Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 26

Figure 2.2.6 Geometry scheme for radiation flux (from Petela, 1962).

where: c 0 = 2 . 9979 · 10 8 m/s is the speed of propagation of radiation in vacuum,

10 − 34 J s is the Planck constant, k 10 − 23 J/K is the Boltzmann

h = 6 . 625 · = 1 . 3805 ·

constant.
The entropy L b ,0, λ , W/(m 3 K sr), of monochromatic directional normal radiation
intensity and for linearly polarized black radiation propagating within a unit solid
angle and dependent on wavelength λ according to Planck (1914) is:

λ 5 i b ,0, λ
c 0 h

c 0 k
λ 4

L b ,0, λ = [(1 + Y )ln(1 + Y ) − Y ln Y ] where Y ≡ (2.2.54)

The total energy or entropy of radiation is respectively the same regardless
whether the spectrum is expressed as function of the wavelength λ or frequency ν .
Therefore, e.g.:

∞ ∞

i b ,0, ν dν = i b ,0, λ dλ (2.2.55)

0 0

To apply such recalculation formula (2.2.55), the formula (2.2.53) for i b ,0, λ has to
be used together with relation λ c 0 . Based on such a possibility, the formulae on

radiation exergy can also be presented as functions of the wavelength λ or frequency ν .
It is assumed that the considered elemental flux propagates between any two
control elementary surface areas d A and d A separated by distance R , in a direction
determined by the flat angles of β (called declination) and φ (called azimuth), as shown
in Figure 2.2.6. The solid angle of propagation dω

· ν =

=

dA /R 2

= · ·

sin β dβ dϕ and the

abbreviation:

d 2 C

≡ cos β sin β dβ dϕ (2.2.56)