Simple Earth Temperature Model - Black Body Approximation · RMPH 2014 #1

Physics · thermodynamics

Problem

Context: Climate change and global warming have become topics of public interest. On a cosmic scale, Earth's energy balance involves only absorption and emission of radiation. Earth's climate depends on the delicate balance between energy received from the Sun and energy radiated into space. The solar constant is wS=1370w_S = 1370 W/m². A blackbody absorbs electromagnetic radiation regardless of wavelength and emits according to its surface temperature. The Stefan-Boltzmann law states that ϵ(T)=σT4\epsilon(T) = \sigma T^4, where ϵ(T)\epsilon(T) is the total energy emitted per unit area per unit time, TT is absolute temperature, and σ=5.67×10−8\sigma = 5.67 \times 10^{-8} W/(m²·K⁴) is the Stefan-Boltzmann constant. Task 1 uses simple modeling where Earth absorbs energy from the Sun and loses energy as a black body. 1.a. Determine the expression of average temperature TPT_P that the Earth's surface should have, in accordance with simple modeling used. (0.70p) 1.b. Calculate the numerical value TPT_P of the average temperature that the Earth's surface should have, according to this model. (0.30p)

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