Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 20

The black emission e b has its exergy b b , however as the rate of emission e of a
gray surface is smaller ( e = ε × e b ) then the exergy b (of this gray surface emission e ),

is also reduced by ε :

b = εb b (2.2.34)

However using the energy emissivity ε in formula (2.2.34) for exergy calculation
is not precise and, as discussed in details by Petela (2010), the smaller is the precision
the smaller is the emissivity ε . The definition of exergy can be applied to the emitted
photon gas. Therefore, the exergy of the emitted photon gas is a function of an instant
state of the gas and of the state of the gas in the instant of eventual equilibrium with
the environment. Such equilibrium determines the reference state in calculation of the
exergy of the photon gas.
The environment consists of many bodies of different temperatures and different
radiative properties (e.g. emissivities or transmissivities). The dominating temperature
of the environment's bodies can be assumed as the standard (averaged) environmental
temperature T 0 . As discussed previously the surface always emits black radiation, thus
the environment surface at temperature T 0 , regardless of the surface properties, emits
black radiation at temperature T 0 . The properties of the surface determine only the
rate at which the emission occurs. Thus, the environment space permanently contains
the black radiation at temperature T 0 and this radiation is in equilibrium with the
environmental surfaces at T 0 .
Therefore, the exergetic reference state for a photon gas (black radiation) is its
state at temperature T 0 , and such reference state depends only on the temperature T 0
and does not depend on diversified values of emissivities of the environmental bodies.
The black emission exergy b b appearing in formula (2.2.33) is always a function
only of temperature T of the considered surface and of the environmental temperature
T 0 , b b = f ( T , T 0 ). No pressure has to be considered for establishing the exergy reference

state for radiation because the pressure of radiation is determined only by the radiation
temperature and any pressure of environmental substance does not affect the radiation,
which is not a substance.
Detailed analyses confirming the independency of radiation exergy on emissivity of
the environment, on the configuration of surrounding environment and on the presence
of other surfaces of different temperatures, are gathered in the topic by Petela (2010).
The exergy b b , S (J/m 3 ) of the photon gas enclosed within a system was discussed
in Paragraph 2.2.4. However the exergy of the photon gas as being the propagating
product of the emitting process, i.e., the exergy b b (W/m 2 ) of emission density of a
black surface is:

σ
3 (3 T 4

T 0 − 4 T 0 T 3 ) b b = + (2.2.35)

The simplest way of obtaining formula (2.2.35) is multiplication of b b , S by factor
c 0 /4, making b b = c 0 · b b , S /4, based on purely geometric considerations and keeping in

mind that σ c 0 /4, where c 0 is the light velocity. Another way to derive formula

(2.2.35) is by application of the exergy definition formula (2.2.3) with interpretation
of energy E and entropy S as respective emission e b and its entropy s .
However for the confirmation of both ways and for the purpose of the well teach-
ing demonstration of the analysis of radiation processes, an additional way can be

= a ×