Let us observe the following simplified model of the Earth’s atmosphere where the atmosphere layer surrounding the Earth a) reflects μ=\SI30% of the Sun’s radiation falling on it back to the cosmos and lets the rest of the radiation through without absorbing any of it; b) absorbs completely all the infrared radiation coming from the Earth’s surface. The irradiance coming from the Sun is w0=\SI1400m2W. Find the average temperature of the Earth’s surface.
Hint. The Stefan-Boltzmann law applies – the power radiated by a black body per unit of area is given as w=σT4 where σ=5,67⋅10−8\SIm2⋅K4W. Assume that the Earth’s surface only radiates infrared radiation and that it can be looked at as an absolutely black body due to this. The surface also absorbs all of the Sun light reaching it.