Energy from the Sun

  2. Energy production
  3. Global thermal energy transfer
  4. Energy from the Sun
    5. 15'

20% of the world's deserts covered with solar panels would supply enough energy for present needs. Here we will learn the first half of a means to calculate this energy: the intensity of the light emitted from the Sun upon the Earth's surface.

Key Concepts

Fusion in the Sun

The fusion of hydrogen to helium is what provides the energy to keep the Sun hot. The Sun remains in equilibrium between the force of the radiation exerted outwards and the force of gravitation inwards.

 

The black body spectrum

A black body is a perfect absorber and emitter of radiation, which means that a full emission spectrum is released. We can visualise this spectrum on a graph of power (or intensity or energy) against wavelength.

The hotter the object, the more power will be produced and the shorter the peak wavelength will be. The sun is a good example.

 

 

Essentials

Stefan Boltzmann law

The higher the temperature, the larger the area of the black body curve above the axis, as this is proportional to the total power emitted. The Stefan Boltzmann law gives the relationship between temperature and power emitted per unit area:

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

  • P = power released (W)
  • e = emissivity (dimensionless quantity = 1 for a black body)
  • σ = constant of proportionality
  • A = surface area (m2)
  • T = absolute temperature (K)

NB: It is worth taking note of the power of 4, making the temperature of the body much more significant in determining the power than the area.

 

Wien's law

The higher the temperature, the lower the wavelength of the peak of the black body curve. This is intuitive, as shorter wavelengths correspond with higher freqencies and energies. However, it does have the effect that the very hottest stars in terms of temperature actually release much more gamma and X-ray radiation than infrared (thermal).

Remarkably, the product of this peak wavelength and the absolute temperature is a constant. Wien's law relates the peak wavelength and temperature:

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

 

Inverse square law

The further from the sun you go the less the power per square meter becomes. This can be measured as the physical quantity intensity, which is the power arriving per unit area.

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

NB: The bottom line of this fraction is the surface area of the 'sphere' of radiation being emitted from the Sun. If you were interested in finding the intensity of the Sun's radiation landing on the Earth, you would substitute r as the distance from the Sun to the Earth. This value, 1388 Wm-2, is known as the solar constant.

 

 

Test Yourself

Use quizzes to practise application of theory.


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Exam-style Questions

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