Topic 8.5: Blackbody Radiation

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Presentation transcript:

Topic 8.5: Blackbody Radiation Global Warming Topic 8.5: Blackbody Radiation

Black-body radiation Black Body - any object that is a perfect emitter and a perfect absorber of radiation Object does not have to appear "black" Sun and Earth's surface behave approximately as black bodies

Black-body radiation P = eσAT4 The amount of energy per second (power) radiated from a body depends on its surface area and absolute temperature according to P = eσAT4 where σ is the Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4) and e is the emissivity of the surface (=1 for a black object)

Example By what factor does the power emitted by a body increase when its temperature is increased from 100ºC to 200ºC? Emitted power is proportional to the fourth power of the Kelvin temperature, so will increase by a factor of 4734/3734 = 2.59

Surface heat capacitance Cs Surface heat capacitance is defined as the energy required to increase the temperature of 1 m2 of a surface by 1 K. Cs is measured in J.m-2.K-1. Q = ACsΔT

Example Radiation of intensity 340 W.m-2 is incident on the surface of a lake of surface heat capacitance Cs = 4.2 x 108 J.m-2.K-1. Calculate the time to increase the temperature by 2 K. Comment on your answer. Q = ACsΔT In time t, Q/t = ACsΔT/t Q/tA = CsΔT/t 340 = (4.2 x 108 x 2)/t t = (4.2 x 108 x 2)/340 = 29 days Sun only shines approx 12 hours a day so would take at least twice as long