SCIENCE DEPAR DEPARTMENT TMENT COLEGIO NUEVA YORK A Journa Jou rnall develo de velo ped by chil children dren for scie scientifi ntificc research rese arch purp purposes oses Number: I
K&U: _____ I&D: _____ P&E: _____ R: _____
Date: May 2! 2"#$
TACH C%MM*TS
_____________________________________________________ _________________________ ________________________________________________________ _______________________________ ___ Specific Heat Capacity of Three Different Metals Seba%ta' G(')a*e)# Abstract (152 words)
I' t+% P+y%,% SL ,(ur%e %e,('-.% *ab re/(rt! t+e /r',/a* am a'- (b0e,t1e a% t( 3'-! ,a*,u*ate! a'- -eterm'e t+e %/e,3, +eat ,a/a,ty (3 t+ree -33ere't matera*% 4r('! a*um'um! a'- ,(//er56 I' (r-er t( -( t+%! t+e ,(ur%e re%ear,+e-! by t+er ('! +( t( ,a*,u*ate t+e %/e,3, +eat ,a/a,ty (3 a matera*6 T+e met+(-(*(7y met+(-(*(7 y a% %m/*e t( 3(**( a% t % ay t(( /u',tua*6 T+e re%u*t% ere a*m(%t ,erta' a% t+e /re-,te- r(' 1a*ue t( be a% (3 89!±0,2 a'- t+e (bta'ea% 3 89!8 ;6<7=#6>C=#6 I' t+e %ame ay! t+e /re-,te- 1a*ue (3 a*um'um a% (3 !? a'- t+e (bta'e- a% (3 !@6 I% t+ t+% t+at b(t+ meta*% +a- a' err(r (3 ar(u'- "!"9#8 ,(',*u-'7 t+% *ab(rat(ry a% %u,,e%3u*! but! a% a' m/r(1eme't a'- a*
General -eterm'e t+e %/e,3, +eat ,a/a,ty (3 r('! a*um'um! a'- ,(//er T( -eterm'e T( u%e a te,+'(*(7,a* re%(ur,e +e' /r(,e%%'7 -ata a'- a*
T( %
m ∆ T
5
T( %(*1e 3(r c ' t+e eFuat(' 2! e/(%e- ' t+e 'tr(-u,t('! a'- 3'- t+e %*(/e (3 t+e Q 1% m ∆ T
7ra/+ ' (r-er t( 3'- t+e %ame c A'- ,+e,<'7 (ut 3 b(t+ c’s are eFua* Hypothesis
I3 e 3'- t+e %/e,3, +eat ,a/a,ty ' t+e %*(/e (3 Q 1%
∆ T 7ra/+! t+e' t (u*- be t+e %ame
%/e,3, +eat a% t+e ('e (bta'e- ' t+e eFuat(' 26
+ntrod$ction T+ere.% a t(/, ' t+e (r*- (3 P+y%,% t+at 'Fure% ab(ut 3a,t(r% t+at /er1a-e (ur *1e% ' e1ery ,('tet y(u *((< at t6 It.% ab(ut t+erma* /+y%,%6 I' a 1ery 7e'era* ay t ta*<% ab(ut +eat! e'er7y a'tem/erature! a'- +y I.m %ay'7 t+at t+e%e 3a,t(r% / er1a-e (ur *1e% ;u%t ta
I' t+% %ame (r-er (3 -ea%! t+ere.% a'(t+er t(/,! '%-e t+e a*rea-y ta*
,('ta,t t+ ea,+ (t+er6 T+% %tuat(' % <'(' a% t+e )er(t+ *a (3 t+erm(-y'am,% %',e t+% %ee'7 'te**7e't*y 7(e% be3(re t+e t+(u7+t% ,('ta'e- ' t+e e%%e'ta* r%t a'- Se,('- La% (3 T+erm(-y'am,%6 4Na1e! 2"#25 A'- t+e *a%t term t( taC=#5! a'- ∆ T % t+e ,+a'7e ' tem/erature mea%ure- ' >C (r K6 Ht+ t+e %ame -ea! e mu%t %tate t+e term +eat ,('%er1at(' 4+eat *(%t % eFua* t( +eat 7a'e-5 a% %+( be*( 4'ame t a% eFuat(' 25: −Q1 =Q2
−( mc∆T ) =mc∆T Jut! t+ere.% a 'e 1arab*e e +a1e'.t 'tr(-u,e 't( t+% *ab! c (r %/e,3, +eat ,a/a,ty6 A,,(r-'7 t( t+e eb%te! T+e P+y%,% C*a%%r((m! %/e,3, +eat % t+e am(u't (3 +eat /er u't ma%% reFure- t( ra%e t+e tem/erature by ('e=-e7ree Ke*1' (r Ce*%u% 4K (r >C56 T+e re*at('%+/ betee' +eat a'tem/erature ,+a'7e % u%ua**y e/re%%e- ' t+e 3(rm %+(' ab(1e +ere , % t+e %/e,3, +eat6 4T+e P+y%,% C*a%%r((m! #??$=2"#$5 Jy t+e %ame -ea! a'- 3(,u%'7 t+ t+e (b0e,t1e% *%te- ' t+e /a7e '(6 # (3 t+% re/(rt! e ,a' 3'- a',a*,u*ate t+e %/e,3, +eat ,a/a,ty (3 a' u'<'(' (b0e,t by t( ay%6 T+e 3r%t! a'- t+e(r,a* ('e! % %(*1'7 3(r , ' t+e +eat eFuat('! (r eFuat(' #: 4See be*( t+e mat+emat,a* /r(,e%% a'- a*
Q =c m∆ T He ,a' (b%er1e t+at! a% t+e ma%% a'- t+e ,+a'7e ' tem/erature ere mu*t/*y'7 t+ t+e %/e,3, +eat! t+ey /a%% t( -1-e t+e +eat6 Ver3y'7 t+at t+% 'e eFuat(' % ,(rre,t! e ma-e a -me'%('a* a'a*y%% 4%+(' be*(5:
⊏
Q ⊐=⊏ c ⊐ m∆ T J =J ∙ k g−1 ∙ ℃−1 kg ∙ ℃ −1
−1
−1
J∙kg ∙ ℃ = J ∙ k g ∙ ℃
−1
A'- t+e %e,('- ay t( 3'- t+e 1a*ue (3 t+e %/e,3, +eat ,a/a,ty % by 7ra/+,a* a'- mat+emat,a* a'a*y%%6 r%t! y(u +a1e t( ta
y =mx + b Q ( y )=c ( m) m ∆ T ( x )
Jy t+% -ea! t+e 7ra-e't (3 t+e *'e % eFua* t( t+e %/e,3, +eat ,a/a,ty! %( 7 % eFua* t( c 4a% %+(' be*( a'- a*
g= m
Materials -
-
-
-
-
-
Ver'er.% Lab ue%t & Gra/+ S(3tare Ja*a',e !"#"$g) 8 Ver'er.% T+erm(meter 4±0,01ºC) 8 Jea
-
-
-
-
-
T+reaHater Meta*% 4r('! a*um'um a'- ,(//er5 Ca*(rmeter 4a*um'um5 Lab Jur'er! U'1er%a* Su//(rt! Meta* Gr- a'- Tr/(-
Classification of 'ariables %ontrolled& T+e r((m tem/erature a'- /re%%ure ' t+e r((m a%
-
-
Methods #6 Set u/ a %m/*e ,a*(rmeter a% ' 7ure 2 %+(' ' A//e'- A -
26 Mea%ure 8""m* (3 3au,et ater ut*)'7 a 7ra-uate- barre* a'- /(ur t ' a $""m* mea%ur'7 bea
-
es$lts
I' +arm('y t+ t+e eFuat(' 2 −Q1 =Q2
−( mc∆T ) =mc∆T A% t+% %,e't3, art,*e re%ear,+e% 3(r t+e %/e,3, +eat (3 a' u'<'(' matera*! e +a1e t( %tate t+at:
-
−Q1 = Heatlost by the material
-
Q2= Heat gained bythe system
-
Ht+ t+%! t+e %y%tem % 3r%t 'tr(-u,e- a'- t % <'(' a% t+e %um (3 b(t+ +eat% /re%e't ' t! 3(r ('e +a'- t+e ater a'- 3(r t+e (t+er! t+e a*um'um ,a*(rmeter6 A,,(r-'7 t( t! e +a1e a 3'a* eFuat(' t+at ** +e*/ u% ' 3'-'7 t+e %/e,3, +eat ,a/a,ty (3 t+e matera*: 4Name t a% eFuat(' @5
mc∆T (¿¿ Material )=mc ∆T Water + mc ∆T Calorimeter
-
−¿
-
Data collection Shon in a table ith their respective explanation and numeration
Part I: Ra -ata tab*e%
-
*ater added
Mass, in kg (±0,01) - Materials - "!@$@ $sed
-
%alorimeter
-
"!"9$
- (ron
-
"!#2?
- Aluminum
-
-
Materials $sed
-
-
Hater "!"9#"
"!#9@# - A*um'um Tab*e #: Ma%%e% (3 t+e matera*% u%e-! ,a*(rmeter ' <*(7ram%
-
Syste " Ti"e (s)
-
-
-
82""
-
Tab*e 2: S/e,3, +eat ,a/a,ty (3 t+e %y%tem matera*%! ' ;6<7 =#6>C=#
-
%opper
-
Specific heat capacity, in J.kg 1 .ºC -1 (±2)
-
-
-
"
-
-
$"
-
Tr a* # #! @ #! 2
Te"perat$res of the Syste"s, in ºC (±0,1)
*ith iron
-
-
Tr a* 2 #! 2 #!
-
*ith aluminum
-
Tr a* # #! $ #?!
-
-
-
Tr a* 2 #! # #! $
-
-
Tab*e 9: Tem/erature% (3 t+e %y%tem%! ' Ce*%u% -e7ree% 4ta
*ith copper Tr a* # #! 2 #! 8
-
-
Tr a* 2 #! ? #! #
-
#2"
-
-
#"
-
-
28"
-
-
9""
-
-
9$"
-
-
82"
-
-
8"
-
#! $ #! #?! 2 #?! 9 #?! 2 #?! 2 #?! 2
-
#?! 2 #?! 2"
-
2"! # #?! ? #?! ? #?! ?
-
#! 9 #! #! #?
-
#! ? #! ? #! ?
-
#! ? #?! 2 #?! 9 #?! 8 #?! 8 #?! 8 #?! 8
-
#! $ #! $ #! #! #! $ #! $ #! $
#! 2 #! 9 #! 2 #! 9 #! 8 #! 8 #! 8
-
Materials
-
-
Tr a* # - ?2! - " 2 - #! - $" 2 - #! - #2" $ - #! - #" - #?! - 28" 2 - #?! - 9"" 9 - #?! - 9$" 2 - #?! - 82" 2 - #?! - 8" 2 Pr(,e%%e- -ata tab*e% Ti"e (s)
-
-
-
Te"perat$re of the Materials, in ºC (±0,1)
(ron
-
Tr a* 2 ?2! 2 #! #?! 2 #?!
Aluminum
%opper
Tr - Tr - Tr a* 2 a* # a* 2 - ?2! - ?2! - ?2! 2 2 2 - #! - #! - #! $ 8 # - #! - #! - #! ? $ 2 - #?! - #! - #! 2 $ 9 - #?! - #! - #! 2" 9 2 2"! - #?! - #! - #! - #? # 8 9 #?! - #! - #?! - #! - #! ? ? 8 $ 8 Tab*e ' Ce*%u%- -e7ree% #?! 8: Tem/erature% #?!matera*%! #! - #! -(3 t+e - #! ? " % a% t+e?'ta*! a'- 8" 8 % a% t+e 3'a* $ tem/erature%5 8 4ta
-
Tr a* # ?2! 2 #?! #! 9 #! #!
-
-
Pa rt II:
-
I' (r-er t( +a1e a be%t a,,ura,y ' t+e 3'a* /r(/a7at(' (3 err(r! a mea' 4e/re%%e- a% μ 5 (3 b(t+ tra*% (3 t+e t+ree matera*% a% (bta'e-6
-
'-'7 t+e mea' (3 -ata % t+e %um (3 a** t+e -ata
(∑ x ) -1-e- ' t+e 'umber (3 -ata
,a*,u*ate- 4n56 Jy t+% e ,a' 3'- t+e 'et eFuat(': 4Name t a% eFuat(' $5
μ=
-
∑x n
Mean Te"perat$res of the Syste"s, in ºC (±0,1)
-
-
ime s)
-
*ith iron
-
" $"
-
#2" #" 28" 9"" 9$" 82" 8"
-
#!? #!@
*ith aluminum
-
#!? #?!9 #?!$ #?! #?!$ #?!$ #?!$
#!@ #?!2
-
*ith copper #!"@ #!2@
-
#!$ #!?@ #?!"@ #?!2 #?!#@ #?!#@ #?!#@
#!8 #!8@ #!8@ #!@ #!@ #!@ #!@
Tab*e @: Tem/erature% mea' (3 t+e %y%tem%! ' Ce*%u% -e7ree% 4ta
-
Ti"e (s)
-
- " - $" - #2" - #"
-
-
Mean Te"perat$res of the Materials, in ºC (±0,1)
- (ron - ?2!2 - #!@ - #!? - #?!9
- Aluminum - ?2!2 - #?!9 - #!@ - #?!2
%opper
-
- ?2!2 - #!2@ - #!8 - #!8@
-
28"
-
#?!$
-
#?!8
-
#!8@
-
9""
-
#?!
- #?!@@ - #?!8 - #?!8 - #?!8
-
#!@
9$" 82" 8"
#?!$ #?!$ #?!$
Tab*e @: Tem/erature% mea' (3 t+e matera*%! ' Ce*%u% -e7ree% 4ta
#!@ #!@ #!@
-
Data process Shon in each respective material calculating the s,h,c, by to different methods# in the same ay during process# units ere not included,
-
Part I: Ir(' =r%t met+(-: EFuat(' '(6 @ a'- BS(*1'7 3(r c.
-
mc∆T (¿¿ Iron)= mc∆T Water + mc∆T Calorimeter
−¿
-
(r
mc ∆T (¿¿ Iron) −Q1 =−¿
-
−( ( 0,1298 ± 0,01 ) c ( 19,6 ± 0,1− 92,2 ± 0,1 ) )
-
−( ( 0,1298 ± 0,01 ) c (−72.6 ± 0,2 ) )
-
( 9,42348 ± 0,7 ) c =J
-
(r
Q2=mc ∆T Water
-
( ( 0,565 ± 0,01 ) ∙ ( 4200 ± 2 ) ∙ ( 19,6 ± 0,1 −17,9 ± 0,1 ) )
-
( 2373 ± 4,3 ) ∙ ( 1,7 ± 0,2 )
-
( 4034,1 ± 4,8 )= J
-
(r
Q2=mc ∆T Calorimeter
(( 0,0736 ± 0,01 )∙ ( 878 ± 2 )∙ ( 19,6 ± 0,1 −17,9 ± 0,1 ) ) ( 64,6208 ± 8,9 ) ∙ ( 1,7 ± 0,2 )
-
(109,85536 ± 2,8 ) = J
Since now both sides of the equation are simplied we can determine that the specic heat capacit of the iron is!
-
mc∆T (¿¿ Iron)= mc∆T Water + mc∆T Calorimeter
−¿
( ( 9,42348 ± 0,7 ) c )=( 4034,1 ± 4,8 ) +( 109,85536 ± 2,8 ) c=
( 4143,95536 ± 7,6 ) ( 9,42348 ± 0,7 )
c =( 438,3532697 ± 3,365 )
−1
−1
c 438,4 ± 3,4 J ∙ k g ∙ ℃
-
-
m ∆ T 7ra/+
=Se,('- met+(-: Gra-e't (3 t+e Q 1%
Gra/+ #: L(7art+m, 3u',t(' (3 t+e -ata (3 r('! Q 1% m ∆ T ! t+ a** +% err(r bar% a'- t+e ,ur1e (3 be%t -
A% t+e 3u',t('
! ( x )= 4.384 ∗0.9049
x
'-,ate%! t+e 7ra-e't%*(/e % eFua* t(
4.384 6 Ta
' m'- t+at t+% re%u*t a% 3(u'- ta<'7 't( a,,(u't t+e ma%% ' 7! %( ' <7! t+e 7ra-e't ** be x
89!8! a% %+(' ab(1e6 T+e 0.9049
-
Part II: A*um'um
% b! <'(' a% y='ter,e/t6
-
=r%t met+(-: EFuat(' '(6 @ a'- BS(*1'7 3(r c. mc∆T (¿¿ Iron)= mc∆T Water + mc∆T Calorimeter
−¿
-
(r
mc ∆T (¿¿ "l#min#m) −Q1 =−¿
−( ( 0,04955 ± 0,01 ) c ( 19,4 ± 0,1− 92,2 ± 0,1 ) )
−( ( 0,04955 ± 0,01 ) c (−72,8 ± 0,2 ))
( 3.60724 ± 0,7 ) c = J -
(r
Q2=mc ∆T Water
-
( ( 0,565 ± 0,01 ) ∙ ( 4200 ± 2 ) ∙ ( 19,15 ± 0,1−17,85 ± 0,1 ) )
-
( 2373 ± 4,3 ) ∙ ( 1,3 ± 0,2 )
-
( 3084,9 ± 4,8 )
-
(r
Q2=mc ∆T Calorimeter
-
(( 0,0736 ± 0,01 )∙ ( 878 ± 2 ) ∙ ( 19,15 ± 0,1 −17,85 ± 0,1 ) )
-
( 64,6208 ± 8,9 ) ∙ ( 1,3 ± 0,2 )
-
-
Since now both sides of the equation are simplied we can determine that the specic heat capacit of the aluminum is! mc∆T (¿¿ "l#min#m )=mc ∆ T Water + mc ∆ T Calorimeter
−¿
( 3,60724 ± 0,7 ) c =( 3084,9 ± 4,8 ) +( 84,00704 ± 2,4 ) c
-
=
( 3168,90704 ± 7,2 ) (3,60724 ± 0,7 )
c =( 878,4852242 ± 1,7 ) −1
-
( 84,00704 ± 2,4 )
−1
c 878,5 ± 1,7 J∙kg ∙ ℃
Part III: C(//er =r%t met+(-: EFuat(' '(6 @ a'- BS(*1'7 3(r c.
-
mc ∆T (¿¿ Co$$er )= mc∆T Water + mc∆T Calorimeter
−¿
-
(r
mc∆T (¿¿ Co$$er ) −Q1=−¿
-
−( ( 0,036475 ± 0,01 ) c ( 18,5 ± 0,1−92,2 ± 0,1 ) )
-
−( ( 0,036475 ± 0,01 ) c (−73.7 ± 0,2 ) )
-
( 2,68819 ± 0,5 ) c = J
-
(r
Q2=mc ∆T Water
-
( ( 0,565 ± 0,01 ) ∙ ( 4200 ± 2 ) ∙ ( 18,5 ± 0,1−18,05 ± 0,1 ) )
-
( 2373 ± 4,3 ) ∙ ( 0,45 ± 0,2 )
-
( 1067.85 ± 4,8 )= J
-
(r
Q2=mc ∆T Calorimeter
(( 0,0736 ± 0,01 )∙ ( 878 ± 2 )∙ ( 18,5 ± 0,1 −18,05 ± 0,1 ) ) ( 64,6208 ± 8,9 ) ∙ ( 0,45 ± 0,2 )
-
( 29.07936 ± 1,7 ) = J
Since now both sides of the equation are simplied we can determine that the specic heat capacit of the iron is!
-
mc∆T (¿¿ Iron)= mc∆T Water + mc∆T Calorimeter
−¿
( ( 2,68819 ± 0,5 ) c ) =( 1067.85 ± 4,8 )+( 29.07936 ± 1,7) c=
( 1096.92936 ± 6,5 ) ( ( 2,68819 ± 0,5 ) )
c =( 408,0549961 ± 12,5 ) −1
-
c 408,1 ± 12,4 J∙kg ∙ ℃
-
−1
Concl$sion A% t+e re%ear,+ Fue%t(' a//r(a,+e%! -o the specific heat capacity of three metals can be determined# focusing into to .) methods# during a calorimetry laboratory/0# a'- ' +arm('y t+ t+e re%u*t% (bta'e- t+e 3r%t met+(- t( ,a*,u*ate t+e %/e,3, +eat ,a/a,ty (3 a matera* % B%(*1'7 3(r ,. ' t+e eFuat(' (3 +eat ,('%er1at(' 4/re%e't ' t+e +(*e art,*e5! +ere a ,(m/ar%(' betee' t+e *ab(rat(ry 3'a* re%u*t% a'- t+e rea* re%u*t% 4a,,(r-'7 t( t+e IJ.% 7u-e5 % %+(' 'et ' t+e 'et tab*e a'- ' t+e %ame ay! t+e %e,('- met+(- % %
-
,a/a,ty! t+% 7ra/+ % %+(' ' t+e A//e'- J:
-
-
Co"parisson of the res$lts
S/e,3, eat Ca/a,ty 4Q#!"5
-
IJ%
-
-
-
Ir
-
8
-
Obta'e-
8
-
-
-
A*u m 'u m !?
-
!@
-
C(
9?
8"
Tab*e $: C(m/ar%(' (3 t+e S/e,3, eat Ca/a,ty Re%u*t% Let u% <'( ,(m/are t+% art,*e t+ t+e %,e't3, ,('tet6 It.% 1ery m/(rta't t( %tu-y a'a,<'(*e-7eab*e t((! t+e %/e,3, +eat ,a/a,ty (3 a matera* be,au%e % t+e 'tr(-u,t(' t( (ur (r*- 3u** (3 t+erma* ,(',e/t%! t+ t+% a'- ' *ab (r t+ (ur re%u*t% e ,a' 3'a**y ,(',*u-e t+at t+e %/e,3, +eat ,a/a,ty (bta'e- (3 t+e r(' a'- a*um'um a% ,*(%e t( /er3e,t('6 T+% 'Fure% ab(ut +at a% r('7 -ur'7 t+e met+(-(*(7y (3 t+% *ab! a'- 3'a**y! t+ere a% /re%e't a ra'-(m err(r %',e t+% ty/e (3 err(r % +uma'! a'- I! Seba%t' G(')*e)! I.m a +uma'6 Im/r(1eme't%: T( -%/*ay a better %(*ut(' 3(r t+e *ab(rat(ry ',*u-'7 m(re /re,%e a'- a,,urate matera*% a'a*%(! -33ere't %y%tem% 4e*e,tr,a* ,urre',e5
-
eferences
-
K6A6 T%(<(%6 42"#"56 1hysics for the (2 'iploma# Standard and -igher 3evel, Great Jrta': Cambr-7e U'1er%ty Pre%%6
-
Cam/be**! M6 4May 2! 2"#@56 T+erma* # = Im/(rta't De3't('%6 (2 1hysics S3 4evision 6 Ca'a-a: Y(uTube6
-
T+e P+y%,% C*a%%r((m6 4#??$=2"#$56 1hysics utorial 6 4S6 G(')*e)! E-t(r5 Ta
- Na1e! C6 R6 42"#256 -yper 1hysics6 4S6 G(')*e))! E-t(r! & G6 U6 State! Pr(-u,t(r5 Ta
Appendi- A//e'- A: 7ure%
-
-
"igure 1! #hermal equilibrium
-
"igure $! %abelled diagram of a simple calorimeter. ! #hermal equilibrium
-
A//e'- J: Gra/+
-
Gra/+ #: L(7art+m, 3u',t(' (3 t+e -ata (3 r('! Q 1% m ∆ T ! t+ a** +% err(r bar% a'- t+e ,ur1e (3 be%t 3t
