The spectral transmissivity of a 50-m-thick polymer film is measured over the wavelength range 2.5m <

The spectral transmissivity of a 50-μm-thick polymer film is measured over the wavelength range 2.5μm < λ < 15μm. The spectral distribution may be approximated as τλ = 0.80 for 2.5μm < λ < 7μm, τλ = 0.05 for 7μm < λ < 13μm, and τλ = 0.55 for 13μm < λ < 15μm. Transmissivity data outside the range cannot be acquired due to limitations associated with the instrumentation. An engineer wishes to determine the total transmissivity of the film.

(a) Estimate the maximum possible total transmissivity of the film associated with irradiation from a black body at T = 30°C.

(b) Estimate the minimum possible total transmissivity of the film associated with irradiation from a black body at T = 30°C.

(c) Repeat parts (a) and (b) for a blackbody at T = 600°C.