1) Let us make an attempt at solving humanity\'s energy problem. Assume a surfac
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Question
1) Let us make an attempt at solving humanity's energy problem. Assume a surface of a wood stove, A-1m2 which is at a temperature T=500K. Use the blackbody energy density as given by Planck's law; convert the energy density into intensity; from that calculate the energy of the radiation spectrum emitted per time from this surface. Assume that all of the radiation energy impinges on and is absorbed by photovoltaic panels. The semiconductor of the photovoltaic elements has a minimum bandgap E-1.5eV; convert this energy into frequency wg. Only radiation with frequency dog results in the creation of electrons in the conduction band and in the generation of electric current. Assume that 100% of this thermal radiation is absorbed and converted into electric energy.Explanation / Answer
Planck's energy density in terms of frequency v:
uv(T) = 8pihv2/c3 . e-hv/kT since it is the energy density therefore, in terms of power it will be
Power, P = E/t = uv(T)/t , where t is time which is in seconds, therefore,
P = E/t = uv(T)/t = 8pihv2/c3 . e-hv/kT /t ,therefore the intensity will be Power per unit area which is
Intensity, I = P/A = 8pihv2/c3 . e-hv/kT/t A , since A is 1m2 , therefore,
I = P/A = 8pihv2/c3 . e-hv/kT = E, since the time is 1sec , therefore, P = E and I = E, therefore, by Stefan's Boltzmann Law,
P = E = sigma(T4) ,where sigma is the stefan - boltzmann's constant which is equal to 5.67 x 10-8 , therefore, E = 5.67 x 10-8 x (500)4
E = 5.67 x 10-8 x 625 x 108 = 5.67 x 625 = 3543.75 K4.
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