Page 510 - Bird R.B. Transport phenomena

490 Chapter 16 Energy Transport by Radiation

§16.2 ABSORPTION AND EMISSION AT SOLID SURFACES
Having introduced the concepts of absorption and emission in terms of the atomic pic-
ture, we now proceed to the discussion of the same processes from a macroscopic view-
point. We restrict the discussion here to opaque solids.
Radiation impinging on the surface of an opaque solid is either absorbed or re-
flected. The fraction of the incident radiation that is absorbed is called the absorptivity
and is given the symbol a. Also the fraction of the incident radiation with frequency v
that is absorbed is designated by a v. That is, a and a v are defined as
a = a =
^T) » \) (16.2-1,2)

in which cffdv and cftdv are the absorbed and incident radiation per unit area per unit
time in the frequency range v to v + dv. For any real body, a u will be less than unity and
will vary considerably with the frequency. A hypothetical body for which a,, is a con-
stant, less than unity, over the entire frequency range and at all temperatures is called a
gray body. That is, a gray body always absorbs the same fraction of the incident radiation
of all frequencies. A limiting case of the gray body is that for which a,, = 1 for all frequen-
cies and all temperatures. This limiting behavior defines a black body.
All solid surfaces emit radiant energy. The total radiant energy emitted per unit area
{e)
per unit time is designated by q , and that emitted in the frequency range v to v + dv is
called q^dv. The corresponding rates of energy emission from a black body are given the
symbols <$ and q^dv. In terms of these quantities, the emissivity for the total radiant-en-
ergy emission as well as that for a given frequency are defined as
n(e)
e = (16.2-3,4)
The emissivity is also a quantity less than unity for real, nonfluorescing surfaces and is
equal to unity for black bodies. At any given temperature the radiant energy emitted by
a black body represents an upper limit to the radiant energy emitted by real, nonfluo-
rescing surfaces.
We now consider the radiation within an evacuated enclosure or "cavity" with
isothermal walls. We imagine that the entire system is at equilibrium. Under this condi-
tion, there is no net flux of energy across the interfaces between the solid and the cavity.
We now show that the radiation in such a cavity is independent of the nature of the
walls and dependent solely on the temperature of the walls of the cavity. We connect
two cavities, the walls of which are at the same temperature, but are made of two differ-
ent materials, as shown in Fig. 16.2-1. If the radiation intensities in the two cavities were
different, there would be a net transport of radiant energy from one cavity to the other.
Because such a flux would violate the second law of thermodynamics, the radiation in-
tensities in the two cavities must be equal, regardless of the compositions of the cavity
surfaces. Furthermore, it can be shown that the radiation is uniform and unpolarized
throughout the cavity. This cavity radiation plays an important role in the development

Material 1 Material 2

Fig. 16.2=1, Thought experiment for proof that cavity radi-
ation is independent of the wall materials.