Lab experiment THE STEFAN-BOLTZMANN LAW

THE STEFAN-BOLTZMANN STEFAN-BOLTZMANN LAW

Objective • •

To study the relationship between the power related by a blackbody to its temperature To determine the Stefan-Boltzmann constant c onstant

Theory

Resistivity The resistance of wire is given by (1

R=ρL/A

!here L " length of wire A " cross-sectional area ρ " resistivity (#m

The relative resistivity is defined as the ratio of its resistivity at temperature T to its resistivity at $%%&' f ) $%% is its temperature at $%%& and R $%% $%% is it resistance at $%%&* the relative resistance can be written as ρ’ = ρ/ρ!!

(+

,ssuming that  and , does not change* the temperature te mperature T &elvin of a tungsten wire can be appro.imated as T = "! # "$ρ’ # "%ρ’

($

!here "! " 1%$'/0/* "$ " +1'0$ and "% " +'00 The Stefan-Boltzmann aw The power radiated from a blackbody is given by b y* & = 'AT(

(

!here A " cross-sectional area T " temperature in &elvin ' " Stefan-Boltzmann constant

n this* e.periment* the filament of a light bulb is assumed to behave as a blackbody' Since the area surrounding the tungsten filament is a vacuum* the electrical power to the filament is wholly radiated as thermal radiation' A))"r"t*+

ight bulb (tungsten filament* 1+2* power supply (%-1+2* ammeter* voltmeter* rheostat and wires'

Metho,

1' The apparatus was arranged as shown in diagram below3

% 8 1+ 29:

Bulb* 1+2

2

, +' 4ower supply then has been

set to 1% volts and the rheostat was set to the high

resistance' $' The I  and V has been recorded when the switch is closed' 4. The resistance of the rheostat then decreased to obtain the different value of  I  and V  5. Step  then has been repeated for several times

Re+*t No. $. %. . (.

 / 7 6 5

0 1'05 1'/% 1'65 1'5%

& 15'6% 1+'6% 0'0% 7'5%

Lo1 & 1'10 1'1% 1'%% %'//

R '1% $'/0 $'6 $'$$

ρ’ %'%5+ %'%0 %'%6 %'%+

T 115'+$ 11'5/ 11$'0+ 11$'%5

Lo1 T +'%6+ +'%50 +'%56 +'%5$

2. 3. 4. 5.

 $ + 1

1'$5 1'15 %'05 %'7%

5'% $'5 1'0% %'7%

%'7$ %'5 %'+/ -%'15

+'06 +'61 +'1% 1'$

%'%$7 %'%$$ %'%+6 %'%1/

111'06 111'%0 1%0'56 1%7'/+

+'%0 +'%6 +'%$0 +'%$$

6"c*"tio7+ & = 0 $. 4 " / . 1'05 4 " 15'6% %. 4 " 7 . 1'/% 4 " 1+'6% . 4 " 6 . 1'65 4 " 0'0% (. 4 " 5 . 1'5% 4 " 7'5% 2. 4 "  . 1'$5 4 " 5'% 3. 4 " $ . 1'15 4 " $'5 4. 4 " + . %'05 4 " 1'0% 5. 4 " 1 . %'7% 4 " %'7%

R = /0 $. R " (/;(1'05 R " '1% %. R " (7;(1'/% R " $'/0 . R " (6;(1'65 R " $'6 (. R " (5;(1'5% R " $'$$ 2. R " (;(1'$5 R " +'06 3. R " ($;(1'15 R " +'61 4. R " (+;(%'05 R " +'1% 5. R " (1;(%'7% R " 1'$

T = "! # "$ρ’ # "%ρ’

(!here "! " 1%$'/0/* "$ " +1'0$ and "% " +'00 1' T " 1%$'/0/ = >(+1'0$(%'%5+? = >(+'00(%'%5+? T " 115'+$ +' T " 1%$'/0/ = >(+1'0$(%'%0? = >(+'00(%'%0? T " 11'5/ $' T " 1%$'/0/ = >(+1'0$(%'%6? = >(+'00(%'%6? T " 11$'0+ ' T " 1%$'/0/ = >(+1'0$(%'%+? = >(+'00(%'%+? T " 11$'%5 5' T " 1%$'/0/ = >(+1'0$(%'%$7? = >(+'00(%'%$7? T " 111'06 6' T " 1%$'/0/ = >(+1'0$(%'%$$? = >(+'00(%'%$$? T " 111'%0 7' T " 1%$'/0/ = >(+1'0$(%'%+6? = >(+'00(%'%+6? T " 1%0'56 /' T " 1%$'/0/ = >(+1'0$(%'%1/? = >(+'00(%'%1/?

ρ’ = R/R!!  8R !! = 49.(%%:; $. )< " ('1%;(70'++ )< " %'%5+ %. )< " ($'/0;(70'++ )< " %'%0 . )< " ($'6;(70'++ )< " %'%6 (. )< " ($'$$;(70'++ )< " %'%+ 2. )< " (+'06;(70'++ )< " %'%$7 3. )< " (+'61;(70'++ )< " %'%$$ 4. )< " (+'1%;(70'++ )< " %'%+6 5. )< " (1'$;(70'++ )< " %'%1/

T " 1%7'/+

A7"y+i+

$' @radient graph log 4 versus og T y " 1'1/ 8 %'+ " %'0/ . " +'%575 8 +'%$0 " %'%1/1 0.98

A"

0.0181

" 5'1 ' ,rea of circle " r + " (%'%%%++ " 1'+57 . 1% -7 m+ ,rea of filament " (1'+57 . 1%-7 . %'%$

" $'77 . 1% -0m+ 5'

4 " C,T 1'0% " C($'77 . 1% -0(1%0'56 C " '6% . 1% -6 w;m+& 


The relationship between power radiated by blackbody radiation to temperature was clearly seen by conducting this e.periment' This e.periment has been conducting by using a regular 1+2 light bulb with its filament as the radiating body' The temperature of the filament can be varied from room temperature (when no current flows through it'The power radiating from the filament (4 may be determined from the electrical power input to the lamp bulb* which is simply the product of the current through it ( and the voltage across it (2' The result of the e.periment can be seen by the graph plotted which 4ower* 4 versus Temperature* T' Drom the graph it is clearly shown when temperature are increases the power also increases' The shape of the graph is E-shape graph* which is e.ponential increases' Drom the og 4 versus og T graph it is clearly seen the graph is in linear shape' The gradient of the graph is 5'1 '

9uring this e.periment* the precautions step that has been taken are to make sure all the apparatus eFuipment such as connecting wire* power supply* bulb and rheostat are in good conditions' !e have try to avoid from choosing any broken or damage eFuipment that will effect

on our result to become not accurate' Gthers* when taking the voltmeter and ammeter reading our eyes should be perpendicularly position to the reading the scale to avoid any paralla. error occurs' The ammeter and voltmeter also has been calibrated to the zero point of the instrument to ensure there is no systematic errors'

6o7c*+io7

n conclusion* the main obHective which to study the relationship between the power radiated by a blackbody to its temperature and to determine the Stefan Boltzmann constant are achieved' The results of the e.periment are accepted by comparing to the theory'