature according to P = eσAT 4 where σ is the Stefan-Boltzmann constant (5.67 x W.m -2.K -4 ) and e is the emissivity of the surface ( e = 1 for a black object)

Example By what factor does the power emitted by a body increase when its temperature is increased from 100ºC to 200ºC?

Example By what factor does the power emitted by a body increase when its temperature is increased from 100ºC to 200ºC? Emitted power is proportional to the fourth power of the Kelvin temperature, so will increase by a factor of /373 4 = 2.59

Graph sketching

Global Warming

The Sun The sun emits electromagnetic waves (gamma X-rays, ultra-violet, visible light, infra-red, microwaves and radio waves) in all directions.

The earth Some of these waves will reach the earth

Reflected Around 30% will be reflected by the earth and the atmosphere. This is called the earth’s albedo (0.30). (The moon’s albedo is 0.12) Albedo is the ratio of reflected light to incident light. 30%

Albedo The Albedo of a body is defined as the ratio of the power of radiation reflected or scattered from the body to the total power incident on the body.

Albedo The albedo depends on the ground covering (ice = high, ocean = low), cloud cover etc.

Absorbed by the earth Around 70% reaches the ground and is absorbed by the earth’s surface. 70%

Absorbed by the earth Infrared This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum)

Temperature of the earth with no atmosphere? Remember the solar constant is around 1360 W.m -2. This can only shine on one side of the Earth at a time, and since the silhouette of the earth is a circle, the power incident = 1360 x πr 2 = 1360 x π x (6.4 x 10 6 ) 2 = 1.75 x W

Temperature of the earth with no atmosphere? Power incident on earth = 1.75 x W Since the albedo is 30%, 70% of the incident power will be absorbed by the Earth 70% of 1.75 x W = 1.23 x W

Temperature of the earth with no atmosphere? Power absorbed by Earth = 1.23 x W At equilibrium, the Power absorbed = Power emitted Using the Stefan Boltzmann law; 1.23 x = eσAT 4

Temperature of the earth with no atmosphere? Using the Stefan Boltzmann law; 1.23 x = eσAT x = 1 x 5.67 x x 4πr 2 x T 4 This gives T = 255 K (-18°C)

Temperature of the earth with no atmosphere? T = 255 K (-18°C) This is obviously much colder than the earth actual temperature. WHY?

Absorbed by the earth Infrared This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum)

Absorbed Various gases in the atmosphere can absorb radiation at this longer wavelength (resonance) C O O C H H H H They vibrate more (become hotter) HH O

Greenhouse gases These gases are known as “Greenhouse” gases. They include carbon dioxide, methane, water and N 2 O. C O O C H H H H HH O

Transmittance curves

Re-radiated These gases in the atmosphere absorb the infra-red radiation and re-emit it, half goes into space but half returns to the earth.

It’s complex!!!

Balance There exists a balance between the energy absorbed by the earth (and its atmosphere) and the energy emitted. Energy in Energy out

Balance This means that normally the earth has a fairly constant average temperature (although there have been big changes over thousands of years) Energy in Energy out

Balance Without this normal “greenhouse effect” the earth would be too cold to live on. Energy in Energy out

Greenhouse gases Most scientists believe that we are producing more of the gases that absorb the infra-red radiation, thus upsetting the balance and producing a higher equilibrium earth temperature. This is called the enhanced greenhouse effect.

What might happen?

Polar ice caps melt

What might happen? Higher sea levels and flooding of low lying areas as a result of non-sea ice melting and expansion of water

Coefficient of volume expansion Coefficient of volume expansion is defined as the fractional change in volume per unit temperature change

Coefficient of volume expansion Given a volume V 0 at temperature θ 0, the volume after temperature increase of Δθ will increase by ΔV given by ΔV = γV 0 Δθ

Definition Coefficient of volume expansion is the fractional change in volume per unit temperature change. ΔV = γV 0 Δθ

Example The area of the earth’s oceans is about 3.6 x 10 8 km 2 and the average depth is 3.7 km. Using γ = 2 x K -1, estimate the rise in sea level for a temperature increase of 2K. Comment on your answer.

Example The area of the earth’s oceans is about 3.6 x 10 8 km 2 and the average depth is 3.7 km. Using γ = 2 x K -1, estimate the rise in sea level for a temperature increase of 2K. Comment on your answer. Volume of water = approx depth x area = 3.6 x 10 8 x 3.7 = 1.33 x 10 9 km 3 = 1.33 x m 3 ΔV = γV 0 Δθ ΔV = 2 x x 1.33 x x 2 = 5.3 x m 3 Δh = ΔV/A = 5.3 x /3.6 x = 1.5 m Evaporation? Greater area cos of flooding? Uniform expansion?

What else might happen? More extreme weather (heatwaves, droughts, hurricanes, torrential rain)

What might happen? Long term climate change

What might happen? Associated social problems (??)

Evidence?

Ice core research Weather records Remote sensing by satellites Measurement! How do ice cores allow researchers to see climate change? | GrrlScientist | Science | guardian.co.uk How do ice cores allow researchers to see climate change? | GrrlScientist | Science | guardian.co.uk

Other possible causes of global warming? Increase in solar activity Volcanic activity increasing CO2 concentrations Earth orbitting closer to sun?!

Surface heat capacitance C s Surface heat capacitance is defined as the energy required to increase the temperature of 1 m 2 of a surface by 1 K. Cs is measured in J.m -2.K -1. Q = AC s ΔT

Example Radiation of intensity 340 W.m -2 is incident on the surace of a lake of surface heat capacitance Cs = 4.2 x 10 8 J.m -2.K -1. Calculate the time to increase the temperature by 2 K. Comment on your answer.

Example Radiation of intensity 340 W.m -2 is incident on the surface of a lake of surface heat capacitance Cs = 4.2 x 10 8 J.m -2.K -1. Calculate the time to increase the temperature by 2 K. Comment on your answer. Each 1m 2 of lake receives 340 J.s -1 Energy needed to raise 1m 2 by 2 K = Q = AC s ΔT = 1 x 4.2 x 10 8 x 2 = 8.4 x 10 8 J Time = Energy/power = 8.4 x 10 8 /340 = seconds = 29 days Sun only shines approx 12 hours a day so would take at least twice as long