TITLE.PM5

838 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th15-4.pm5

where, ()Eλb = Monochromatic (single wavelength) emissive power of a black body,

c = Velocity of light in vacuum, 2.998 × 10^8 ~− 3 × 10^8 m/s,

h = Planck’s constant = 6.625 × 10–34 js,

λ = Wavelength, μm,

k = Boltzmann constant = 1.3805 × 10–23 J/K, and

T = Absolute temperature, K.

Hence the unit of ()Eλb is W/m^2. μm

Quite often the Planck’s law is written as

()

exp

E

C

C

T

λb

λ

λ

=

L

NM

O

QP

−

−

1

5

(^21) ...(15.77)
where, C 1 = 2πc^2 h = 3.742 × 10^8 W.μm^4 /m^2 ;
C 2 = ch
k
= 1.4388 × 10^4 μmK
Equation (15.76) is of great importance as it provides quantitative results for the radiation
from a black body.
The quantity ()Eλb, monochromatic emissive power, is defined as the energy emitted by the
black surface in all directions at a given wavelength λ per unit wavelength interval around λ ; that is,
the rate of energy emission in the interval dλ is equal to ()Eλb dλ. The total emissive power and
monochromatic emissive power are related by the equation
Eb =
0
∞
z ()Eλb^ dλ ...(15.78)
A plot of ()Eλb as a function of temperature and wavelength is given in Fig. 15.50.
0
100
200
300
400
500
01234
Monochromatic emissivepower [(E ) ]k, W/m
.m
λb
2 μ
2000 K
λmax.T = C
Visible range
Visible range
1500 K
1000 K
Wavelengthλ, μ
Fig. 15.50. Variation of emissive power with wavelength.