Isothermal furnaces with small apertures approximating a blackbody are frequently used to calibrate heat flux gages, radiation thermometers, and other radiometric devices. In such applications, it is necessary to control power to the furnace such that the variation of temperature and the spectral intensity of the aperture are within desired limits.

  (a) By considering the Planck spectral distribution, Equation 12.24, show that the ratio of the fractional change in the spectral intensity to the fractional change in the temperature of the furnace has the form.

                   dI_λ/I_λ  =  C₂               1            

                  dT/T       λT   1 - exp ( - C₂/λT)

  (b) Using this relation, determine the allowable variation in temperature of the furnace operating at 2000 K to ensure that the spectral intensity at 0.65 jum will not vary by more than 0.5%. What is the allowable variation at 10 μm?