Chapter 12, Problem 12.61P

The spectral transmissivity of a 1-mm-thick layer of liquid water can be approximated as follows:

$\begin{array}{l}{\tau }_{\lambda 1}=0.99\text{ 0}\le \lambda \le \text{1}\text{.2}\mu \text{m}\\ {\tau }_{\lambda 2}=0.54\text{ 1}\text{.2}\mu \text{m<}\lambda \le \text{1}\text{.8}\mu \text{m}\\ {\tau }_{\lambda 3}=0\text{ 1}\text{.8}\mu \text{m<}\lambda \end{array}$

(a) Liquid water can exist only below its critical temperature, $T_c=647.3K$ .Determine the maximum possible total transmissivity of a 1-mm-thick layer of liquid water when the water is housed in an opaque container and boiling does not occur. Assume the irradiation is that of a blackbody.

(b) Determine the transmissivity of a 1-mm-thick layer of liquid water associated with melting the platinum wire used in Nukiyama’s boiling experiment, as described in Section 10.3.1.

(c) Determine the total transmissivity of a 1-mm-thick layer of liquid water exposed to solar irradiation. Assume the sun emits as a blackbody at $T_s=5800K$ .