For a prescribed wavelength A, measurement of the spectral intensity I.c (, T) = I, b

For a prescribed wavelength A, measurement of the spectral intensity Iλ.c (λ, T) = ελ Iλ, b of radiation emitted by a diffuse surface may be used to determine the surface temperature, if the spectral emissivity ελ is known, or the spectral emissivity, if the temperature is known.

(a) Defining the uncertainty of the temperature determination as dT/T, obtain an expression relating this uncertainty to that associated with the intensity measurement, dIλ/Iλ. For a 10% uncertainty in the intensity measurement at λ = 10λm, what is the uncertainty in the temperature for T = 500 K? For T = 1000K?

(b) Defining the uncertainty of the emissivity determination as dελ/ελ, obtain an expression relating this uncertainty to that associated with the intensity measurement, dIλ/Iλ. For a 10% uncertainty in the intensity measurement, what is the uncertainty in the emissivity?