MAT MATA KULI KULIAH AH
: TERMOD RMODIN INAM AMIK IKA A KEB KEBUMIA UMIAN N
DOSEN
: Dr. Imran Hilman
TUGAS KE -
:1
KELOMPOK
:1
Soal: A. Hala Halama man n 25, 25, (Zemans! Mar . "# Di$$man Ri%&ar' H. 1()*. Kalor dan Termodinamika. Ban'+n,.
1.1
ITB
Sis$em A# B# B# 'an a'ala& a'ala& ,as 'en,an //r'ina$ //r'ina$ P# P# 0 P2# 02 02 P3# 03. 03. Bila A 'an 'alam ese$im4an,an $ermal# 5ersamaan 4eri+$ 'i5en+&i. P0 6 n4P 6 P303 7 8 Bila B 'an 'alam ese$im4an,an $ermal# &+4+n,an 4eri+$ 'i5en+&i P202 - P303 9
'
n B P V } over over {V'} {V'} 7 8
¿
Lam4an, n# 4# 'an B2# a'ala& $e$a5an. a Ti,a Ti,a ;+n,si a5aa& !an, sama sa$+ sa$+ 'en,an lainn!a 5a'a ese$im4an,an ese$im4an,an $ermal $ermal 'an masin,-masin, ;+n,si i$+ sama 'en,an $# 'en,an $ men!a$aan $em5era$+r em5iris < 4 H+4+n,an a5aa& a5aa& !an, men!a$aan ese$im4an,an ese$im4an,an $ermal an$ara an$ara A 'an B <
1.=
Sis$em Sis$em A 'an B a'ala& a'ala& ,aram 5aram 5arama,ne a,ne$i $i 'en,an 'en,an //r'in //r'ina$ a$ masin,-m masin,-masin asin, , χ # M 'an χ ' # M2. Sis$em a'ala& ,as 'en,an //r'ina$ // r'ina$ P# 0. Bila A 'an 'alam 'a lam ese$im4an,an $ermal# 5ersamaan 4eri+$ 'i5en+&i 4 πnRC
%
χ − MPV =0
Bila B 'an 'alam ese$im4an,an $ermal# i$a 'a5a$an '
nRΘ M + 4 πnRC πnRC ' Den,an n# R# %# 2% 'an
Θ
%
χ ' − M ' PV = 0
$e$a5an.
a Ti,a Ti,a ;+n,si manaa& manaa& !an, sama sa$+ sama lainn!a lainn!a 5a'a ese$im4an,an ese$im4an,an $ermal < 4 4 Sam Samaan aan ;+n, ;+n,si si i$+ i$+ 'en, 'en,an an $em $em5era 5era$+ $+rr ,as ,as i'ea i'eall
θ # 'an 'an li&a li&a$l $la& a& a5a a5aa& a&
5ersamaan i$+ mer+5aan mer+5a an 5ersamaan ea'aan !an, !an , 'i4a&as 'alam 4a4 =.
1.>
Dalam $a4le 4eri+$ini# 4ilan,an5a'a4arisa$asmen!a$aan$e 4ilan,an5a'a4ar isa$asmen!a$aan$eanan anan ,as 'alam$a4+n, $&erm/me$er ,as ?/l+m$e$a5s+'a&'en,an/resi+n$+r+an,4+n$+# 5em+aian$ermal$a4+n,# 'anse$er+sn!a e$ia$a4+n,i$+'i4en e$i a$a4+n,i$+'i4enaman'alamsel$i$i$ri5 aman'alamsel$i$i$ri5el el air. Baris4a@a&men!a$aan5em4a%aan$eanan !an, 4erses+aiane$ia$a4+n,'ielilin, 4erses+aiane$i a$a4+n,'ielilin,i/le&4a&an5a'a$ i/le&4a&an5a'a$em5era$+r$e$a5 em5era$+r$e$a5 !an,
4el+m'ie$a&+i4esarn!a. Hi$+n,la& $em5era$+re ,as i'eal θ 'ari 4a&an i$+ G+naan lima an,a 4er5eran.
1.C
Ptp , mm H,
1888#8
8#88
88#88
=8#88
P # mm H,
1>#>
111#*
*#)=
>)>#(
Ham4a$an R2 'ari&am4a$ar4/n$er$en$+memen+&i5ersamaan
√
log R ' θ
= a + b log R '
#
Den,an a 7 -1#1*'an 47 8#*. a Dalamri/s$a$ &eli+m %air# &am4a$ann!a$ern!a$asama'en,an 1888 . Bera5aa&$em5era$+rn!a< 4 B+a$la&,ra;i l/,-l/, R2 $er&a'a5 θ 'alam isaran &am4a$an 'ari 1888 &in,,a >8.888
1.
Ham4a$an Kris$al ,ermani+m !an, 'i'/5memen+&i5ersamaan '
log R = 4,697−3,917 log θ . a Dalamri/s$a$ &eli+m %air# &am4a$ani$+'i++r'an$ern!a$asama'en,an =1) . Bera5aa&$em5era$+rn!a< 4 B+a$la&,ra;i l/,-l/, 'ari R2 $er&a'a5 θ 'alam isaran &am4a$an an$ara =88 &in,,an >8.888.
Jawaban: A.
1. K//r'ina$ +n$+ sis$em A 7 P # 0 B 7 P2 # 02 7 P3 # 03. sis$em A 'an se$im4an, $ermal 'en,an 5ersamaan P0 6 n4P 6 P303 7 8. Sis$em B 'an se$im4an, $ermal 'en,an 5ersamaan P202 6 P303 9
nB ' P V V '
7 8
n # 4 'an B2 a'ala& $e$a5an. Un$+ A 7 P0 6 n4P 6 P303 7 8 memisalan A 'an !an, se$im4an, $ermal 4er'asaran sis$emn!a. A 7 P0 6 n4P - P303 7 8 P0 6 n4 - P303 7 8 an ² Men,in,a$ 0 7 0 6 an 'an P 7 P 9 # maa 0 'ia$as 7 0 6 n4. Ar$in!a A V ' ² $er'iri 'ari: - P 0 6 n4 P3 03 - P 0 P3 03 Un$+ sis$em A 7 P0 6 n4 'an 7 P303 Un$+ B 7 P2 02 6 P3 03 9
B 7 P2 02 6 P3 03 9
nB' P V V '
7 8
nB ' P V V '
7 8
P2 0 6 P3 03 9 nB2 P2 7 8 =. Garam 5arama,ne$i 'en,an //r'ina$ +n$+ sis$em : A ϰ # M B ϰ # M Sis$em a'ala& ,as 'en,an //r'ina$ P# 0. A 'an se$im4an, $ermal !an, memen+&i 5ersamaan C π nR% ϰ 6 MP0 7 8 Ki$a 5isa&an /m5/nen sis$em A 'an C π nR% ϰ 6 MP0 7 8 C π nR% ϰ 7 MP0 PV 4 πCcϰ 7 M nR Men,in,a$ 5ersamaan ,as i'eal# !ai$+: P0 7 nRT Se&in,,a 'i5er/le&:
PV nR Kea'aan se$im4an, $erm/'inami 5a'a$an 5arama,ne$i 'a5a$ 'in!a$aan /le& 5ersamaan ea'aan !an, men!an,+$ //r'ina$# 'imana ma,ne$isasi seF+mla& 4esar 5a'a$an 5arama,ne$i mer+5aan ;+n,si 'ari &asil 4a,i in$ensi$as ma,ne$i 'en,an $em5era$+r# se&in,a 'i5er/le& : Sis$em A 7
4 πCc ϰ
sis$em A 7
M
A5a4ila B 'an se$im4an, $ermal# maa: ' n R Θ M + 4 πnRC ' %
ϰ
' − M ' PV = 0
'
Θ M + 4 πC '
%
n R¿
ϰ
' ¿− M ' PV =0
'
Θ M + 4 πC ' % nR ¿
ϰ
' ¿= M ' PV
' PV Θ M + 4 π C ' c ϰ ' 7 nR M '
Dari 5ersamaan $erse4+$ 4erar$i : '
Θ M + 4 π C ' c ϰ '
Sis$em B 7
M '
PV nR
Sis$em 7
a. Ti,a ;+n,si !an, se$im4an, $ermal sa$+ sama lain : 4 πCcϰ Sis$em A 7 M ' ' ' Θ M + 4 π C c ϰ Sis$em B 7 ' M
PV nR
Sis$em 7
Se&in,,a A# B# 7
4 πCc ϰ M
'
'
Θ M + 4 π C c ϰ
#
'
#
'
M
PV nR
4. +n,si $erse4+$ sama 'en,an $em5era$+r ,as i'eal θ A7
θ
B7 7
θ θ
A 7
4 πCcϰ M
7
θ '
Θ M + 4 π C ' c ϰ ' B 7 7 M ' PV 7 7 θ nR
θ
# se&in,,a :
>.
θ P 7 a P $5 θ
7 =>.1*
P P tp
maa: Un$+ $em5era$+r
θ
1
7 =>.1*
1535.3 1000.0
7 C=8.= Un$+ $em5era$+r
θ
=
7 =>.1*
1151.6 750.00
7 C1(.C=) Un$+ $em5era$+r
θ
>
7 =>.1*
767.82 500.00
7 C1(.C Un$+ $em5era$+r
θ
C
7 =>.1*
383.95 250.00
7 C1(.1(
θ 7
θ 1 +θ 2 +θ 3 +θ 4 4
7
1678.62 4
7 C1(.* K
√
C. a.
log R ' θ
= a + b log R '
'en,an a 7 - 1#1* 4 7 8.* R2 7 1888
θ
√
log R '
√ √
log1000
θ
θ
θ= … .?
= a + b log R ' =−1,16 + 0.675 log 1000
log1000 =−1,16 + 0.675 ( 3.1) θ 7 -1#1* 9 8.* > 7 - 1.1* 9 =#8= 7 8.*) log1000 7 8.C)== θ > 1 7 8.C)== θ 3 7 θ 0.748225 7 C.88( K
Grafik log-log R' terhadap θ (Nomor 1.4 b) X = R' (Ω) dan = θ (!) 2.5 2 1.5 1 0.5 0 0
5000
10000
15000
20000
25000
Ki$a am4il $i$i sam5el 'en,an selan, 888 Ω log R ' = a + b log R '
4.
-
√
θ
+n$+ R2 7 888 Ω log5000 =−1,16 + 0.675log 5000
√
θ
√ √
3,69 =−1,16 + 0.675 ( 3.69) θ 3,69 7 -1#1* 9 =#C( θ
30000
35000
√
3,69
7 1#>>
θ
3,69 7 1#*)( θ 3,69 θ= 1,7689 θ= 2,086 K
-
+n$+ R2 7 18.888 Ω log 10.000 =−1,16 +0.675 log 10.000 θ 4 =−1,16 + 2,7
√ √
θ
7 1#C 4 7 =#> θ 4 θ 7 2,37 θ 7 1#*) K
-
+n$+ R2 7 1.888 Ω log15.000 =−1,16 + 0.675 log 15.000
√ √
θ
4,17 =−1,16 +2,81 θ 7 1#* 4,17 7 =#= θ 4,17 θ= 2,72 θ=1,53 K
-
+n$+ R2 7 =8.888 Ω log20.000
√
√
θ
=−1,16 + 0.675 log20.000
4,3 =−1,16 + 2,9 θ
-
7 1#C 4,3 7 >#8> θ 4,3 θ 7 3,03 θ 71#C1( K
+n$+ R2 7 =.888 Ω log 25.000 =−1,16 + 0.675 log25.000 θ
√
√
4,39 θ
=−1,16 + 2,96 7 1#)
4,39 θ θ
-
7 >#=C 71#> K
+n$+ R2 7 >8.888 Ω log30.000
√
θ
=−1,16 + 0.675 log 30.000
√
4,47 θ θ
4,47 =−1,16 + 3,01 θ 7 1#) 7 >#C= 71#>8 K
. l/, R2 7 C.*( 6 >.(1 l/, θ a. +n$+ R2 7 =1) maa θ 7 . < l/, R2 7 C.*( 6 >.(1 l/, θ l/, =1) 7 C.*( 6 >.(1 l/, θ =.>>) 7 C.*( 6 >.(1 l/, θ - =.>( 7 6 >.(1 l/, θ −2.359 l/, θ 7 −3.917 l/, θ 7 8.*8= θ 7 C
4. Grafik log-log R' terhada ! " # R' ($% dan & # ! (% 7 RJ
7 K
888
1.)
18888
1.C
1888
1.>
=8888
1.=)
=888
1.=
>8888
1.1C
Grafik log-log R' terhadap θ (Nomor 1." b) X = R' (Ω) dan = θ (!) 2 1.5 1 0.5 0 0
.
5000
10000
15000
20000
25000
30000
35000
Menen$+an n/l m+$la 'an sala /# /R# /. Un$+ mene$a5an sala $em5era$+r em5iris# 'i5ili& 4e4era5a sis$em 'en,an //r'ina$ 'an se4a,ai sis$em 4a+ 'an men,am4il se5eran,a$ ai'a& +n$+ menen$+an &ar,a n+meri 5a'a $em5era$+r !an, 4erai$an 'en,an masin,-masin, is/$&erm. Ki$a se$im4an,an sis$em lain 'en,an sis$em 4a+ 'an memili& 4ilan,an !an, men+nF+an sama $em5era$+rn!a. ia i$a am4il 'ari ,ra;i # i$a 4+a$ lin$asan !an, mem/$/n, 4e4era5a lin$asan is/$erm 5a'a $i$i !an, masin,-masin, mem5+n!ai //r'ina$ !an, sama nam+n 4er4e'a. Ki$a am4il $em5era$+r 4erai$an 'en,an masin,-masin, is/$erm se4a,ai ;+n,si 5a'a $i$i 5/$/n,. Den,an 'emiian ;+n,si
θ ( X ) menen$+an sala $em5era$+r. Ki$a $en$+an θ 4er4an'in, l+r+s 'en,an # maa 'en,ann!a 'i4erian 5ersamaan
( )
θ X = aX
# 'en,an $e$a5.
Har,a a 5a'a 5ersamaan 'i a$as mer+5aan /ns$an$a# maa +n$+ menen$+an sala $em5era$+r &ar+s i$a $en$+an $erle4i& 'a&+l+ &ar,a a# s$ela& i$+ 4ar+ i$a mem5+n!ai &+4+n,an n+meri% an$ara $em5era$+r
θ ( X )
'an . Den,an 'emiian i$a menen$+an
$i$i $e$a5. Ti$i $e$a5 ini 'i$en$+an 'en,an ea'asan air m+rni se4a,ai %am5+ran se$im4an, 'ari es# a$ %air 'an +a5 !an, 'ise4+$ $i$i $ri5el air. Tem5era$+r 5a'a $i$im se$im4an, ini 'i4eri &ar,a =>#1* Kel?in# se&in,,a:
a= Men,in,a$ 5ersamaan
273,16 Xtp
θ ( X )= aX maa 5ersamaann!ase%ara +m+m 'i$+lis: θ ( X ) =273,16 K
X 'en,an $e$a5 Xtp
Men,in,a$ $i$i s$an'ar +n$+ $em5era$+r !ani Kel?in 'en,an &ar,a =>#1* =>#1* K maa $i$i s$an'ar ini 'a5a$ 'i,+naan +n$+ menen$+an sala %el%i+s# ream+r 'an a&ren&ei$. Ti$i $e$a5 sala %el%i+s# ;a&ren&ei$ 'an ream+r men,,+naan $i$i 4e+ 'an $i$i 'i'i& air. Men,in,a$ $i$i 'i'i& 'an 4e+ selal+ 4er+4a& $er&a'a5 $eanan s$an'ar# !ani 1 a$m.$i$i 4e+ 'i,+naan +n$+ menen$+an sala !an, men+nF+an 4a$as $eren'a&# 'an $i$i 'i'i& menen$+an 4a$as $era$asn!a# 'en,an a$a lain menen$+an ren$an, nilai minim+m 'an masim+m 'ari $ia5 sala. Un$+ menen$+an sala %el%i+s# maa 'i$en$+an 'en,an mem4+a$ sala se4an!a 188 'ian$ara $i$i 4e+ $i$i minim+m 'an $i$i 'i'i& $i$i masim+m# 'en,an %ara !an, sama +n$+ ream+r se4an!a )8 'an a&ren&ei$ se4an!a 1)8. Se%ara ma$ema$is 5en,/n?ersian sala $em5era$+re %el%i+s e a&ren&ei$ 'an se4alin!a# %el%i+s e ream+r 'an se4alin!a# ser$a a&ren&ei$ e ream+r 'an se4alin!a# !ai$+ 'en,an mem4an'in,an e'+a s+&+ 'an selan, $i$i 4e+ 'an $i$i 'i'i& an$ar e'+a $em5era$+re. Se%ara ma$ema$is 'a5a$ 'i$+lis : Misal +n$+ 8 'an 8 :
T ˚ C −0 T ˚ F − 32 T ˚ C −0 T ˚ F − 32
Un$+
7
100 180
7
5 9
˚ C =˚ F
T ˚ C −0 T ˚ F − 32 5 9
T 6 8 7
5 9
T 7
T 6 >=
T 6 >=
˚ F =˚ C
Un$+
T ˚ C −0 T ˚ F − 32 9 5
T 6 8 7
T 7
5 9
7
9 5
5 9
7
T 6 >=
T 6 >=
An,a >= m+n%+l +n$+ a&ren&ei$ arena $i$i 4e+ a&ren&ei$ 'im+lai 'ari >= . A'a5+n ˚ C 'an ˚ R sama 6 sama 'im+lai 'ari 8 n/l . Men,in,a$ $i$i $e$a5 ˚C 'an ˚ R masain, 6 masin, a'ala& 188 'an )8# Se&in,,a 5ersamaann!a :
T ˚ C −0 T ˚ F − 32 T ˚C − 0 T ˚ R −0 Un$+
5 4
T 6 8 7
Un$+
5 4
5 4
7
T R 6 8
T R
˚ R =˚ C
T ˚C − 0 T ˚ R −0 TR 6 8 7
5 4
7
˚ C =˚ R
T ˚C − 0 T ˚ R −0
T 7
100 80
7
4 5
7
5 4
T 6 8
4 5
TR 7
T
Se'an,an +n$+ Kel?in #arena $i$i 4e+n!a 'im+lai 'ari an,a =>#1 se&in,,a: Un$+
˚ C =˚ K
T ˚ C −0 T ˚ K −273,15
7
100 100
T 6 8 7 TK 6 =>#1 T 7 TK 6 =>#1 Un$+
˚ K =˚ C
T ˚ C −0 T ˚ K −273,15
7
100 100
TK 6 =>#1 7 T 6 8 TK 7 T 9 =>#1
100
212
80
373
Titik
100
Titik
180
0
100
80 skala
0
32
273,1
Nol absolut/ mutlak
/
/
/
R
K
