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# Illustration 19.3: Heat Transfer, Radiation

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Heat from the Sun is transferred via radiation to planets. A planet, in turn, radiates energy back out into space. A planet reaches its equilibrium temperature when the power delivered to it from the Sun is equal to the power a planet radiates. The power it radiates is given by the following equation:

P = σ ε A T^{4},

where σ is the Stefan-Boltzmann constant (5.67 x 10^{-8} W/m^{2} ⋅ K^{4}), ε is the emissivity (1 for a "blackbody" absorber/emitter; 0 for a perfect reflector), A is the surface area (4πR^{2}), and T is the temperature. The power/area delivered to a planet varies as the inverse square of the distance from the Sun. Note that the effective area of a planet that the Sun's radiation hits is πR^{2}, where R is the radius of the planet. However, the total area over which the planet radiates is equal to its surface area, which is the surface area of a sphere (4πR^{2}) of radius R. Restart.

If we neglect the planet's atmosphere (which reflects some of the light from the Sun and traps some of the radiation from the planet's surface), we can predict the temperature of the planet. Drag the red planet in the animation to different distances from the sun and see the various surface temperatures that result. Notice that when the red planet is at Earth's position, its temperature is below Earth's true average temperature of 287 K. Once the effect of the atmosphere is taken into account, the power delivered to Earth's surface is reduced further (since the atmosphere reflects some light). What keeps Earth from being a frozen planet? The greenhouse effect, in which gases in the atmosphere do not allow some of the radiation (in the infrared) that Earth radiates to escape from the atmosphere, does that. This radiation is trapped in Earth's atmosphere, thus warming Earth up to its current average temperature. As "greenhouse" gases increase in the atmosphere, Earth's average temperature will increase.

Illustration authored by Anne J. Cox.

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