Energy, Power and Climate Change

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Energy, Power and Climate Change

• Wiens Law and Stefan-Boltzmann Law

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Black-body Radiation

• Radiation given out from a hot object depends on
  many things.
• Black-body radiation is the radiation emitted by
  a perfect emitter - a perfect emitter emits all
  the radiation that it absorbs
• A perfect emitter is also a perfect absorber - a
  black object absorbs all of the light energy
  falling on it.

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Black-body radiation depends on temperature -
each temperature has a range of emitted
wavelengths
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Wiens Law
Relates wavelength to surface temperature
?0T constant 2.90 x 10-3 K m
Equation in Astrophysics Option E of Reference
Table
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Wiens Law Example

• The sun has an approximate black-body spectrum
  with most of the energy radiated at a wavelength
  of 5.0 x 10-7 m. Find the surface temperature
  of the sun.

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Radiation from Stars

• Surface temperature is much less than the core
  temperature
• Hot stars emit all frequencies of visible light
  and will tend to appear white
• Cooler stars emit higher wavelengths and appear
  red
• Radiation from planets peaks in the infrared range

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Radiation from Matter

• All objects above absolute zero radiate
  electromagnetic waves
• Radiation is in the infrared range for everyday
  objects
• At constant temperature, rates of absorption and
  radiation are the same
• A good radiator is a good absorber

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Radiation from Matter (continued)

• Surfaces that are light in color and smooth
  (shiny) are poor radiators and poor absorbers (ex
  - wear white in summer)
• Dark and rough surfaces are good radiators and
  good absorbers
• As temperature increases, rate at which energy is
  radiated also increases
• Radiation can travel through a vacuum (space)

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Stefan-Boltzmann Law

• Relates total power radiated (luminosity) by a
  black body (per unit area) to temperature

where T4 is proportional to total power radiated

• Stefan-Boltzmann constant 5.67 x 10-8 W m-2
  K-4

A 4pR2 (surface area)
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Example

• The sun (radius 7.0 x 108 m) radiates a total
  power of 3.9 x 1026 W. Find its surface
  temperature.

T 5781K
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Equilibrium

• Constant temperature - power absorbed equals rate
  at which energy is radiated - thermal equilibrium
• If more energy is absorbed than radiated,
  temperature goes up
• If more energy is radiated than absorbed,
  temperature goes down

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Emissivity

• Emissivity - ratio of power radiated by an object
  to power radiated by a black body at the same
  temperature

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Surface Heat Capacity Cs

• Energy required to raise the temperature of a
  unit area on a planets surface by one degree
• measured in J m-2 K-1

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Total Power Absorbed

• Total power absorbed by planet

Where r planet radius P power received
per unit area ? albedo
Remember albedo? This is the fraction of the
radiation that is reflected back into space
before it reaches the Earths surface!
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Total Power Radiated

• Total power radiated from the surface of a planet
  (Stefan-Boltzmann Law and concept of emissivity)
• Total power radiated

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Soat equilibrium

• Total power absorbed total power radiated

Temperature at equilibrium
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What if we dont have equilibrium?

• If incoming radiation power and outgoing
  radiation power are not equal, we have a
  temperature change.
• Temperature of a planet can be predicted
• Assumptions
• Planets variations in temperature due to
  interactions are ignored
• Changes that occur due to temperature change are
  ignored (ex. changes in albedo or emissivity)

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Calculating Temperature Change