Experiment No.2 Inverse Square Law for Heat and Stefan-Boltzmann Law I.
O!e"tives #. $o s%ow s%ow t%at t%e intensit intensit& & of radiation radiation on t%e surfa"e surfa"e is inversel& inversel& proportio proportional nal to t%e square of t%e distan"e of t%e surfa"e from t%e radiation sour"e. 2. $o s%ow t%at t%e intens intensit it& & of radiat radiatio ion n vari varies es as t%e t%e four fourt% t% power power of t%e sour sour"e "e temperature.
II.
'aterials(Equipm uipmeents nts Needed #. $%er $%erma mall )ad )adia iati tion on *nit *nit
III.
Equipment Set *p
I+.
$%eor& Inverse Square Law for Heat $%e total ener,& d from an element d "an e ima,ined to flow t%rou,% a %emisp%ere of radius r. a surfa"e element on t%is %emisp%ere d # lies on a line ma/in, an an,le wit% t%e normal and t%e solid an,le sutended & d# at d is d0# 1 d#(r 2. Note3 Solid an,le w%i"% is & definition t%e inter"epted area on a sp%ere divided & r 24.
If t%e rate of flow t%rou,% d # is d# t%en d# 1 i50# d w%ere i5is t%e intensit& of radiation in t%e 5 dire"tion i.e.6 d# 7 #( r 2. Stefan-Boltzmann Law $%e Stefan-Boltzmann law states t%at3 q b=δ ( T S−T A ) 4
4
8%ere3 q 1 ener,& emitted & unit area of a la"/ od& surfa"e 8m-24 9 1 Stefan-Boltzmann "onstants :.;< x #=-> 8 m-2? @4 $s 1 Sour"e temperature ?4 $ 1 $emperature of radiometer and surroundin,s ?4
In"ident )adiation and Emitted )adiation $%e di,ital meter indi"ates t%e intensit& of t%e radiation re"eived & t%e radiometer in 8(m24 and not t%e radiation emitted & t%e %eated surfa"e at w%i"% it is pointed. $%ou,% e&ond t%e s"ope of t%is manual it "an e s%own t%at t%e relations%ip etween radiation re"eived & t%e sensor and radiation emitted & t%e %eated sour"e is as follows3
Hen"e as t%e sensor is removed from t%e %eated surfa"e and L in"reased t%e an,le A de"reases.
$%e model is exa"t for a la"/ "ir"ular emitter and re"eiver. s it is not possile to utilize "ir"ular pla"es due to t%e s%ape of t%e %eater availale an approximation is made to t%e effe"tive diameterC of a "ir"ular plate t%at would e equivalent to t%e re"tan,ular plates supplied. $%is diameter is #2;mm and %en"e r 1 ;Dmm.
or t%e dia,ram
Hen"e
sin
2
( )
θ=
v
v
2
2
+ L
2
( )
qincident = qemitted∗
(
qincident = qemitted∗
v
v
2
m
2
2 2
0.063 + L
(
( ) W
2
L
+
0.063
Or Radiometer Reading
2
2
=q emitted∗
)
0.063
2
2
2
2
2
0.063 + L
)
¿
Or q emitted = Radiometer Reading
( )( W m
2
∗
0.063 + L 0.063
2
)
Note t%at t%e sensor surfa"e is ;:mm from t%e "entre line of t%e radiometer mountin, rod. Hen"e for t%e position of t%e radiometer sensor ;:mm must e sutra"ted from t%e mar/ed "entre of t%e dete"tor stand. +.
Fro"edure . Inverse Square Law for Heat #. Set power "ontrol to wide position and follow approximatel& #: minutes for t%e %eater to rea"% a stale temperature efore e,innin, t%e experiment. 2. )e"ord t%e radiometer readin, )4 and t%e distan"e from t%e %eat sour"e G4 for a numer of positions of t%e radiometer alon, %orizontal tra"/. It will ta/e
approximatel& 2 minutes for t%e radiometer to stailize after ein, moved to ea"% new position. •
Initial Values of Variables to be Used
istan"e from t%e %eat sour"e G4 1 >== mm. note t%at radiometer sensor surfa"e is ;:mm from t%e "enter line of dete"tor "arria,e and t%erefore "enter line position will e >;: mm.
B. Stefan-Boltzmann Law #. Set power "ontrol to maximum on t%e instrument "onsole. 2. )e"ord t%e radiometer readin, )4 and t%e temperature $4 at amient "onditions t%en for sele"ted in"rements of in"reasin, temperature up to maximum wit%in a pra"ti"al ran,e. Bot% readin,s s%ould e noted simultaneousl& at an& ,iven point. It is re"ommended t%at w%ile waitin, for t%e la"/ plate temperature to stailize etween ea"% in"rease of t%e %eater power "ontrol t%e refle"tive dis" is pla"ed in t%e radiometer aperture to prevent %eatin, effe"ts and zero drifts. •
Initial Values of Variables to be Used istan"e from radiometer to la"/ plate G4 istan"e from la"/ plate to %eat sour"e 4 1 := mm
1
2==
mm
+I.
)esults and is"ussion
. Inverse Square Law of Heat
B. Stefan-Boltzmann Law
)eadin,s $emp )eadin, $4
Jal"ulations
)adiometer )eadin, )4
$s
$
1 ##.=
1 $s@ - $@4
8(m2
?
?
8(m2
8(m2
:;
2=
D2A.#:
D==.#:
22#.@
2=:.D@
:>
2#
DD#.#:
D==.#:
2D2.@<
22#.;<
;>
2<
D@#.#:
D==.#:
2A>.>A
D=<.>@
>@
@#
D:<.#:
D==.#:
@:D.><
@;2.D>
>A
@;
D;2.#:
D==.#:
:=A.22
:#:.#@
#=D
:<
D<;.#:
D==.#:
;D=.AA
;<@.A@
#DD
A=
@=;.#:
D==.#:
AA;.D
#=>2.<;
℃
+II.
Jon"lusion $%e inverse square law is important as it ,ives a measure of %ow t%e intensit& of radiation falls off wit% distan"e from a sour"e. $%is %as impli"ations for t%e stora,e and use of radioa"tive sour"es. point sour"e of ,amma ra&s emits in all dire"tions aout t%e sour"e. It follows t%at t%e intensit& of t%e ,amma ra&s de"reases wit% distan"e from t%e sour"e e"ause t%e ra&s are spread over ,reater areas as t%e distan"e in"reases. n& o!e"t at elevated temperature ,ives off li,%t /nown as t%ermal radiation. $%e %otter an o!e"t ,ets t%e more li,%t it emits. s t%e temperature of t%e o!e"t in"rease6 it emits most of its li,%t at %i,%er and %i,%er ener,ies. s one moves furt%er from t%e sour"e6 t%e emitted parti"les are dispersed and are t%erefore less li/el& to stri/e t%e radiation measurement devi"e. Sin"e t%e area over w%i"% t%e emissions are dispersed is t%at of an expandin, sp%ere aout t%e sour"e6 t%e radiation intensit& follows t%e inverse square law as one move awa& from t%e sour"e
+III.
)eferen"es
http://www.s-cool.co.uk/a-level/physics/radioactive-decay-equations/revise-it/inverse-squarelaw-and-radiation
ppendi"es ppendix 3 Experimental ata . Inverse Square Law of Heat
istan"e6 G mm4
#==
)adiometer )eadin,6 ) 8(m24
B. Stefan-Boltzmann Law
$emperature )eadin, MJ4 )adiometer )eadin,6 ) 8(m24 $ ?4
ppendix B3 Sample Jomputation . Inverse Square Law for Heat -
Lo,-Lo, Flot
Lo, istan"e6 G mm44 Lo, )adiometer )eadin,6 ) 8(m244
B. Stefan-Boltzmann Law ppendix J3 ttendan"e S%eet
