Global thermal energy transfer

  2. Energy production
  3. Global thermal energy transfer
    4. 20'

This concluding topic is a bit of everything and is a great check of so much that you have already studied:

  • conservation of energy
  • waves
  • electromagnetic spectrum
  • nuclear fusion
  • electron energy levels

This page is a quick summary, but for fuller details, go to:

Key Concepts

Energy from the fusion of hydrogen in the core of the Sun heats the gas on the outside causing it to emit light across the electromagnetic spectrum.

Energy from the sun

Black body radiation

When a body is heated it gives out energy in the form of EM radiation. A perfect black body emits all radiation that is incident upon it, making e = 1.

\(P=e\sigma AT^4\)

This is the Stefan-Boltzmann law.

The constant σ = 5.67 x 10-8 Wm-2K-4

Emissivity (e)

Not all bodies are perfect black bodies.

The emissivity is the ratio of radiation emitted by a body to that which is incident. A body with emissivity 0.5 will emit half the radiation of a black body.

The black body spectrum

A black body spectrum shows the intensity at each wavelength. The distinctive shape of this curve is the same, no matter what the body's temperature or surface area.

Wien's displacement law

This gives the peak wavelength for a given temperature:

\(\lambda_{\text {peak}}={0.00289\over T}\)

Inverse square law

The radiation from the sun spreads out in an ever-increasing sphere.

Intensity is defined as power per unit area:

\(I={P\over 4\pi r^2}\)

The power per unit area at the Earth is 1400 Wm-2 , where r is the total distance from the Sun to the Earth.

 

EM radiation and the atmosphere

The way different EM radiation interacts with different gases can be shown by these absorption spectra.

 

 

Essentials

Radiation absorbed by the Earth

The Earth absorbs energy only on the side facing the sun so the total power absorbed = 1400 x πr2

When energy is absorbed by a body the increase in temperature depends upon the specific heat capacity of the material and its mass. When heat is absorbed by the earth the temperature rise depends on the surface heat capacity and the area.

capital delta T space equals space fraction numerator Q over denominator C subscript s A end fraction

The average surface heat capacity is 4 x 108 Jm-2K-1 if the intensity of radiation is 350 Wm-2 .

Radiation reflected by the Earth

The fraction of radiation reflected (or scattered) depends on the albedo of the surface (this is related to the colour):

A l b e d o space equals space fraction numerator T o t a l space s c a t t e r e d space p o w e r over denominator T o t a l space i n c i d e n t space p o w e r end fraction

Summary

EM radiation from the sun is mainly in the visible region. This passes through the atmosphere without being absorbed. The radiation lands on the Earth where some is reflected. The rest is absorbed, causing the temperature to rise. The Earth emits radiation in the infrared region of the spectrum which is absorbed by the atmosphere and re-radiated in all directions. Some of the radiation goes back to the Earth causing the temperature to rise: the greenhouse effect.

 

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