Page 516 - Bird R.B. Transport phenomena

496 Chapter 16 Energy Transport by Radiation

Fig. 16.3-2. Comparison of the emit-
ted radiation from black, gray, and
real surfaces.

Planck's law (black body)

A typical real surface
Gray body with e - 1 /3

7
an empiricism that fitted the available data. However, before the end of the year, 8 Planck
succeeded in deriving the equation, but at the expense of introducing the radical notion
of the quantization of energy, an idea that was met with little enthusiasm. Planck himself
had misgivings, as clearly stated in his textbook. 9 In a letter in 1931, he wrote: ".. . what I
did can be described as an act of desperation.... I had been wrestling unsuccessfully for
six years... with the problem of equilibrium between radiation and matter, and I knew
.
that the problem was of fundamental importance .." Then Planck went on to say that
he was "ready to sacrifice every one of my previous convictions about physical laws" ex-
cept for the first and second laws of thermodynamics. 10 Planck's radical proposal ush-
ered in a new and exciting era of physics, and quantum mechanics penetrated into
chemistry and other fields in the twentieth century.

EXAMPLE 16.3-1 For approximate calculations, the sun may be considered a black body, emitting radiation
with a maximum intensity at Л = 0.5 microns (5000 A). With this information, estimate (a) the
Temperature and surface temperature of the sun, and (b) the emitted heat flux at the sun's surface.
Radiant-Energy
Emission of the Sun SOLUTION
(a) From Wien's displacement law, Eq. 16.3-12,

0.2884 0.2884 cm К
T = 4 = 5760K = 10,400 R (16.3-13)
ax 0.5X10" cm
(b) From the Stefan-Boltzmann law, Eq. 16.2-10,
8
cjf = aT 4 = (0.1712 X 10~ )(10,400) 4
7
= 2.0 X 10 Btu/hr-ft 2 (16.3-14)

7 O. Lummer and E. Pringsheim, Wied. Ann., 63, 396 (1897); Ann. der Physik, 3,159 (1900).
8 M. Planck, Verhandl. d. deutsch. physik. Ges., 2, 202 and 237 (1900); Ann. Phys., 4, 553-563, 564-566
(1901).
9 M. Planck, The Theory of Heat Radiation, Dover, New York (1991), English translation of Vorlesungen
iiber die Theorie der Warmestrahlung (1913), p. 154.
10 A. Hermann, The Genesis of Quantum Theory, MIT Press (1971), pp. 23-24.