WM Paper 2

f
rr\
-4^
Ya
[
| - , Dar
6rur^^r
e'rf)te*:Sitn'
tPl<
IE-
I
- /
/ th z'n{'
pti'l€ts
LtY'
fi
ttY
aY nt't n'a'fuel
MeasureBoltzmann's
ConstantUsinga Diode,/
\'/
=rrr-
George C. Zhang
F,xn'&in-y
Abstraqt
Fnrst
r tll]{istv?t. /)Ftt'peuf;cfufirmtt';e
EtllrLJ
Fin e
c*t'i u c-o&&
tnlrp in#ym,alr.,
t\a-^4r*
ln6re
e^''g'l '
';l
1";d
;'t;;;;';de,the
.,,...n$FP,i?a'oaffi;,orr^g@n"aioa"
u." (r:,
!:a,# Al'tY,
#
1:n1ty"1x';*lv(
measire,iin order,o ."rHil#Jot,r.n"nn's
consta#/Asa resuh,the measured
/
/l'laj
u<'
fu
c ,n 'g'wc-tc'n€le
f^ ':
Wu
j""A
Boltznrann
Boltznrann
constantis (1.380
constant
(1.380-+
* 0.006)x1
- ' - - " / " 0-23
0.006)x1g-23t
t /g
/K,.
wruyq Vilttdgv
Intrq'iuctill
c.,' ,,lcr, *{
9to;t-8nra'
'
(alt,< wyt,it \
5 / t a t k b r 4' f f i I
'E'ft*"'t .
,i ;:1
\,/
8"lrJ{fr+t
A diorl,:is a two-terminalcircuitelementthat minimizescurrentflow in one
WfuU I
directigl Eloltzmann'sconstant is an important physical constant that relates
Vvlti't
energ)at tt e individualparticlelevelwith temperatqndIn 19
1949,William Shockley
ly_ T/-r 6-B
\,/
\
st?tg,qhis diodeequationthat relatesthu
4jElg.EIUfSnfl of ti
{$qggJrffi{:
IJoltzmann's
c-onstant.
T/iisrelationship
is thediode/ - Z
\'\\-\\
6jtrapa6'ssisti€;lrl
.>)
whclr
'\
ffind
(urPt<':
n
Fc n,tva
rv
'fl/,rIJA
,
4t:froJs".
on,f, i,'X.a'( rot,
fr/tie fu,6 oh/l"iliot{t e at€
r,o+ e -Bj*rftg
lv u,'fu/ f uY €f k,:t{,r,t
"
'fit t,,^6.
rw
A((AL'kI"
t
c'nnt**
" r ".
cr, ,r r,,. .r...n, ,h;"r;; thediode,/,fr*A
1oisthereverse
saturation
curreng tatt l/
u^e
v.Xp b,t,, ,"tl;4k- t'11
I/ is flrevoltageacrossrhediodgr,,"
,/
e is themagnitude
-ofchargeaf}$1g
,yy#ri.
ftheetemen
it
fto'fsrBoltzmann'sconsra?z'
(*t i
ttre .1't''at6t'ta4/5
f is the absolutetemperatureoF#ffin,
'#a diorlo1
iSlte,gt^t-
WJ*,
-*EEc,
HN
h*,1
'7
t.e measure Boltzmann'sctnstant through a diode, We describehow to
linear.$zc
thc Shockle,Orf"jr,ation.^Finally,we discussthesignificant
of our
measuremenr.,/
Merhad
. I
r
_,
Ggtt4 '
lt ; sf'ttt,'l +o a/p@^ *14'
oluY,<
W W t"fno
''ffiPaawt
'
A
f(E'*'ur
r ..L ^..-;/a - 1 ydu
'
W!n0'/' )t'i/n[LL(r71.
r vue tl,ht ttdlj\-' a frs)n,
(,)
ly
f/^!L
In this,experiment, assuming th{junction
YV*r *- /tu-bsd €8,
ev
O)
ac7p
v'v
\
of E-$ris a perfect diode".ttrediode
voltagcssLfpose to be largeenoug$th.a&,,ctar
))& so thq,ifiormulS
canbe simVlifielz
16.rrJ
AP@
ky*n
S.efryade6,'ssutyfrt/ns.
v
r=roe#o Lu)
r'/ {lt
'fhe
di'rde's
I - 7 curve is nonlinear as the simplified Shockleydiode equation
]I'r,
Ul rahz
ut
/+ yl*
ral* +
#1-
tlttr
i i
describes.FIowever,a linear relationshipof tXg1dlg4gqryqlljo
the diodevoltage
7 is irtrplicitand describesa*t1l
e
Inl=lnlo*n;rv,
C )),
Therefore,Boltzmann's
constantis calculated
from the abovelinearrelationship
. HOrl
Plure@
to avo:io{
iistnS
^')^
, ,],
1'hecomponentssuch as a 2N3904transistor
'
g5nfilw*"asurement.
trr".t*uiii
..,,,n1..:^
,!
,o'r7hf,un
/. /
..
lt w';t
^ f r ,.- .L h,) ,/isrrik
,A,v f/.t- fow|/t'4
WlVfr
.ua'bJ
P*,iole, 9P[;t, oj*tr,
li'
ii
{
y:';{::
vlg sI'|
#; ;* #.f:
'[*'udt+i'w'rcspectivelv'
{'*ct*,s
/,1124€.
PB-503
rtt/tconstructed orpaGlobalSpecialties
,/
---*J42aC4
"
6it;u*^
W**i;:; ;;il;;;;
in /i,tia/r*{
/Aanu'{
4o f,t P,ttan lqu
n6 tt4('0t( "
amplifier,a 5.0kO(5Tt+Flresistor,and a 10.0kOlmeZf\esistor are usedin the
||e:::l:,;^"ProtoBoard"circuir
"f
BAa,gW
No.zlwuekiLHpn"Kto"
-*,
!-on,a LF356
7
'*tn'va"-b"
eaot' to"pdna"'#s?
t
2
t' /ilwurq"
al;tvo(, (mt"u"t' refv{tu
,"'riir
I
nI
cr\nnt'
NIc:t-
*s=*fl+
5111F
5ko
r
10ko
r
t
tzax+
\-7
+15V
L
E zrulgo+
Potentiometer
1kn
II
VoltmeterA
/
VoltmeterB
{ ano(#,2 W +^,4
Tg*!Bc.
iI
where 76 is the potential at Point B,
Rroozris the actual resistanceof a 10.0kCl(1
In orderto calculatlgg@$gr.Stanford
Research
SR715LCRMetermeasures
the actual tt0*Rre si stancetaafi}9-9 940 ! 0,00 1B
Ff
I the absolute
$lz
tempbratureoithe diodeis assumedto be room temperaluret{6t is298J + 0.5K.,)
,.
-/'
\ l ,{
:: i ,
! I i'ilr
v
l,/
t |
' l1w',1
w(4
/
,'t
1., '
6'tettr+vne4l
n
. l
Duringmeasurements,
startingthe potenti alVt at0V,the potential76 shouldbe \
f
However'
asI/uincreases'
,,ssatur
** ^o'"/'
fr;;
#:"
;"ffi;,sro*rv
b"iuw"
Trleeare (ot lhanui'|
experimentallymeasuredBoltzmann constant is
1,380x 10-2311rc.ptncethe diodecurrentI andthe diodevoltage7 are implicitly
--^---
,
r=.--
,S
linearrelated,the slopeis calculatedby MATLABtrydSa.O 475; inaddit*ena{,:
Bottzmann's
constant
isproportional
to*"_t:?
"t fu
-?,,4uK
4P )
lnt nee(
r,={{
0 Pef+t t't Srur Plx
0+ b-'&)rs V Aar€.
with the valueof fi
wherem is the slopefrom linearregression
knT
{,U
V*ltu-rtLs
StouVhu
Qian hsPt
nrt h/r(s'e.
{k-vJ'ut
('h"v( n '
@Ailo,n fiq- met/wct'of
e is 1.602x70-1eJ.I3l
\ ,ri'
.
runE,,pt;y ..
$fu! Unft
l@-fr-sgwe
L'n€ar(,t
hwe, ono{
,; ilir
relative uncertainty formula is describedas:
,iri)
Am
W|er 4o
,p
AT
(;)' + ( r)'
n
'
A relwvnwslhit'lter fb'a s affMw&,4
constan,{(.OO0*
$s aresult,the relativeuncertaintyof measuredBoltzmann's
,n",r4teb,tt,"e
to-r3J/K.
,/
Un 6or{a),-{3
\
t\ fot"aaU
:{
ri:
r:
r,.i.
, , .,',
tllr'
j
I
Ir
Vri::*eo V5 ln
-x\w-d
*
3$.${7tua-.33CSe?
,d*ms0 r{$f
Cnflr*S.0&?9Et
e* 0 00ssd
aA
f1 .
LotUn
frqurc
\| L//
Itu
tcsr E9 Mlil
fa
coL'l,,l
lst*
no*M (l'ts
o
i, ,: i"
;l
,,r,:l nr
or,2
or"1
ot/,
o6f,
o6it
oiz
I
o6rl
Uc{fl{t'5 {V)
I'fJ
i:i*## lfii',U+##-fiH
Ti;I;'='J
i'nt
u
tttt=squar*{ee)-is0.999g4, and reducedChi-square (rcs) is
'
69.9412.
,
/ ll
CC (s VAI ryb*a
ori,PJ
l'!
v
i,'r*o
I
{itu'
cow({;4.t.
''
o
;.
;##:.;',:ffi
#w*:,;ilT;ru.
T"";:*roW1.3B066x1o_}3]/4(pr@rangeofim€$ureo*-o,.,*"nn,,
V'
!
,
**'d;crysi''' "'"Yr;"rraee
Wl w\ w\VIOS
in,o,,tlil6edoconstant3hadditiffin|y0,43o/oofun..,t"iffiffitheresultsoflinear
N
llr,rh ,yy^,,
nn 4 Qft
,-
'/"bj%/e
ttlumoin
ou{ff:,ttot,sothemeasured
Boltzmann's
constantis preciseandaccurat".
ry@-,
-,
wen@sssllindicatesthattheLiffi@eddlodswm,6isltrongly
L
of a perfectdiodeberweenthe
T"qI"9the diodevoltage7, sotheassumptions
g
jundtibnof
E-B^na"#))
lforthediodevoltagesar@&g*.nthisexperiment,
stuA^''(!-ulhsttw
e%;;l i";;ffi""^;';;''g)n,n'4
'"
vlLhr%4 (,V, T,be#-,
gurrnwe,{'9 vtsiy f/Apga
l 1::,.
it.:i
af
t'*l <<| mwtts wv,re*oln-kl
I r.:..
'I
I
Becqg,$e
of
ror variances,reduced Chi-squareis much larger thafr,:
.;i
] r
1
-,r,
,,
i
eatu$slan
i,r..
e current through a diode and the voltage acrossa diode,the linearized
diodecurrentis stronglycorrelatedto the diodevoltagelffihermore, Boltzmann's
constantis WgffiWgim b& the slopeof that corretration.
The experimentally
/
'/r
with 680/0.ffi"n...
measuredBoltzmann's
constantis (1.380+ 0.006)x1O-zt11K
(" 4l-
ur1//rl?n,
yla'1x- yp'?@*
i'l
. ,.i,tts'
r
I
:,,'l t^6hft
h4,v< lBA.r,/r*+f
trl
ho,',t
I 1i{ i.},'i
/)
^Urr
WIL& arc- Vl-"
f"[w(&
full
l
v0/b5 ,
4--F
2- a#ufi"a
6
l!
a c4ie r,€/dz6
References
R.,
Roller,
D.8.,
Flum,
Physics
VolumeTwo:Electricity,magnetism,aryd /
[1]
[1982)
light.HoldenDay.,SanFrancisco,
CA.
V
Man,
W.,
49A:
Advanced
LabT:
Manual
and
Blend,R.,
supplerhentaty
[2013)."Ph
[2]
information".,
SanFranciscoStateUniversity,,SanFrancisco,CA.
| ,/
Burke,
Lpa,
S.M.,
TheNatureof Things".Brooks/Cole V
I.R.,(1996)."Physics:
[3]
PublishingCompany.,PacificGrove,CA,
,
,/'
lfrg nzrul*l
mNV-fv'W*^-u4
f r:
,l
-I
i
':
I
I
tL,
"
r
V
b
3
I
in Qk- -u/xt'v