A patio heater uses a quartz-sheathed element that behaves as a black radiator at and…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Origins of quantum theory · Origins of quantum theory
Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids
Problem
A patio heater uses a quartz-sheathed element that behaves as a black radiator at 2000K and delivers 2.0kW of radiant power. Its surroundings are at 290K; treat all surfaces as black and ignore convection and conduction.
((a)) What radiating area must the element have? Justify neglecting the radiation returned by the surroundings.
((b)) Find the frequency at which the spectral energy density inside a cavity at this temperature peaks, using νmax=2.821kBT/h, and the wavelength at which the spectrum per unit wavelength peaks, using λmaxT=2.90×10−3mK. Say in one sentence why these are not the same photons.
((c)) A radio engineer monitoring the heater measures the cavity radiation at ν=300GHz. Show that this frequency lies in the Rayleigh-Jeans region of the spectrum, and evaluate the spectral energy density u(ν,T) there. Use σSB=5.67×10−8Wm−2K−4, kB=1.381×10−23JK−1, h=6.626×10−34Js, c=2.998×108ms−1.