Chapter 12, Problem 12.68P

The spectral transmissivity of a $50-\mu m$ -thick polymer film is measured over the wavelength range $2.5\mu m\le \lambda \le 15\mu m$ . The spectral distribution may be approximated as ${\tau }_{\lambda }=0.80for\text{ 2}\text{.5 }\mu m\le \lambda \le 7\mu m,{\tau }_{\lambda }=0.05for\text{ 7}\mu m<\lambda \le 13\mu m,\text{ and }{\tau }_{\lambda }=0.55\text{ for 13 }\mu m<\lambda \le 15\mu m$ Transmissivity data outside the range can- not 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 blackbody at $T={30}^{\circ }C$ .

(b) Estimate the minimum possible total transmissivity of the film associated with irradiation from a blackbody at $T={30}^{\circ }C$ .

(c) Repeat parts (a) and (b) for a blackbody at $T={600}^{\circ }C$ .