4.Radiation basic and definitions, irradiation

radiation

1. Radiation
?
Radiation

2. 0.1







Q
Q
Q
Q
Q
Q
r
a
t REFLECTED IS WHICHRADIATION INCIDENT OF FRACTION
ABSORBED IS WHICHRADIATION INCIDENT OF FRACTION
DTRANSMITTE IS WHICHRADIATION INCIDENT OF FRACTION





 Absorptivity,Reflectivity,andtransitivity
Anymattercanabsorb,emitandtransmitradiantenergy.SayQisthetotalradiantenergyincidentuponasurface,somepartof
radiantenergy(Q
a
)willbeabsorbed,somepart(Q
r
)isreflectedandsomepart(Q
t
)istransmittedthroughthebody.Byenergybalance,
Q=Q
a
+Q
r
+Q
t
Q/Q=Q
a
/Q+Q
r
/Q+Q
t/Q

3. 0,0.1,0   0.1,0   Blackbody:Blackbodyisonewhichneitherreflectsnortransmitsanypartoftheincidentradiationbutabsorbs
allofit.Forperfectlyabsorbingbody,
Inpractice,aperfectblackbodydoesnotexist.Howeveritsconceptisveryimportant.
Opaquebody:Whennoincidentradiationistransmittedthroughabody,calledopaquebody,
Mostsolidsdonottransmitanyradiationareopaque.Thereflectivitydependsonthecharacterofsurface.
Thereforetheabsorptivityofanopaquebodycanbeincreasedordecreasedbyappropriatesurfacetreatment.
Rougheningasolidsurfacemeanslessreflectivityenhancesabsorptivityaccordingly.
Surfacetype Properties
Opaquesurface
Whitesurface
Transparentsurfaces
Blackbodies0 0.1,0  0.1 0.1

4. Emissivepower
Iftheradiationfromaheatedbodyisdispersedintoaspectrumbyaprism,itisfoundthattheradiantenergyis
distributedamongvariouswavelengths.
TotalemissivepowerofabodyE,isdefinedasthetotalradiantenergyemittedbythebodyEatacertain
temperatureperunittimeandperunitsurfaceareaatallwavelengths.
ThemonochromaticemissivepowerofabodyE
istheradiantenergyemittedbythebodyperunittimeperunitsurfaceareaataparticularwavelengthand
temperature.
Therateofemissionofradiationbyabodydependentuponthefollowingfactors:
•Temperatureofsurface
•Natureofsurface
•Wavelengthorfrequencyofradiation4
TE
b 428
/1067.5 KmW


Theradiationenergyemittedbyablackbodyperunittimeandperunitsurfaceareaisgivenby
(W/m
2
)where iscalledStefan-BoltzmanconstantandTistheabsolutetemperatureofthe
surfaceinKelvin.ThisequationisStefan-Boltzmanlaw.

5. bE ) Ifwecanplotmonochromaticemissivepower( )vswavelength( atdifferenttemperatureasshowninFig.
(Area under the curve at that temperature)



0
dEE
bb
Thereforeataparticulartemperature,
dEdE
bb bdE  d to
(if isthechangeoftotalemissivepowerforwavelengthsrangingfrom )

d
dE
E
b
b

Which is called spectral or radiation intensity of a black body. The figure shows that area
increases with temperature ie emissive power increases with temperature.

6.    Emissivity():Theemissivityofasurfaceisdefinedastheratioofradiationemittedbythesurfacetotheradiationemittedbyablackbodyat
thesametemperature.
Variesfrom0to1,forblackbody =1,)(
)(
)(
TE
TE
t
b
 4
TEE
b
Kirchhoffs law

7. AsmallbodyofsurfaceareaA
1isplacedinahollow
evacuatedspacekeptataconstantuniformtemperatureT *
11EA 1
Let the energy fall on the unit surface of the body at the rate E
*
of this
energy, generally a fraction
will be absorbed by a small body. Thus the
energy absorbed by the small body A
1
is
,
=is the absorptivity of the small body
When thermal equilibrium (steady state) is attained.
Energy absorbed by the body =Energy emitted (error In
fig)
EnergyabsorbedbyA
1
=*
11 EA
E
1=Energy emitted by A
1surface/area
Atsteadystate,11
*
11 AEEA 
SimilarlyifwereplacethebodyA
1
byA
2
,Then22
*
22 AEEA  





b
b
b
b
E
E
E
EEEE
E
2
2
1
1*
Kirchhoff’slawalsostatesthatthe
emissivityofabodyisequaltoits
absorptivitywhenthebodyremains
inthermalequilibriumwithits
surroundings.
Thelawstatesthatatany
temperaturetheratiooftotal
emissivepowerEtothetotal
absorptivityisconstantsforall
substanceswhichareinthermal
equilibriumwiththeirenvironment.

8. Planck’slaw
1
52
exp
2









KT
Ch
hC
E
b


 
K re, temperatuAbsT
J/K101.380constantBoltzman K
μm,Wavelengthλ
Js106.625constant Planksh
m/s103in vacuumlight ofVelocity C
)(W/mbody black a ofpower emmisive ticMonochromaE
23-
34
8
2
bλ






 
1
2
5
1
exp
as written is law Planks often the Quite









KT
C
C
E
b

 


0
bE power, emmisive Total 

dE
b max constant..
maxT 
Wein’sdisplacementlaw:Itstatesthattheproductof andTisconstant,i.e.,
ThemaximumvaluesoftheemissivepowerE
b
can
beobtainedbydifferentiating
Planck’sEquationwrt andequatingittozero,therefore,  
    
  
 
mKT
T
C
x
x
e
xe
e
C
T
C
T
e
e
eTCe
CeeTCeC
eC
d
d
d
Ed
x
x
x
TC
TC
TCTC
TCTCTC
TC
b
3
max
max
2
22
2
1
/
/
1/2
2
1
/
6
1
1
//2
2
2
/5
1
1
/5
1
10898.2
965.4
01
5
5
1
55
1
5/1
05.1/11
01
2
2
22
222
2












































