Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 24

If the emission density e b from formula (2.2.32) and exergy b b of emission density
from formula (2.2.35) are used in (2.2.44) then:

T 0
T

4

1
3

4
3

T 0
T

ψ = 1 + − (2.2.45)

where T is the temperature of the considered radiation. This characteristic ratio ψ in
thermodynamics of radiation has a significance similar to that of the Carnot efficiency
for heat engines.
The ratio ψ represents the relative potential of maximum energy available from
radiation. However, the real exergy conversion efficiency η B of thermal radiation into
work can be defined as the ratio of the work W , performed due to utilization of the
radiation, to the exergy b of this radiation:

W
b

η B = (2.2.46)

Introducing (2.2.43) to (2.2.46) to eliminate the work W , and then using equation
(2.2.44) to eliminate the exergy b , one finds that the real exergy efficiency of conversion
of radiation exergy to work is equal to the ratio of the real and the maximum energy
efficiencies:

η E
η E ,max ≤

η B = 1 (2.2.47)

Using equation (2.2.44) in (2.2.47) to eliminate η E ,max , the ratio ψ becomes also
the ratio of energy-to-exergy efficiency of the radiation conversion to work:

η E
η B

ψ = (2.2.48)

300 K. With
the growing temperature T from zero to infinity the value ψ decreases from infinity
to the minimum value zero for T

Figure 2.2.5 presents the example of the ratio ψ (dotted line) for T 0 =

T 0 and then increases to unity. However in spite
of ψ approaching unity for infinite temperature T , the difference ( e b

=

− b b ) does not

approach the expected zero but approaches infinity.
Although the ψ is not defined as efficiency, it can be recognized like an efficiency
of a maximum theoretical conversion of radiation energy to radiation exergy. For
example, for any arbitrary radiation of the known energy and at certain presumable
temperature T , the exergy of this radiation could be approximately determined as
the product of the considered energy and the value ψ taken from (2.2.45) for this
temperature T.

Example 2.2.5.1 The value ψ

= 0 . 2083 for a black emission at temperature T =

473 K (200 C) is calculated from formula (2.2.45) at T 0 = 300 K. In paragraph 2.2.6,

example 2.2.6.1, the ψ wv value for water vapor at T = 473 K and T 0 = 300 K is cal-

culated based on the radiation spectrum as ψ wv = 0 . 185. The smaller value of ratio

ψ wv for water vapor, in comparison to black surface radiation ( ψ wv <ψ ) results from
a significant difference in spectra of the water vapor and black surface. However,