3. (10 points) radiative cooling: consider a soil layer that is 10cm thick, has a density of 1800 kg m-3, a specific heat capacity of 1000 j kg-k-, an initial temperature of 300 k, and an emissivity (€) of l. (a) over the course of a 12-hour night (without any sunlight), by how much would this layer cool through radiative emission, in the absence of any atmosphere? assume that the soil radiates at a constant rate throughout the night, and does not conduct heat to and from deeper soil. (b) repeat your calculation, but now assume that there is an overlying atmosphere, radiating downward to the surface at 342 wm? (the global and annual mean, according to ipcc ar5), and that the soil absorbs all of this radiation.