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D APPENDIX D: TECHNOLOGY SOLUTIONS FOR ENERGY RECOVERY A theoretical blackbody radiation spectrum at 1250 K can be converted into useful electrical energy by an infrared-responding GaSb PV cell with bandgap energy of 0.73 eV (Figure D.6). The convertible portion of the spectrum for a Si cell with bandgap energy 1.12 eV is included for comparison. Power radiated is proportional to T4 by Stefan-Boltzmann Law (Halliday et al., 1978) for an identical body that explains why the area under the blackbody curves (total energy) increases rapidly for small temperature increases. P = σAT4 (5) P is the power radiated, σ is Stefan’s constant (5.67 e10-8 Wm-2K-4), A is the surface area (m2), and T the temperature of the body (K). Stefan’s law illustrates the magnitude that temperature has on power generation and accentuates the scientific challenge in develop- ing materials for energy conversion at relatively low exposure temperatures. An emitter with a “blackbody” emissive power spectrum radiates the theoretical maximum amount of power at a specific wavelength, P (λ, T), at a given temperature T as described by Planck’s Law (Kreith et al., 1980): 2#hc2"!5 P = exp(hc"kT !1) (6) Figure D.6: Emissive power spectrum for 1600K-blackbody emitter with shaded portion where energy conversion is possible with Si and GaSb photovoltaic cells. For compar- ison, the emissive power spectrum for a broadband radiator is included. Note that beyond 1.7 μm, photon energy is insufficient to promote electrons to the conduction band; thus, no power conversion takes place (Coutts, T.J. et al., 1998). 108PDF Image | Analysis for Recovering Energy from Industrial Waste Heat
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