1. Topic 8.5: Blackbody Radiation
Global Warming
Topic 8.5:
Blackbody Radiation

2. 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

3. 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)

4. 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

5. 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

6. 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