What is blackness? What is absorptivity? Relationship between blackness and absorbance?

Relation between absorptivity and blackness. Suppose two parallel plates are so close to each other that its length and width are much greater than the distance between them. Thus the radiant energy emitted by one plate can fall entirely on the other plate.

Let surface 1 be a blackbody surface, and the radiative force, absorptivity, and surface temperature are Eb, αb=1, and T1, respectively.

Surface 2 is an arbitrary surface, and the radiative force, absorptivity, and surface temperature are E2, α, and T2, respectively.

Figure 7-19 Radiative heat transfer between parallel flat plates

Now, let's discuss the energy gain and loss on surface 2.

Surface 2 emits radiant energy E per unit area per unit time, which is projected onto surface 1 and is fully absorbed. At the same time the radiation Eb emitted by surface 1 falls on the indication, absorbing αEb, and the rest (1-α)Eb is emitted to surface 1 and absorbed by surface 1. The difference between the expenditure and the income of the plate 2 is the heat flow density q of the radiative heat transfer between the two plates:

q=E- αEb (a)

When the system is in thermal equilibrium, T2 = T1, q=0

So the above equation becomes: E/α= Eb (b)

The generalization of this relationship to an arbitrary object yields:

Kirchhoff's Laws Expression: (Conditions: thermal equilibrium, one side is a blackbody)

E1/α1= E2/α2= E3/α3=......E/α= Eb (7-25a)

α=E/ Eb=ε (7-25b)