The Stefan-Boltzmann law tells us how much infrared energy Earth will emit per unit area. σ = Stefan-Boltzmann constant = 5.670373 x 10 -8 watts / m 2 K 4 (m = meters, K = kelvins).j * = energy flux = energy per unit time per unit area (joules per second per square meter or watts per square meter).Energy emissions go up A LOT as temperature rises! Notice that the amount of energy emitted is proportional to the 4th power of the temperature. It was determined experimentally by Joseph Stefan in 1879 and theoretically derived by Ludwig Boltzmann in 1844. The equation for this relationship is called the Stefan-Boltzmann law. In the 1800s, two scientists determined that the amount of radiation emitted by an object depends on the temperature of the object. In the case of Earth, this EM radiation takes the form of longwave, infrared radiation (or IR "light"). Any object with a temperature above absolute zero emits electromagnetic (EM) radiation. The sunlight Earth absorbs heats our planet. Now that we have a value for the energy flowing into the Earth system, let's calculate the energy flowing out. Our equation for total energy absorbed becomes: To determine how much energy Earth absorbs from sunlight, we must multiply the energy intercepted (that we calculated above) times one minus the albedo value since albedo represents the light reflected away, one minus albedo equals the light energy absorbed. A planet completely covered with snow or ice would have an albedo close to 100%, while a completely dark planet would have an albedo close to zero. Scientists use the term albedo to describe how much light a planet or surface reflects away. Since Earth is not completely black, some of this energy is reflected away and not absorbed by our planet. Plugging in values and solving for E, we find that our planet intercepts about 174 petawatts of sunlight. K S = solar insolation ("solar constant") = 1,361 watts per square meter.E = total energy intercepted (technically, energy flux = energy per unit time, in watts).If we multiply this area by the amount of energy per unit area - the solar "insolation" mentioned above, we can determine the total amount of energy intercepted by Earth: In this case, the circle's radius is simply the radius of Earth, which is about 6,371 km (3,959 miles) on average. The area of a circle is pi times the radius of the circle squared.
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