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Section 3.2 Solar energy

The energy balance of the planet as a whole depends on radiation: how the Earth exchanges energy with space. To understand the role of solar energy, we first need to explore the behavior of temperature and radiation.

The Electromagnetic Spectrum

The electromagnetic spectrum refers to the entire distribution of electromagnetic radiation (or more generally, "light") over all wavelengths. We recognize that visible light occupies only a very narrow range of this entire spectrum. The following table provides a quick summary of the major types of electromagnetic radiation.

Table 3.2.1. Electromagnetic radiation
type wavelength range
\(\gamma\) rays and X-rays \(10^{-12}-10^{-9}\) m
ultraviolet \(10^{-8}-10^{-7}\) m
visible \(4\times10^{-7}-7\times10^{-7}\) m
infrared \(10^{-6}-10^{-3}\) m
microwave \(10^{-3}-10^{-1}\) m
radio \(10^{-3}-10^{8}\) m

Radiation Laws

  • Every object with a temperature above 0 K emits radiation.

  • Stefan-Boltzmann Law: objects with higher temperature emit more radiation per unit area (W/m^2), to the fourth power of temperature \(F=\sigma T^4\)

  • Wien’s Law is written as \(\lambda=\frac{2898}{T(K)}\text{;}\) this means that objects with higher temperature emit radiation at shorter wavelengths

These laws explain the how different objects emit light. The Sun's photosphere is very hot (5800 K), and so it emits much of if its radiation over visible wavelengths. Cooler objects will emit much less radiation, and radiation at longer wavelengths. For example, most objects with temperatures near that of the Earth's surface (288 K) will emit radiation at infrared wavelengths.

This also explains the application of thermal or “night vision” technologies: mammals are typically much warmer than their surroundings (e.g., humans are typically about 310 K), and thus emit much more infrared energy than their surroundings.

The Sun

The Sun is the main source of energy for the weather and climate, and reaches the Earth via radiation.

  • The source of solar energy is the nuclear fusion of H into He in interior

  • The outer layers of the Sun have temperature of 5770 K (incandescent: this gas/plasma is so hot that it glows, primarily at visible wavelengths)

  • The total energy output is given by \(F=\sigma T^4\) where \(T=5780\) where the Stefan-Boltzmann constant is \(\sigma=5.67\times10^{-8}\) W m\(^-2\) K\(^4\text{.}\)

  • This yields a total energy output of \(6.3\times10^{8}\) W per m\(^2\) on the solar photosphere;

  • the radius of the Sun is \(6.957\times10^{8}\) m so the Sun has a surface area of \(6.08\times10^{18}\) m\(^2\text{.}\)

  • the total solar output (or solar luminosity) is therefore \(3.82\times10^{26}\) W.

At the distance of the Earth’s orbit, the Sun’s radiation is spread out over an area \(A=4\pi r^2\) where \(r=1.496\times10^{11}\) m, giving \(A=2.81\times10^{23}\) m\(^2\text{.}\)

This yields an energy flux of about 1360 W/m^2, a value sometimes referred to as the solar constant. This is the incoming solar flux at the top of the Earth’s atmosphere. We will return to this value when we explore the energy budget of planet Earth.