A radiation thermometer is a device that responds to

Chapter 12, Problem 12.45

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A radiation thermometer is a device that responds to aradiant flux within a prescribed spectral interval and iscalibrated to indicate the temperature of a blackbodythat produces the same flux.(a) When viewing a surface at an elevated tempera-ture Tsand emissivity less than unity, the ther-mometer will indicate an apparent temperaturereferred to as the brightness or spectral radiancetemperature T?. Will T?be greater than, less than,or equal to Ts?(b) Write an expression for the spectral emissivepower of the surface in terms of Wiens spectraldistribution (see 12.27) and the spectralemissivity of the surface. Write the equivalentexpression using the spectral radiance temperatureof the surface and show thatwhere ? represents the wavelength at which thethermometer operates.(c) Consider a radiation thermometer that responds to aspectral flux centered about the wavelength 0.65?m.What temperature will the thermometer indicatewhen viewing a surface with ??(0.65?m)?0.9and Ts?1000 K? Verify that Wiens spectral dis-tribution is a reasonable approximation to Planckslaw for this situation.