termodinamika modul kuliah.ppt
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TERMODINAMIKATERMODINAMIKA
IR. SUGIYANTO, MTIR. SUGIYANTO, MT
Oleh:Oleh:
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REFERENSI:REFERENSI:
1. FUNDAMENTALS of ENGINEERING1. FUNDAMENTALS of ENGINEERINGTHERMODYNAMICSTHERMODYNAMICS
Michael . Mo!a"Michael . Mo!a"
Ho#a!$ N. Sha%i!oHo#a!$ N. Sha%i!o
&. LECTURE NOTES ON THERMODYNAMICS&. LECTURE NOTES ON THERMODYNAMICS
o'e%h M. (o#e!o'e%h M. (o#e!
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1.1. HUKUM TERMODINAMIKAHUKUM TERMODINAMIKA )ERO *)EROTH LA+)ERO *)EROTH LA+
&.&. HUKUM TERMODINAMIKA (ERTAMAHUKUM TERMODINAMIKA (ERTAMA *FIRST LA+*FIRST LA+-.-. HUKUM TERMODINAMIKA KEDUAHUKUM TERMODINAMIKA KEDUA *SECOND LA+*SECOND LA+
.. HUKUM TERMODINAMIKA KEHUKUM TERMODINAMIKA KETIGA *THIRD LA+TIGA *THIRD LA+
/A/ I KONSE( DASAR /A/ I KONSE( DASAR TERMODINAMIKATERMODINAMIKA
(!i"'i% h002 3e!2o$i"a2ia $i40"aa" %a$a 3eo"olo4i(!i"'i% h002 3e!2o$i"a2ia $i40"aa" %a$a 3eo"olo4i
e"e!4i, 2eli%03i:e"e!4i, 2eli%03i: '3ea2 a"$ "0clea! %o#e! %la"3', i"3e!"al'3ea2 a"$ "0clea! %o#e! %la"3', i"3e!"alco250'3io" e"4i"e', 4a' 30!5i"e', ai! co"$i3io"i"4,co250'3io" e"4i"e', 4a' 30!5i"e', ai! co"$i3io"i"4,
!ef!i4e!a3io", 4a' $6"a2ic', 7e3 %!o%0l'io", co2%!e''o!',!ef!i4e!a3io", 4a' $6"a2ic', 7e3 %!o%0l'io", co2%!e''o!',
che2ical %!oce'' %la"3'che2ical %!oce'' %la"3' $a" lai"8lai"$a" lai"8lai"
Te!2o$i"a2iaTe!2o$i"a2ia a$alah il20 6a"4 2e2a$alah il20 6a"4 2e25aha' 3e"3a"45aha' 3e"3a"4
h050"4a"h050"4a" *%e!30a!a"*%e!30a!a" a"3a!aa"3a!a e"e!4ie"e!4i %a"a' $e"4a"%a"a' $e"4a" e"e!4ie"e!4i2ea"i *2ea"i *e!7ae!7a. H050"4a". H050"4a" 3e!'e5033e!'e503 $i$ifo!20la'ifo!20la'ia"a" ee
$ala2$ala2 e2%a3e2%a3 h002 $a'a! 3e!2o$i"a2ia, 6ai30h002 $a'a! 3e!2o$i"a2ia, 6ai30::
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H002 Te!2o$i"a2ia 9e!o *)e!o3h la# 3he!2o$6"a2icH002 Te!2o$i"a2ia 9e!o *)e!o3h la# 3he!2o$6"a2ic
ia 'i'3e2 *5e"$a e!7a 5e!3e2%e!a30! 3i"44i 5e!'i"440"4a"ia 'i'3e2 *5e"$a e!7a 5e!3e2%e!a30! 3i"44i 5e!'i"440"4a"
$e"4a" 6a"4 5e!3e2%e!a30! le5ih !e"$ah, 2aa 3e!7a$i$e"4a" 6a"4 5e!3e2%e!a30! le5ih !e"$ah, 2aa 3e!7a$i
%e!%i"$aha" %a"a' $a!i 'i'3e2 5e!3e2%e!a30! 3i"44i e 'i'3e2%e!%i"$aha" %a"a' $a!i 'i'3e2 5e!3e2%e!a30! 3i"44i e 'i'3e25e!3e2%e!a30! !e"$ah $a" 2e"ca%ai 3e2%e!a30! e'ei25a"4a".5e!3e2%e!a30! !e"$ah $a" 2e"ca%ai 3e2%e!a30! e'ei25a"4a".
Defi"i'i h002 Te!2o$i"a2ia 9e!o: 7ia $0a 'i'3e2 %a$aDefi"i'i h002 Te!2o$i"a2ia 9e!o: 7ia $0a 'i'3e2 %a$a
#a30 6a"4 'a2a $ala2 e'ei25a"4a" %a"a' *3e2%e!a30!#a30 6a"4 'a2a $ala2 e'ei25a"4a" %a"a' *3e2%e!a30!
'a2a $e"4a" 'i'3e2 e3i4a, 2aa 2a'i"482a'i"4 'i'3e2 $ala2'a2a $e"4a" 'i'3e2 e3i4a, 2aa 2a'i"482a'i"4 'i'3e2 $ala2o"$i'i e'ei25a"4a" %a"a' *3e2%e!a30! 'a2a.o"$i'i e'ei25a"4a" %a"a' *3e2%e!a30! 'a2a.
ia A $a" C 2e2%0"6ai e'ei25a"4a" %a"a' $e"4a" /,ia A $a" C 2e2%0"6ai e'ei25a"4a" %a"a' $e"4a" /,
2aa 3e2%e!a30! A 'a2a $e"4a" /.2aa 3e2%e!a30! A 'a2a $e"4a" /.
AA // CCAA// CC
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E"e!4i %a"a' 3i$a $a%a3 $io";e!'i 'eca!a e'el0!0ha"E"e!4i %a"a' 3i$a $a%a3 $io";e!'i 'eca!a e'el0!0ha"
2e"7a$i e"e!4i 2ea"i oleh 'e50ah MESIN ENERGI,2e"7a$i e"e!4i 2ea"i oleh 'e50ah MESIN ENERGI,
a!e"a 'e5a4ia" e"e!4i %a"a' %a$a 3e2%e!a30! !e"$aha!e"a 'e5a4ia" e"e!4i %a"a' %a$a 3e2%e!a30! !e"$ahha!0' $i50a"4 e 'eelili"4"6a.ha!0' $i50a"4 e 'eelili"4"6a.
Se5a4ia" e"e!4i %a"a' 6a"4 3i$a $a%a3 $io";e!'ia"Se5a4ia" e"e!4i %a"a' 6a"4 3i$a $a%a3 $io";e!'ia"
2e"7a$i e"e!4i 2ea"i $i00! $e"4a" "ilai ENTRO(I.2e"7a$i e"e!4i 2ea"i $i00! $e"4a" "ilai ENTRO(I.
/a4ia" e"e!4i %a"a' 6a"4 $a%a3 $io";e!'ia" 2e"7a$i/a4ia" e"e!4i %a"a' 6a"4 $a%a3 $io";e!'ia" 2e"7a$i
e"e!4i 2ea"i $i'e503 ENERGI a3a0 KERA.e"e!4i 2ea"i $i'e503 ENERGI a3a0 KERA.
SISTEM TERMODINAMIKASISTEM TERMODINAMIKA
Dala2Dala2 3e!2o$i"a2ia, 5e"$a e!7a 6a"4 $i2a'0$a"3e!2o$i"a2ia, 5e"$a e!7a 6a"4 $i2a'0$a" $i'e503 $e"4a"$i'e503 $e"4a" sistemsistem $a"$a" $i%aai 0"30 2e"0"70 $i%aai 0"30 2e"0"70 a"a"
5a3a'a" 5e"$a5a3a'a" 5e"$a e!7ae!7a $ala2 %e!20aa"$ala2 %e!20aa" 3e!3030%3e!3030% $e"4a"$e"4a"
'eelili"4"6a.'eelili"4"6a.
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I'3ilah %e!20aa" 3e!3030% $a%a3 5e!0%a %e!20aa"I'3ilah %e!20aa" 3e!3030% $a%a3 5e!0%a %e!20aa"
3e!3030% ha6ala" *3e!3030% ha6ala" *imaginaryimaginary a3a0 5e!0%a %e!20aa" a3a0 5e!0%a %e!20aa"
3e!3030% 'e5e"a!"6a.3e!3030% 'e5e"a!"6a.
U$a!a $io2%!e'i $i $ala2 'ili"$e!U$a!a $io2%!e'i $i $ala2 'ili"$e!:: $ala2 hal i"i$ala2 hal i"i 'i'3e2 a$alah 0$a!a 6a"4'i'3e2 a$alah 0$a!a 6a"4
$io2%!e'i $a"$io2%!e'i $a" %e!20aa"%e!20aa" 3e!3030%3e!3030%
a$alaha$alah 'ili"$e! *3e!3030% 'e5e"a!"6a.'ili"$e! *3e!3030% 'e5e"a!"6a.
0$a!a0$a!a
'ili"$e!'ili"$e!
Se5o"4ah e' 3e!a%0"4 $i a3a' ai!:Se5o"4ah e' 3e!a%0"4 $i a3a' ai!: $ala2 hal i"i$ala2 hal i"i 'i'3e2'i'3e2 a$alaha$alah e' 6a"4e' 6a"4
3e!a%0"43e!a%0"4 $a" %e!20aa"$a" %e!20aa" 3e!3030%3e!3030%
a$alaha$alah 5e!0%a ai! *3e!3030% ha6ala".5e!0%a ai! *3e!3030% ha6ala".
e'e'
ai!ai!
Se5o"4ah e' $a" ai! $i $ala2 3a"4i:Se5o"4ah e' $a" ai! $i $ala2 3a"4i:
$ala2 hal i"i$ala2 hal i"i 'i'3e2 a$alah'i'3e2 a$alah e' $a" ai!,e' $a" ai!,
%e!20aa"%e!20aa" 3e!3030%3e!3030% a$alaha$alah 5e!0%a5e!0%a
%e!20aa"%e!20aa" 6a"46a"4 $i5a3a'i 3a"4i$i5a3a'i 3a"4i
*3e!3030% 'e5e"a!"6a.*3e!3030% 'e5e"a!"6a.
ai!ai!e'e'
3a"4i3a"4i
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MACAM8MACAMMACAM8MACAM SISTEM TERMODINAMIKASISTEM TERMODINAMIKA
A"ali'i' %!o'e' 3e!2o$i"a2ia 2eli%03i '30$i 3e"3a"4A"ali'i' %!o'e' 3e!2o$i"a2ia 2eli%03i '30$i 3e"3a"4
%e!%i"$aha" 2a''a $a" e"e!4i 2elal0i 5a3a' 'i'3e2. Maca28%e!%i"$aha" 2a''a $a" e"e!4i 2elal0i 5a3a' 'i'3e2. Maca28
2aca2 %!o'e' %a$a 'i'3e2 *5e"$a e!7a $a%a32aca2 %!o'e' %a$a 'i'3e2 *5e"$a e!7a $a%a3$ila'ifia'ia" 2e"7a$i - 5a4ia" 03a2a, 6ai30:$ila'ifia'ia" 2e"7a$i - 5a4ia" 03a2a, 6ai30:
1.1. Si'3e2 3e!50a,Si'3e2 3e!50a,
&.&. Si'3e2 3e!3030%,Si'3e2 3e!3030%,
-.-. Si'3e2 $ii'ola'i.Si'3e2 $ii'ola'i.
11 SISTEMSISTEM TER/UKATER/UKA
Yai30 'i'3e2 6a"4 $a%a3 5e!05ah 5ai 2a''a $a" e"e!4i
*%a"a' $a" e!7a $e"4a" 'eelili"4"6a. Ma''a 'i'3e2 3i$ao"'3a" $a" hal 3e!'e503 3e!7a$i %a$a 7e"i' 'i'3e2 6a"4
2e"4ali!.22i"i" 22o03o03
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Co"3oh 'i'3e2 3e!50a: /oile!, 30!5i", hea3 e
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&& SISTEMSISTEM TERTUTU(TERTUTU(
Si'3e2 3e!3030%, 6ai30 702lah 2a''aSi'3e2 3e!3030%, 6ai30 702lah 2a''a
'i'3e2 %a$a %e!20aa" 3e!3030% 3e3a%,'i'3e2 %a$a %e!20aa" 3e!3030% 3e3a%,
3i$a 3e!$a%a3 2a''a 'i'3e2 6a"4 el0a!,3i$a 3e!$a%a3 2a''a 'i'3e2 6a"4 el0a!,3e3a%i e"e!4i 6a"4 5e!0%a e!7a a3a0 %a"a'3e3a%i e"e!4i 6a"4 5e!0%a e!7a a3a0 %a"a'
$a%a3 $ie"aa" %a$a 'i'3e2.$a%a3 $ie"aa" %a$a 'i'3e2.
Si'3e2 3e!3030%, 2a''a $a" ;ol02e o"'3a"Si'3e2 3e!3030%, 2a''a $a" ;ol02e o"'3a"
Si'3e2 3e!3030%, 2a''a 3e3a%Si'3e2 3e!3030%, 2a''a 3e3a%
$a" ;ol02e 5e!05ah$a" ;ol02e 5e!05ah
(i'3o" $a%a3 5e!4e!a (i'3o" $a%a3 5e!4e!a
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ia 2a''a $a" e"e!4i %a"a' 3i$a $a%a3 $ie"aa" e 'i'3e2,ia 2a''a $a" e"e!4i %a"a' 3i$a $a%a3 $ie"aa" e 'i'3e2,
2aa 'i'3e2 3e!'e503 $ala2 ea$aa" $ii'ola'i 'e2%0!"a.2aa 'i'3e2 3e!'e503 $ala2 ea$aa" $ii'ola'i 'e2%0!"a.
-- SISTEMSISTEM DIISOLASIDIISOLASI
SISTEM KHUSUSSISTEM KHUSUS
1.1. Si'3e2 A$ia5a3i:Si'3e2 A$ia5a3i: 3i$a3i$a 3e!$a%a33e!$a%a3 %a"a' 6a"4 $iel0a!a"%a"a' 6a"4 $iel0a!a"
a3a0a3a0
$i3e!i2a 'i'3e2$i3e!i2a 'i'3e2
$a!i a3a0$a!i a3a0
3e!ha$a% 'eelili"4"6a3e!ha$a% 'eelili"4"6a
. Hal
. Hal
i"i 3e!7a$i, a!e"a 'i'3e2 $ii'ola'i 'e2%0!"a. Co"3oh:i"i 3e!7a$i, a!e"a 'i'3e2 $ii'ola'i 'e2%0!"a. Co"3oh:
3e!2o' ai! %a"a'.3e!2o' ai! %a"a'.
&.&. Si'3e2 Ho2o4e": 'i'3e2 3e!$i!i $a!i %ha'e 30"44al.Si'3e2 Ho2o4e": 'i'3e2 3e!$i!i $a!i %ha'e 30"44al.
Co"3oh: ca2%0!a" 0$a!a $e"4a" 0a% ai!.Co"3oh: ca2%0!a" 0$a!a $e"4a" 0a% ai!.
-.-. Si'3e2 He3e!o4e": 'i'3e2 3e!$i!i $a!i $0a a3a0 le5ih %ha'e.Si'3e2 He3e!o4e": 'i'3e2 3e!$i!i $a!i $0a a3a0 le5ih %ha'e.Co"3oh: ca2%0!a" ai! $e"4a" 0a% ai!, e' $a" ai! $e"4a"Co"3oh: ca2%0!a" ai! $e"4a" 0a% ai!, e' $a" ai! $e"4a"
oli, ai! $a" 2i"6a.oli, ai! $a" 2i"6a.
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TUGAS = KERAKAN DI KELASTUGAS = KERAKAN DI KELAS
*1*1 Ref!i4e!a3o!,Ref!i4e!a3o!,
*&*& Ki%a' a"4i" *Fa",Ki%a' a"4i" *Fa",
*-*- The!2o2e3e! $i $ala2 20l03,The!2o2e3e! $i $ala2 20l03,** Ko2%!e'o! 0$a!a,Ko2%!e'o! 0$a!a,
*> Ra$ia3o! 2o5il.*> Ra$ia3o! 2o5il.
Kla'ifia'ia" %e!ala3a" $i 5a#ah i"i, a%aahKla'ifia'ia" %e!ala3a" $i 5a#ah i"i, a%aah
5ee!7a $e"4a" 'i'3i2 3e!50a a3a0 3e!3030% $a"5ee!7a $e"4a" 'i'3i2 3e!50a a3a0 3e!3030% $a"5e!ia" ala'a""6a.5e!ia" ala'a""6a.
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SISTEM INTERNASIONAL *S ISISTEM INTERNASIONAL *S I
NAMANAMA UNITUNIT DIMENSIDIMENSI SIM/OLSIM/OL
2a''a2a''a ilo4!a2ilo4!a2 MM 44
%a"7a"4%a"7a"4 2e3e!2e3e! LL 22
#a30#a30 $e3i *'eco"$$e3i *'eco"$ 33 ''
SATUAN DASAR:SATUAN DASAR:
SISTEM SATUANSISTEM SATUAN
NAMANAMA UNITUNIT SIM/OLSIM/OL DIMENSIDIMENSI SATUANSATUAN
4a6a4a6a 42?'42?'&& NN ML3ML38&8& Ne#3o"Ne#3o"
ece%a3a"ece%a3a" 2?'2?' 88 L3L38181 88
%e!ce%a3a"%e!ce%a3a" 2?'2?'&& 88 L3L38&8& 88
$e"'i36$e"'i36 4?24?2-- 88 MLML8-8- 88
3ea"a"3ea"a" 42?'42?'&&?2?2&& *N?2*N?2&& (a(a MLML8181 338&8& (a'cal(a'cal
e"e!4ie"e!4i 4242&&?'?'&& *N2*N2 MLML&&338&8& o0leo0le
$a6a$a6a 4242&&
?'?'--
*?'*?' ++ MLML&&
338-8-
+a33+a33
SATUAN TURUNAN:SATUAN TURUNAN:
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FAKTOR FAKTOR SATUANSATUAN SIM/OLSIM/OL
1@1@1&1&
Te!aTe!a TT1@1@ Gi4aGi4a GG
1@1@BB Me4aMe4a MM
1@1@ KiloKilo
1@1@ He3oHe3o hh
1@1@11 DeaDea $a$a
1@1@8181 De'iDe'i $$
1@1@8&8& Ce"3iCe"3i cc
1@1@8-8- MiliMili 22
1@1@8B8B Mi!oMi!o
1@1@88 Na"oNa"o ""
1@1@81&81& (io(io %%
A+ALAN SISTEM SATUAN S I:A+ALAN SISTEM SATUAN S I:
EKIALEN SATUAN:EKIALEN SATUAN:N?2N?2 (a'cal *(a(a'cal *(a
42?'42?' Ne#3o" *NNe#3o" *N
N2N2 o0le *o0le *
N2?'N2?' o0le?' *?'o0le?' *?'
o0le?'o0le?' +a33 *++a33 *+
1 c21 c2 1 cc1 cc
1@1@-- N?2N?2&& 1 (a1 (a
1@1@>> N?2N?2&& 1 5a!1 5a!
1@1@BB N?2N?2&& 1 M%a1 M%a
1@@ (a1@@ (a 1 5a!1 5a!
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KOORDINAT DAN KEADAAN SISTEMKOORDINAT DAN KEADAAN SISTEM
(a$a(a$a %e25aha'a"%e25aha'a" 3e!2o$i"a2ia3e!2o$i"a2ia:: ;ol02e;ol02e **, 3e2%e!a30!, 3e2%e!a30!
**TT, 3ea"a", 3ea"a" *%*%, e!a%a3a", e!a%a3a" **densitydensity $a" lai"8lai" $i'e503 $a" lai"8lai" $i'e503 'e5a4ai oo!$i"a3 'i'3e2'e5a4ai oo!$i"a3 'i'3e2, co"3oh: 4a' $i $ala2 3a"4i, co"3oh: 4a' $i $ala2 3a"4i
2e2%0"6ai2e2%0"6ai ;ol02e;ol02e **, 3e2%e!a30!, 3e2%e!a30! **TT $a" $a" 3ea"a"3ea"a" *%.*%.
Kea$aa" 'i'3e2Kea$aa" 'i'3e2 3e!4a"30"43e!4a"30"4 %a$a oo!$i"a3 'i'3e2%a$a oo!$i"a3 'i'3e2 *, T, % *, T, % ,,
5ila oo!$i"a3 'i'3e25ila oo!$i"a3 'i'3e2 5e!05ah5e!05ah 2aa ea$aa" 'i'3e22aa ea$aa" 'i'3e2 704a 704aaa" 5e!05ahaa" 5e!05ah..
Dala2 3e!2o$i"a2ia, 5e'a!a" 'i'3e2Dala2 3e!2o$i"a2ia, 5e'a!a" 'i'3e2 a$alah:a$alah:
1.1.
/e'a!a" e
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U"30 2e"e"30a" 5e'a!a" i"3e"'if a3a0 e
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Da!i 5e'a!a" e
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&.&. ol02eol02e '%e'ifi '%e'ifi 22ola!ola!
ol02eol02e '%e'ifi '%e'ifi 22ola!ola! **molal spesific volumemolal spesific volume ; a$alah ; a$alah
%e!5a"$i"4a" a"3a!a ;ol02e * $e"4a" 702lah 2ole *"%e!5a"$i"4a" a"3a!a ;ol02e * $e"4a" 702lah 2ole *"
$a!i 'i'3e2.$a!i 'i'3e2.
sistemmole jumlah
extensif besaranmolar spesifik Nilai =
n
V v =*
;ol02e;ol02e
**
2ole2ole
*"*"
Ta50"4Ta50"4
'i'3e2'i'3e2
;: ;ol02e 7e"i' 2ola! *2;: ;ol02e 7e"i' 2ola! *2?482ole J f3?5282ole?482ole J f3?5282ole
: ol02e *2 : ol02e *2 J f3 J f3
" : 702lah 2ole *4!a282ole J 482ole" : 702lah 2ole *4!a282ole J 482ole
−− molelb ft
molekg
m 33;
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SU/STITUSI RUMUS:SU/STITUSI RUMUS:
sistemmolekul berat BM BM
mn == ;
02lah 2ole a$alah %e!5a"$i"4a" a"3a!a 2a''a *2 $e"4a"02lah 2ole a$alah %e!5a"$i"4a" a"3a!a 2a''a *2 $e"4a"
5e!a3 2ole0l */M $a!i 'i'3e2.5e!a3 2ole0l */M $a!i 'i'3e2.
m BM V
BM
mV v ==*
m
V
v =
v BM v =*
Sehi"44aSehi"44a
Se$a"4a"Se$a"4a"
a$i,a$i,
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19
-. Ke!a%a3a" 2a''a-. Ke!a%a3a" 2a''a
Ke!a%a3a" 2a''a *Ke!a%a3a" 2a''a *densitydensity,, a$alah %e!5a"$i"4a" a"3a!aa$alah %e!5a"$i"4a" a"3a!a
2a''a *2 $e"4a" ;ol02e * $a!i 'i'3e2.2a''a *2 $e"4a" ;ol02e * $a!i 'i'3e2.
=
33 ; ft
lb
m
kg
V
m ρ
m BM V v =* ρ
BM
v =→ *
m
V v =
v
1=→ ρ
a!ia'i $e"'i36 4a' 3e!ha$a% 3ea"a" $a" 3e2%e!a30!,a!ia'i $e"'i36 4a' 3e!ha$a% 3ea"a" $a" 3e2%e!a30!,
Tea"a" "aiTea"a" "ai $e"'i36 "ai $e"'i36 "ai
Te2%e!a30! "aiTe2%e!a30! "ai $e"'i36 30!0".$e"'i36 30!0".
U"30 'oli$ a3a0 li0i$ 5e!3ea"a", $e"'i36 ha2%i! o"'3a".U"30 'oli$ a3a0 li0i$ 5e!3ea"a", $e"'i36 ha2%i! o"'3a".
Ke!a%a3a" 2a''aKe!a%a3a" 2a''a *!ho*!ho 2e!0%aa" e5alia" $a!i ;ol02e2e!0%aa" e5alia" $a!i ;ol02e
'%e'ifi ; $a!i 'i'3e2.'%e'ifi ; $a!i 'i'3e2.
Se$a"4a",Se$a"4a",
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. S%e'ifi G!a;i36. S%e'ifi G!a;i36
S%e'ifi 4!a;i36 *SG a$alah %e!5a"$i"4a" a"3a!aS%e'ifi 4!a;i36 *SG a$alah %e!5a"$i"4a" a"3a!a densitydensity
'i'3e2 $e"4a"'i'3e2 $e"4a" densitydensity %e25a"$i"4. Nilai%e25a"$i"4. Nilai densitydensity %e25a"$i"4%e25a"$i"4
0"30 li0i$ a$alah ai! %a$a 3e2%e!a30! 0"30 li0i$ a$alah ai! %a$a 3e2%e!a30! @@C *1@@@ 4?2C *1@@@ 4?2-- $a" $a"0"30 4a' a$alah $e"'i36 0$a!a *&, 4?20"30 4a' a$alah $e"'i36 0$a!a *&, 4?2--
U"30 li0i$U"30 li0i$
O H
sistem sistemSG
2 ρ
ρ =
Da!i "ilai SG $a%a3 $ie3ah0i 5e"$a e!7a *'i'3e2Da!i "ilai SG $a%a3 $ie3ah0i 5e"$a e!7a *'i'3e2
2e"4a%0"4 $i $ala2 ai!, 7ia "ilai SG 1.2e"4a%0"4 $i $ala2 ai!, 7ia "ilai SG 1.
Nilai S%e'ifi 4!a;i36Nilai S%e'ifi 4!a;i36
$a!i 5e5e!a%a li0i$$a!i 5e5e!a%a li0i$
NAMA LIUIDNAMA LIUID S(ESIFIK GRAITYS(ESIFIK GRAITY
Ai!Ai! 1,@1,@
Da!ahDa!ah 1,@>1,@>
Ai! la03Ai! la03 1,@&>1,@&>
/e"'i"/e"'i" @,P@,P
E' !i2E' !i2 @,&@,&
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>. /e!a3 '%e'ifi *S%e'ific +ei4h3>. /e!a3 '%e'ifi *S%e'ific +ei4h3
/e!a3 '%e'ifi a$alah %e!5a"$i"4a" a"3a!a 5e!a3 *+ $e"4a"/e!a3 '%e'ifi a$alah %e!5a"$i"4a" a"3a!a 5e!a3 *+ $e"4a"
;ol02e * $a!i 'i'3e2.;ol02e * $a!i 'i'3e2.
=3m
N g sistem ρ γ
No3a'i 4 a$alah 4!a;i3a'i 502i .. 2?'No3a'i 4 a$alah 4!a;i3a'i 502i .. 2?'&&
===
323 m
N
s
m x
m
kg g sistem ρ γ
=
3m
N
V
W sistemγ
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CONTOH SOAL: KEADAAN SISTEMCONTOH SOAL: KEADAAN SISTEM
OO&&
2 Q 42 Q 4
Q @,B 2Q @,B 2--
'ili"$e!'ili"$e!Sili"$e! 2e2%0"6ai ;ol02e, Q @,B 2 5e!i'i OSili"$e! 2e2%0"6ai ;ol02e, Q @,B 2 5e!i'i O&&
*o'i4e" $e"4a" 2a''a Q 4. Te"30a" a ;ol02e*o'i4e" $e"4a" 2a''a Q 4. Te"30a" a ;ol02e
'%e'ifi, 5 ;ol02e '%e'ifi 2ola!, c 702lah 2ole'%e'ifi, 5 ;ol02e '%e'ifi 2ola!, c 702lah 2ole$a" $ $e"'i36 O$a" $ $e"'i36 O&& $i $ala2 'ili"$e!$i $ala2 'ili"$e!
(ENYELESAIAN:(ENYELESAIAN: a ol02e '%e'ifi,a ol02e '%e'ifi,
kg
m
m
V v
3
15,0
4
6,0 ===
5 ol02e '%e'ifi 2ola!, ; Q /M *;5 ol02e '%e'ifi 2ola!, ; Q /M *;
( )molekg
mv
−==
3
8,415,032*
/M O/M O&& Q 1B *& Q -&Q 1B *& Q -&
c 02lah 2ole,c 02lah 2ole, molekg BM
mn
O
−=== 125,032
4
2
$ De"'i36,3
666,615,0
11
m
kg
v=== ρ
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B. Tea"a"B. Tea"a" ** pressure pressure, %, %
/ila %e!20aa" '0a30 9a3 *%a$a3, cai! $a" 4a' 2e"e!i2a/ila %e!20aa" '0a30 9a3 *%a$a3, cai! $a" 4a' 2e"e!i2a
4a6a84a6a l0a! 2aa 5a4ia" %e!20aa" 9a3 6a"4 2e"e!i2a4a6a84a6a l0a! 2aa 5a4ia" %e!20aa" 9a3 6a"4 2e"e!i2a
4a6a 3e4a l0!0' aa" 2e"4ala2i 3ea"a".4a6a 3e4a l0!0' aa" 2e"4ala2i 3ea"a".Tea"a" a$alah 4Tea"a" a$alah 4a6a 3e4a l0!0'a6a 3e4a l0!0' *F*F %a$a %e!20aa"%a$a %e!20aa" $i5a4i$i5a4i
l0a' %el0a' %e"a2%a"4"6a *A."a2%a"4"6a *A.
h g A
F
p ρ ==
F : 4a6a 6a"4 5ee!7a *NF : 4a6a 6a"4 5ee!7a *N
A : l0a' %e"a2%a"4 *2A : l0a' %e"a2%a"4 *2&&
: $e"'i36 li0i$ *4?2: $e"'i36 li0i$ *4?2--
h : 3i"44i olo2 li0i$ *2h : 3i"44i olo2 li0i$ *2
( ) as!al am
N =
2
2222
;;;in
lb
ft
b
m
N
!m
kg
Seca!a 0202, %e"400!a" 3ea"a" $a%a3 2e"440"aa"Seca!a 0202, %e"400!a" 3ea"a" $a%a3 2e"440"aa"
'a30a" (a a3a0 M(a.'a30a" (a a3a0 M(a.
1 (a Q 1@@@ (a J 1M%a Q 1@@@ (a Q 1@1 (a Q 1@@@ (a J 1M%a Q 1@@@ (a Q 1@BB
(a(a
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Sa30a" 3ea"a" lai" 6a"4 5ia'a $i40"aa" a$alah 5a!.Sa30a" 3ea"a" lai" 6a"4 5ia'a $i40"aa" a$alah 5a!.
1 5a! Q 1@1 5a! Q 1@>> (a Q @,1 M%a Q 1@@ (a(a Q @,1 M%a Q 1@@ (a
Dala2Dala2 3e!2o$i"a2ia, 3ea"a"3e!2o$i"a2ia, 3ea"a" **%% 0202"6a0202"6a 'elal0'elal0
$i"6a3aa" $ala2 ha!4a a5'ol03$i"6a3aa" $ala2 ha!4a a5'ol03. /e'a! 3. /e'a! 3ea"a" a5'ol03ea"a" a5'ol033e!4a"30"43e!4a"30"4 5e'a!"6a5e'a!"6a 3ea"a" %e"400!a"3ea"a" %e"400!a" 2a"o2e3e! *2a"o2e3e! * gauge gauge
pressure pressure %a$a 'i'3e2%a$a 'i'3e2..
i i a 3ea"a" %e"400!a" *a 3ea"a" %e"400!a" * gauge pressure gauge pressure 'i'3e2 $i 'i'3e2 $i a3a'a3a'
3ea"a" a32o'fi!, 2aa:3ea"a" a32o'fi!, 2aa:
(( a5'ol03 Qa5'ol03 Q (( %e"400!a" %e"400!a" (( aa32o'fi!32o'fi!
i i a 3ea"a" %e"400!a" *a 3ea"a" %e"400!a" * gauge pressure gauge pressure 'i'3e2 $i 'i'3e2 $i 5a#ah5a#ah
3ea"a" a32o'fi!, 2aa:3ea"a" a32o'fi!, 2aa:
(( a5'ol03 Qa5'ol03 Q (( a32o'fi! =a32o'fi! = (( %e"400!a"%e"400!a"
Tea"a" %e"400!a"Tea"a" %e"400!a"
*2a"o2e3e!*2a"o2e3e!
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G!afi %e!5a"$i"4a" Tea"a" a32o'fi!,G!afi %e!5a"$i"4a" Tea"a" a32o'fi!,
a5'ol03 $a" %e"400!a"a5'ol03 $a" %e"400!a"
Tea"a" a32o'fi! %Tea"a" a32o'fi! %a32a32
%%4a04e4a04e
%%a5'a5'
%%;a ;a %%a5'a5'
%%a32a32 %%a32a32
a02 a5'ol03 %a02 a5'ol03 %a5'a5' Q @Q @
$i$i a3a' 3ea"a" a32o'fi!a3a' 3ea"a" a32o'fi!
$i$i 5a#ah5a#ah 3ea"a" a32o'fi!3ea"a" a32o'fi!
((a5'a5' Q (Q (a32a32 8 (8 (;a ;a
((a5'a5' Q (Q (a32a32 ( (4a04e4a04e
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Ma'0Ma'0
Kel0a!Kel0a!
(ENYELESAIAN:(ENYELESAIAN:
Si'i 2a'0, 3ea"a" e!7a $iSi'i 2a'0, 3ea"a" e!7a $i5a#ah 3ea"a" a32o'fi!:5a#ah 3ea"a" a32o'fi!:
((a5'a5' Q (Q (a32a32 = ( = (4a04e4a04e Q 1,P = Q >,P %'iaQ 1,P = Q >,P %'ia
Si'i el0a!, 3ea"a" e!7a $i a3a' 3ea"a" a32o'fi!:Si'i el0a!, 3ea"a" e!7a $i a3a' 3ea"a" a32o'fi!:
((a5'a5' Q (Q (a32a32 ( ( 4a04e4a04e Q 1,P -@ Q ,P %'iaQ 1,P -@ Q ,P %'ia
/lo#e! 0$a!a 5e!o%e!a'i %a$a 3ea"a" i'a% */lo#e! 0$a!a 5e!o%e!a'i %a$a 3ea"a" i'a% *suction pressuresuction pressure
%'i4 $a" 3ea"a" el0a! * %'i4 $a" 3ea"a" el0a! *discharge pressuredischarge pressure -@ %'i4. Hi30"4 -@ %'i4. Hi30"43ea"a" a5'ol03 0$a!a %a$a 'i'i i'a% $a" 'i'i el0a!.3ea"a" a5'ol03 0$a!a %a$a 'i'i i'a% $a" 'i'i el0a!.
CONTOH SOAL: TEKANAN A/SOLUTCONTOH SOAL: TEKANAN A/SOLUT
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Tea"a" a32o'fi! a5'ol03 *(Tea"a" a32o'fi! a5'ol03 *(a3aa3a a$alah 3ea"a" a32o'fi! a$alah 3ea"a" a32o'fi!
!a3a8!a3a %a$a 5a!o2e3e! $i a3a' %e!20aa" ai! la03, 6ai30!a3a8!a3a %a$a 5a!o2e3e! $i a3a' %e!20aa" ai! la03, 6ai30
%a$a e3i"44ia", h Q PB@ 22 Q @,PB 2 olo2 ai! !a'a *H4%a$a e3i"44ia", h Q PB@ 22 Q @,PB 2 olo2 ai! !a'a *H4
De"'i36 H4,De"'i36 H4, Q 1-,>B 4?$2Q 1-,>B 4?$2 Q 1-,>> < 1@ Q 1-,>> < 1@-- 4?24?2
Sa30a" a32o'fi! a5'ol03 '3a"$a!:Sa30a" a32o'fi! a5'ol03 '3a"$a!:
1 a3a Q 1@1-&> (a Q 1@1,-&> (a Q 1,@1-&> 5a!1 a3a Q 1@1-&> (a Q 1@1,-&> (a Q 1,@1-&> 5a!
((a3aa3a QQ 4 h4 h
((a3aa3a QQ 1-,>> < 1@1-,>> < 1@-- < ,1 < @,PB Q 1@1-&> N?2< ,1 < @,PB Q 1@1-&> N?2&& Q 1@1,-&> (aQ 1@1,-&> (a
Tea"a" a32o'fi! 2a"o2e3e! a3a0 a32o'fi! 3e"i:Tea"a" a32o'fi! 2a"o2e3e! a3a0 a32o'fi! 3e"i:
22 000.1011 mkg
!mkg atm == De"'i36 H4De"'i36 H4 Q @,@1->> 4?c2Q @,@1->> 4?c2
1 a3a Q @,@1->> 4?c21 a3a Q @,@1->> 4?c2 < PB c2 Q 1,@--& 4?c2 < PB c2 Q 1,@--& 4?c2
a$i, 1 a3a Q 1,@--& a32a$i, 1 a3a Q 1,@--& a32
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1 a3a Q PB@ 22 H4 *%a$a @1 a3a Q PB@ 22 H4 *%a$a @CC
)0(6,7350332,1
76011 0
2 " pa#a Hg mm
!m
kg atm ===
ia 3e2%e!a30! H4 "ai, 2aa 3i"44i olo2 H4 704a "ai,ia 3e2%e!a30! H4 "ai, 2aa 3i"44i olo2 H4 704a "ai,
2aa 3ea"a" a5'ol03 5a!o2e3e! %a$a 3e2%e!a30! @2aa 3ea"a" a5'ol03 5a!o2e3e! %a$a 3e2%e!a30! @CC
$a%a3 $i'ele'aia" $e"4a" !020' e'%e!i2e":$a%a3 $i'ele'aia" $e"4a" !020' e'%e!i2e":
//@@ Q / *1 = @,@@@1P& 3Q / *1 = @,@@@1P& 3
/: 3i"44i olo2 H4 a30al %a$a 3/: 3i"44i olo2 H4 a30al %a$a 3 CC
//@@: %e25acaa" 3i"44i olo2 H4 %a$a @C: %e25acaa" 3i"44i olo2 H4 %a$a @C
Dala2 hal i"i, 3ea"a" 0$a!a a32o'fi! a$alah:Dala2 hal i"i, 3ea"a" 0$a!a a32o'fi! a$alah:
=
2
0
6,735 !m
kg B p
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U"30 o"$i'i 3ea"a" 6a"4 !e"$ah, %e"400!a" $a%a3U"30 o"$i'i 3ea"a" 6a"4 !e"$ah, %e"400!a" $a%a3
2e"440"aa" 3i"44i olo2 ai!. Ti"44i olo2 ai! a$alah2e"440"aa" 3i"44i olo2 ai!. Ti"44i olo2 ai! a$alah
1-,>> ali le5ih 5e'a! $a!i 3i"44i olo2 H4.1-,>> ali le5ih 5e'a! $a!i 3i"44i olo2 H4.
1 22 H4 Q 1-,>> 22 H1 22 H4 Q 1-,>> 22 H&&OO
Sehi"44a: 1 a3a Q PB@ 22 H4Sehi"44a: 1 a3a Q PB@ 22 H4
Q 1-,>> < PB@ Q [email protected]& 22 HQ 1-,>> < PB@ Q [email protected]& 22 H&&OO
Q 1@,--& 2 HQ 1@,--& 2 H&&OO
a$i: 1 a32 Q 1@,--& 2 Ha$i: 1 a32 Q 1@,--& 2 H&&OO
Ha'il %e"400!a" 6a"4 5a40' ha"6a 0"30 ai! 5e!3e2%e!a30!Ha'il %e"400!a" 6a"4 5a40' ha"6a 0"30 ai! 5e!3e2%e!a30!C, 3e3a%i %C, 3e3a%i %a$a o"$i'i a30al %e"440"aa" 3i"44i olo2 ai!a$a o"$i'i a30al %e"440"aa" 3i"44i olo2 ai!
ha"6a 0"30 %e"400!a" 3ea"a" 6a"4 !e"$ah, 'ehi"44aha"6a 0"30 %e"400!a" 3ea"a" 6a"4 !e"$ah, 'ehi"44a
o!e'i 3e2%e!a30! $a%a3 $ia5aia".o!e'i 3e2%e!a30! $a%a3 $ia5aia".
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Dala2 'a30a" /!i3i'hDala2 'a30a" /!i3i'h *i2%e!ial*i2%e!ial, 3ea"a" a5'ol03 $a", 3ea"a" a5'ol03 $a"
3ea"a" %e"400!a" 2a'i"43ea"a" %e"400!a" 2a'i"4 88 2a'i"4 $i"6a3aa"2a'i"4 $i"6a3aa" 'e5a4ai'e5a4ai
5e!i03:5e!i03:
1 a32o'fi!1 a32o'fi! a5'ol03a5'ol03 Q 1,@1-Q 1,@1-&>&> < 1@< 1@>>
N?2N?2&&
Q 1,P l5?i"Q 1,P l5?i"&&
Q 1@Q [email protected]& 4?2--& 4?2&&
QQ 11,,@--& 4?@--& 4?cc22
Q PB@ 22 H4Q PB@ 22 H4
Q &,& i" H4Q &,& i" H4
Q 1@,-&& 2 HQ 1@,-&& 2 H&&OO
psia psia ** pound per pound per square inch absolut square inch absolut
psig psig ** pound per pound per square inch gaugesquare inch gauge
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Tea"a" '3ea2 5oile! $i 2a"o2e3e! 2e"0"70a" 4?c2Tea"a" '3ea2 5oile! $i 2a"o2e3e! 2e"0"70a" 4?c2..
Te"30a" 3ea"a" a5'ol03 '3ea2 7ia %a$a 5a!o2e3e! $iTe"30a" 3ea"a" a5'ol03 '3ea2 7ia %a$a 5a!o2e3e! $i
!0a"4a" 2e"0"70a" 3i"44i olo2 P@@ 22 H4 %a$a 3 Q &>C.!0a"4a" 2e"0"70a" 3i"44i olo2 P@@ 22 H4 %a$a 3 Q &>C.
(ENYELESAIAN:(ENYELESAIAN:
Tea"a" 5a!o2e3e! %a$a 3 Q @C a$alah:Tea"a" 5a!o2e3e! %a$a 3 Q @C a$alah:
//@@ Q P@@ *1 = @,@@@1P& < &> Q BP 22 H4Q P@@ *1 = @,@@@1P& < &> Q BP 22 H4
Tea"a" a5'ol03 '3ea2:Tea"a" a5'ol03 '3ea2: ata p 947,86,735
6978 =+=
CONTOH SOAL: TEKANAN A/SOLUTCONTOH SOAL: TEKANAN A/SOLUT
//@@ Q / *1 = @,@@@1P& 3Q / *1 = @,@@@1P& 3
Tea"a" 0$a!a a32o'fi!:Tea"a" 0$a!a a32o'fi!: 6,735
697
6,735
0
==
B
p
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P. Te2%e!a30! *TP. Te2%e!a30! *T
Sala 3e2%e!a30! 203la a$a $0a 2aca2 6aSala 3e2%e!a30! 203la a$a $0a 2aca2 6ai30i30::DDala2 'a30a" i"3e!"a'io"alala2 'a30a" i"3e!"a'io"al::
TTa5'a5' Q &P- TQ &P- T@@CC .. *K*K Kel;i"Kel;i"
DDala2 'a30a" /!i3i'hala2 'a30a" /!i3i'h *i2%e!ial:*i2%e!ial:
TTa5'a5' Q B@ TQ B@ T@@
FF **@@
RR Ra"i"eRa"i"e
Te!$a%a3 5e'a!a" 3e2%e!a30! 2e"0!03 'ala, 6ai30:Te!$a%a3 5e'a!a" 3e2%e!a30! 2e"0!03 'ala, 6ai30:
KELIN,KELIN, CELCIUS, RANKINECELCIUS, RANKINE $a"$a" FARENHEITFARENHEIT..
TTii33ii $i$ih $i$ih **steam point steam point
TTii33ii 5e0 *5e0 *ice point ice point
Nol a5'ol03Nol a5'ol03 **absolute zeroabsolute zero
@@FF@@R R K K @@CC
-P--P-BP&BP& &1&&1& 1@@1@@
@@ 8 B@8 B@
&& -&-& &P-&P-
@@
@@
8 &P-8 &P-
H050"4a" a"3a!a 'ala 3e2%e!a30!H050"4a" a"3a!a 'ala 3e2%e!a30! K,K, @@C,C, @@R $a"R $a" @@F:F:
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)(5
90 $ % = )(9
5 0 % $ =
( ) 000 325
9+= " & F &
( )000 329
5 −= F & " &
Ko";e!'i "ilai 3e2%e!a30!
1.1. @@C Q -&C Q -&F Q &P-K Q &F Q &P-K Q &R R
&. 1@@C Q &1&F Q -P-K Q BP&R &. 1@@C Q &1&F Q -P-K Q BP&R
-. K Q-. K Q @@C &P- K C &P- K
. R Q F B@ R . R Q F B@ R
CONTOH KONERSI TEM(ERATUR
% $ 0
672)373(5
9373
== $ % 273)492(9
5
492
0
==
F " 00 21232)100(5
9100 =+= " F 00 3,93)32200(
9
5200 =−=
-
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11 Se50ah Ta50"4, ;ol02e 1> f3Se50ah Ta50"4, ;ol02e 1> f3 5e!i'i Ni3!o4e" $e"4a"5e!i'i Ni3!o4e" $e"4a"
2a''a Q 1@ l52. Hi30"4 ;ol02e '%e'ifi, ;ol02e '%e'ifi2a''a Q 1@ l52. Hi30"4 ;ol02e '%e'ifi, ;ol02e '%e'ifi2ola!, 702lah 2ole $a" $e"'i36 "i3!o4e" $ala2 3a50"4.2ola!, 702lah 2ole $a" $e"'i36 "i3!o4e" $ala2 3a50"4.
&& Ko2%!e'o! 0$a!a 5e!o%e!a'i %a$a 3ea"a" el0a! Q Ko2%!e'o! 0$a!a 5e!o%e!a'i %a$a 3ea"a" el0a! Q
4?c24?c2 4a04e, hi30"4 3ea"a" a5'ol03"6a, 7ia 3ea"a"4a04e, hi30"4 3ea"a" a5'ol03"6a, 7ia 3ea"a"
5a!o2e3e! $i !0a"4a" Q P&@ 22H4, -@5a!o2e3e! $i !0a"4a" Q P&@ 22H4, [email protected].
-- Di I"$o"e'ia, 3e2%e!a30! 0$a!a li"40"4a" Q ->C,Di I"$o"e'ia, 3e2%e!a30! 0$a!a li"40"4a" Q ->C,
"6a3aa" 3e2%e!a30! 3e!'e503 $ala2 'a30a" F, K $a" R."6a3aa" 3e2%e!a30! 3e!'e503 $ala2 'a30a" F, K $a" R.
Te2%e!a30! ai! Q 1BPF, "6a3aa" 3e2%e!a30! 3e!'e503Te2%e!a30! ai! Q 1BPF, "6a3aa" 3e2%e!a30! 3e!'e503
$ala2 'a30a" C, K $a" R.$ala2 'a30a" C, K $a" R.
>> Te2%e!a30! 4a' Q B-BR, "6a3aa" 3e2%e!a30! 3e!'e503Te2%e!a30! 4a' Q B-BR, "6a3aa" 3e2%e!a30! 3e!'e503$ala2 'a30a" F, C $a" K.$ala2 'a30a" F, C $a" K.
TUGAS *TUGAS * HOME WORK HOME WORK
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/A/ II. HUKUM DASAR TENTANG GAS/A/ II. HUKUM DASAR TENTANG GAS
(ERSAMAAN KEADAAN GAS IDEAL(ERSAMAAN KEADAAN GAS IDEAL
*GAS SEM(URNA*GAS SEM(URNA
Dala2 3e!2o$i"a2ia, 4a' 6a"4 $i%e!40"aa" 'e5a4aiDala2 3e!2o$i"a2ia, 4a' 6a"4 $i%e!40"aa" 'e5a4ai
5e"$a e!75e"$a e!7aa $ia"44a% 5e!'ifa3 'e5a4ai 4a' i$eal. Hal i"i$ia"44a% 5e!'ifa3 'e5a4ai 4a' i$eal. Hal i"i
$i'e5a5a"$i'e5a5a" 'ifa38'ifa3 4a' i$eal ha"6a 5e!5e$a 'e$ii3 $a!i'ifa38'ifa3 4a' i$eal ha"6a 5e!5e$a 'e$ii3 $a!i
'ifa38'ifa3 4a' 'e5e"a!"6a'ifa38'ifa3 4a' 'e5e"a!"6a..
H050"4a" ;a!ia5el %e!05aha" ea$aa" 4a'?9a3 6a"4 2eli%03iH050"4a" ;a!ia5el %e!05aha" ea$aa" 4a'?9a3 6a"4 2eli%03i
3ea"a" *%, ;ol02e * $a" 3e2%e!a30! *T, $i%e"4a!0hi oleh3ea"a" *%, ;ol02e * $a" 3e2%e!a30! *T, $i%e"4a!0hi oleh
'ifa3 4a' i30 'e"$i!i.'ifa3 4a' i30 'e"$i!i.
(e!'a2aa" ea$aa" 4a' a$alah h050"4a" ;a!ia5el ea$aa"(e!'a2aa" ea$aa" 4a' a$alah h050"4a" ;a!ia5el ea$aa"
*%, , T $e"4a" 2a''a *2 4a'.*%, , T $e"4a" 2a''a *2 4a'.
Ga' i$ealGa' i$eal a$alah 4a'a$alah 4a' 6a"46a"4 3e"a4a ia3 2ole0l82ole0l"6a $a%a33e"a4a ia3 2ole0l82ole0l"6a $a%a3$ia5aia". a$i 'e3ia% 4a'$ia5aia". a$i 'e3ia% 4a',, 7ia 7ia 3e"a4a ia3 2ole0l82ole0l"6a3e"a4a ia3 2ole0l82ole0l"6a$a%a3 $ia5aia" 3e!4olo"4 $ala2 4a' i$eal$a%a3 $ia5aia" 3e!4olo"4 $ala2 4a' i$eal..
-
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%% ; Q R ; Q R TT
Ke3e!a"4a"Ke3e!a"4a"::%% :: Tea"a" a5'ol03 *N?2Tea"a" a5'ol03 *N?2&& J J **l5?l5?i"i"&& JJ **4?24?2&&
;; :: ;ol02e;ol02e '%e'ifi '%e'ifi *2*2--?4?4 JJ **f3f3--?l5?l5
R R :: Ko"'3a"3a 4a' *7o0le?4Ko"'3a"3a 4a' *7o0le?4 KK JJ **f3.l5?l52f3.l5?l52 @@R R
TT :: Te2%e!a30! a5'ol03 *K Te2%e!a30! a5'ol03 *K JJ **@@RR
((e!'a2aa" 4a' i$eal 0"30e!'a2aa" 4a' i$eal 0"30 'e3ia%'e3ia% 'a30a" 2a''a'a30a" 2a''a *2:*2:
iaia 2a''a2a''a **22 $i%e!hi30"4a",$i%e!hi30"4a", %e!'a2aa" 4a' i$eal%e!'a2aa" 4a' i$eal 2e"7a$i:2e"7a$i:
2 % ; Q 2 R T2 % ; Q 2 R T 'e$a"4, 2 ; Q 'e$a"4, 2 ; Q
%% Q 2 Q 2 R R TT
:: ;ol02e 4a' 'e5e"a!"6a *2;ol02e 4a' 'e5e"a!"6a *2--JJ **f3f3--
22 :: 2a''a 4a' *42a''a 4a' *4 JJ **l5l522
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((e!'a2aa" 4a' i$eal 0"30e!'a2aa" 4a' i$eal 0"30 'e3ia%'e3ia% 'a30a"'a30a" 2ole2ole::
%% ; Q R ; Q R oo TT
iaia 702lah 2ole 702lah 2ole *"*" $i%e!hi30"4a", 2aa$i%e!hi30"4a", 2aa %e!'a2aa"%e!'a2aa"4a' i$eal4a' i$eal 2e"7a$i:2e"7a$i:
" % ; Q " R " % ; Q " R oo TT 'e$a"4, " ; Q 'e$a"4, " ; Q
%% Q " Q " R R oo TT
"" :: 702lah 2ole 4a' *482ole 702lah 2ole 4a' *482ole JJ **l5l52282ole82ole
;; :: ;ol02e;ol02e '%e'ifi '%e'ifi 2ola! *22ola! *2--?48?48 2ole2ole JJ **f3f3--?l5?l52282ole82ole
R R @@ :: o"'3o"'3a"3aa"3a 4a' 0"i;e!'4a' 0"i;e!'aal *7o0le?4l *7o0le?4882ole2ole K K JJ **f3.l5?l52f3.l5?l528282oleole @@RR
H050"4a" a"3a!a o"'3a"3a 4a' *R $a" o"'3a"3a 4a'H050"4a" a"3a!a o"'3a"3a 4a' *R $a" o"'3a"3a 4a'0"i;e!'al R 0"i;e!'al R @@ a$alah:a$alah:
BM
% % 0= //M Q 5e!a3 2ole0l 4a'M Q 5e!a3 2ole0l 4a'
*4?4*4?4882ole2ole JJ **l5l522?l5?l528282ole2ole
-
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((e!'a2aa" 4a' i$eal 0"30e!'a2aa" 4a' i$eal 0"30 'e3ia%'e3ia% 'a30a"'a30a" 2ole:2ole:
%% ; Q R ; Q R @@ TT&
v p %
*.0 =→
KONSTANTA GAS UNIERSAL *R KONSTANTA GAS UNIERSAL *R OO
Me"e"30a" "ilai R Me"e"30a" "ilai R OO 'e'0ai $e"4a" h002 4a' i$eal, %a$a'e'0ai $e"4a" h002 4a' i$eal, %a$a
o"$i'i '3a"$a!, T Q &P- K *@C, 3ea"a" 1 a32o'fi! a5'ol03o"$i'i '3a"$a!, T Q &P- K *@C, 3ea"a" 1 a32o'fi! a5'ol03
*PB@ 22 H4, 2aa 'e3ia% 482ole 4a' 2e2%0"6ai ;ol02e*PB@ 22 H4, 2aa 'e3ia% 482ole 4a' 2e2%0"6ai ;ol02e'%e'ifi 2ola!, ; Q &&, 2'%e'ifi 2ola!, ; Q &&, 2
ia 1 a32o'fi! Q 1,@1-&> < 1@ia 1 a32o'fi! Q 1,@1-&> < 1@>> N?2N?2, 2aa:, 2aa:
( ) ( ) $ molekg
Nm
$
molekg
m
m
N
x %
−=−= 8314
273
4,221001325,1
3
2
5
0
R R @@ Q -1 N2?482ole KQ -1 N2?482ole K Q -1 ?482ole K Q -1 ?482ole K
-
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ia 1 a32o'fi! Q 1@--& 4?2ia 1 a32o'fi! Q 1@--& 4?2, 2aa:, 2aa:
( ) ( )
$ molekg
mkg
$
molekg
m
m
kg
%−
=−= 848273
4,2210332
3
2
0
De"4a" ca!a 6a"4 'a2a, 5e'a!a" o"'3a"3a 4a' 0"i;e!'alDe"4a" ca!a 6a"4 'a2a, 5e'a!a" o"'3a"3a 4a' 0"i;e!'alR R OO $ala2 'a30a" /!i3hi'?i2%e!ial:$ala2 'a30a" /!i3hi'?i2%e!ial:
%molelbm
lb ft %
00 1545
−
=
-
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40
Ga'Ga' /e!a3/e!a3
2ole0l2ole0l
R *42?4R *42?4 KK R *f38l5?l52R *f38l5?l52 RR
U$a!aU$a!a &,&, &,PP&,PP >-,->>-,->
COCO&& 1,&>1,&> ->,1&->,1&
HH&& && &@,P&@,P PBB,>PBB,>
NN&& && -@,&B-@,&B >>,1>>>,1>
OO&& -&-& &B,>&B,> ,-,-
Heli02 HeHeli02 He &1&&1& -B,--B,-
A2o"ia NHA2o"ia NH-- 1P1P ,PB,PB @,PP@,PP
Me3ha"e CHMe3ha"e CH 1B1B >&,>&, B,B,
CONTOH TA/EL HARGA R /E/ERA(A GASCONTOH TA/EL HARGA R /E/ERA(A GAS
-
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41
CONTOH TA/EL HARGA R /E/ERA(A GASCONTOH TA/EL HARGA R /E/ERA(A GAS
-
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42
% Q 2 R T
(e!'a2aa" 4a' i$eal $e"4a" 2e2%e!hi30"4a" 2a''a"6a
*2, 2aa:
%% :: Tea"a" a5'ol03 *N?2Tea"a" a5'ol03 *N?2&& a3a0 (aa3a0 (a
:: ;ol02e;ol02e 'i'3e2 ?'i'3e2 ?4a' *24a' *2--
RR :: Ko"'3a"3a 4a' *Ko"'3a"3a 4a' *N2N2?4?4 K JK J **?4?4 KK
TT :: Te2%e!a30! a5'ol03 4a' *K Te2%e!a30! a5'ol03 4a' *K
22 : 2a''a 'i'3e2 *4: 2a''a 'i'3e2 *4
(( :: Tea"a" a5'ol03 *Tea"a" a5'ol03 *44?2?2&&
:: ;ol02e;ol02e 'i'3e2 ?'i'3e2 ?4a' *24a' *2--RR :: Ko"'3a"3a 4a' *Ko"'3a"3a 4a' *4242?4?4 KK
TT :: Te2%e!a30! a5'ol03 4a' *K Te2%e!a30! a5'ol03 4a' *K
22 : 2a''a 'i'3e2 *4: 2a''a 'i'3e2 *4
Sa30a" 6a"4 $i40"aa":
-
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CONTOH SOAL: HUKUM DASAR GASCONTOH SOAL: HUKUM DASAR GAS
(ENYELESAIAN:(ENYELESAIAN:
U"30 4a' hi$!o4e", R Q &@,P 42?4U"30 4a' hi$!o4e", R Q &@,P 42?4 KK
*liha3 3a5el*liha3 3a5el
$ kg
kgm
H BM
% % 424
2
848
2
0 ===
2 Q 1, 42 Q 1, 4
T Q &>T Q &> @@CC
Ta50"4,Ta50"4,
HH&&
% Q & a3a% Q & a3a
Q Q
H050"4a" R $a" R H050"4a" R $a" R OO::
1. Se50ah Ta50"4 hi$!o4e", 2a''a hi$!o4e" Q 1, 4 $a"1. Se50ah Ta50"4 hi$!o4e", 2a''a hi$!o4e" Q 1, 4 $a"
3ea"a" Q & a32o'fi! a5'ol03 *a3a 'e!3a 3e2%e!a30! Q &>C.3ea"a" Q & a32o'fi! a5'ol03 *a3a 'e!3a 3e2%e!a30! Q &>C.
Hi30"4 ;ol02e hi$!o4e" $ala2 3a50"4.Hi30"4 ;ol02e hi$!o4e" $ala2 3a50"4.
Ha!4a R %a$a 3a5el Q &@,P 4?4Ha!4a R %a$a 3a5el Q &@,P 4?4 K, a!e"a 5e!a3K, a!e"a 5e!a3
2ole0l H2ole0l H&& "ilai"6a 3i$a 'a2a %e!'i' Q &"ilai"6a 3i$a 'a2a %e!'i' Q &
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T Q &>T Q &>CC &P- Q & &P- Q & K K
( Q & a3a Q & *1@--& 4?2( Q & a3a Q & *1@--& 4?2
2 Q 1, 42 Q 1, 4
3
2 5,810332)2(
298)7,420(4,1m p
& %mV H ===
ol02e hi$!o4e" $ala2 3a50"4,ol02e hi$!o4e" $ala2 3a50"4,
(e!'a2aa" 4a' i$eal:(e!'a2aa" 4a' i$eal:
2 Q 1, 42 Q 1, 4
T Q &>T Q &> @@CC
Ta50"4,Ta50"4,HH&&
% Q & a3a% Q & a3a
Q Q
% Q 2 R T% Q 2 R T
& S i 1@@ i ii i i i
-
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(ENYELESAIAN:(ENYELESAIAN:Ga' o'i4e", R Q &B,> 42?4Ga' o'i4e", R Q &B,> 42?4 K *liha3 3a5elK *liha3 3a5el
$ kg
kgm
O BM
%
% 5,2632
848
2
0
===
H050"4a" R $a" R H050"4a" R $a" R OO::2 Q 42 Q 4
T Q &@T Q &@ @@CC
Ta50"4,Ta50"4,OO&&
% Q @ a3a% Q @ a3a
&. Se50ah Ta50"4 a%a'i3a' Q 1@@ li3e! $ii'i o'i4e" 'a2%ai&. Se50ah Ta50"4 a%a'i3a' Q 1@@ li3e! $ii'i o'i4e" 'a2%ai
3ea"a" @ a3a $a" 3e2%e!a30! Q &@C. Hi30"4 2a''a o'i4e"3ea"a" @ a3a $a" 3e2%e!a30! Q &@C. Hi30"4 2a''a o'i4e"
$ala2 3a50"4$ala2 3a50"4
Sa2a $e"4a"Sa2a $e"4a"
ha!4a $i 3a5elha!4a $i 3a5el
T Q &@ &P-T Q &@ &P-K K Q &-Q &- KK
Q 1@@ l3 Q 1@@ $2 Q 1@@ l3 Q 1@@ $2--
Q @,1 2Q @,1 2--
kg & %
V pm 322,5
)293(5,26
)1,0()10332(40===
Ma''a o'i4e" $ala2 3a50"4,Ma''a o'i4e" $ala2 3a50"4,
( Q @ a3a Q *@ [email protected]& 4?2( Q @ a3a Q *@ [email protected]& 4?2
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-. Ma''a 4a' Ni3!o4e" *N-. Ma''a 4a' Ni3!o4e" *N&& Q 11,& 4 $ica2%0! $e"4a" 4 Q 11,& 4 $ica2%0! $e"4a" 4
4a' O'i4e" *O4a' O'i4e" *O&& $a" $i7a4a %a$a 3e2%e!a30! &> $a" $i7a4a %a$a 3e2%e!a30! &>@@ C, 3ea"a"C, 3ea"a"
1,> 5a!. Te"30a" 3ea"a" %a!'ial $a!i e$0a 4a' $a" 3e"30a"1,> 5a!. Te"30a" 3ea"a" %a!'ial $a!i e$0a 4a' $a" 3e"30a"
;ol02e ca2%0!a" 4a' 3e!'e503.;ol02e ca2%0!a" 4a' 3e!'e503.
Q Q
T Q &>T Q &> @@CC
NN&& O O&&
% Q 1,> 5a!% Q 1,> 5a!
(ENYELESAIAN:
02lah 2ole N02lah 2ole N&&::molekg
BM
mn
N −=== 4,028
2,11
2
molekg BM
mn
O
−=== 25,032
8
2
02lah 2ole O02lah 2ole O&&::
02lah 2ole *" ca2%0!a" N02lah 2ole *" ca2%0!a" N&& O O&& Q @, @,&>Q @, @,&>
Q @,B> 482oleQ @,B> 482ole
T Q &>T Q &>@@C Q &K, (C Q &K, (
Q 1,> 5a! Q 1>@@@ 4?2Q 1,> 5a! Q 1>@@@ 4?2&&
40
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48
a$i, 3ea"a" %a!'ial Oa$i, 3ea"a" %a!'ial O&&, ( Q @,-> *1,> 5a! Q @,>PP> 5a!., ( Q @,-> *1,> 5a! Q @,>PP> 5a!.
F!a'i NF!a'i N&& $ala2 ca2%0!a":$ala2 ca2%0!a": %615,065,0
4,02 == N '
%385,065,0
25,02 ==O 'F!a'i OF!a'i O&& $ala2 ca2%0!a":$ala2 ca2%0!a":
a$i, 3ea"a" %a!'ial Na$i, 3ea"a" %a!'ial N&&, ( Q @,B1> *1,> 5a! Q @,&&> 5a!., ( Q @,B1> *1,> 5a! Q @,&&> 5a!.
%% Q " Q " R R OO TT
395,10
15000
298)848(65,0m
& %nV O ===
(e!'a2aa" 4a' i$eal:(e!'a2aa" 4a' i$eal:
$ kgmole
kgm %O 848=
Q Q
T Q &>T Q &> @@CC
NN&& O O&&
% Q 1,> 5a!% Q 1,> 5a!
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. Se50ah 3a"4i Q B 2. Se50ah 3a"4i Q B 2--, 5e!i'i o'i4e" %a$a 3ea"a" a5'ol03, 5e!i'i o'i4e" %a$a 3ea"a" a5'ol03
&@@ (a, 3e2%e!a30! @@K. Ga' o'i4e" $i50a"4 %e!laha"&@@ (a, 3e2%e!a30! @@K. Ga' o'i4e" $i50a"4 %e!laha"
hi"44a 3ea"a" $i $ala2 3a"4i 30!0" 2e"7a$i 11@ (ahi"44a 3ea"a" $i $ala2 3a"4i 30!0" 2e"7a$i 11@ (a
a5'ol03 *3e2%e!a30! o"'3a". Te"30a" 2a''a o'i4e" 6a"4a5'ol03 *3e2%e!a30! o"'3a". Te"30a" 2a''a o'i4e" 6a"43e!i"44al $i $ala2 3a"4i $a" 2a''a o'i4e" 6a"4 $i50a"4.3e!i"44al $i $ala2 3a"4i $a" 2a''a o'i4e" 6a"4 $i50a"4.
ia 3e2%e!a30! o'i4e" $i $ala2 3a"4i 30!0" 2e"7a$i 1@ia 3e2%e!a30! o'i4e" $i $ala2 3a"4i 30!0" 2e"7a$i 1@@@C,C,
3e"30a" 3ea"a" ahi! o'i4e" $i $ala2 3a"4i.3e"30a" 3ea"a" ahi! o'i4e" $i $ala2 3a"4i.
(e!'a2aa" 4a' i$eal: %(e!'a2aa" 4a' i$eal: % Q Q 22 R R TT
$ kg
Nm
BM
% %
O
O 260
32
8314
2
===
(ENYELESAIAN:(ENYELESAIAN: ( (11 Q &@@ (a QQ &@@ (a Q
&@@.@@@ (a&@@.@@@ (a((&& Q 11@ (a Q 11@.@@@ (aQ 11@ (a Q 11@.@@@ (aT Q @@K T Q @@K
OO&&
% Q &@@ (a% Q &@@ (a
Q B 2 Q B 2--
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( )kg
& %
V pm 35,6
)400(260
611000022 ===
Ma''a OMa''a O&& 6a"4 3e!3i"44al $i $ala2 3a"4i:6a"4 3e!3i"44al $i $ala2 3a"4i:
( )kg
& %
V pm 54,11
)400(260
620000011 ===
Ma''a OMa''a O&& %a$a o"$i'i a#al:%a$a o"$i'i a#al:
Ma''a OMa''a O&& 6a"4 $i50a"4 Q 11,> = B,-> Q >,1 46a"4 $i50a"4 Q 11,> = B,-> Q >,1 4
(a$a o"$i'i ahi!, 2a''a o'i4e" 2(a$a o"$i'i ahi!, 2a''a o'i4e" 2-- Q 2Q 2&& Q B,-> 4 $a"Q B,-> 4 $a"
TT-- Q 1@Q 1@@@
C Q &-K. Tea"a" ahi!:C Q &-K. Tea"a" ahi!:
aV
& %m p 77872
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T Q @@K T Q @@K
OO&&
% Q &@@ (a% Q &@@ (a
Q B 2 Q B 2--
TUGAS *TUGAS *HOME WORKHOME WORK
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TUGAS *TUGAS * HOME WORK HOME WORK
- /0a3 a!3iel 3e"3a"4 %e!'a2aa" 4a' i$eal $a" 5e!ia"- /0a3 a!3iel 3e"3a"4 %e!'a2aa" 4a' i$eal $a" 5e!ia"co"3oh %e!hi30"4a""6a.co"3oh %e!hi30"4a""6a.
1 /a" 'e%e$a, 3ea"a" 0$a!a $i5a3a'i 2a' Q &&@ (a *4a04e1 /a" 'e%e$a, 3ea"a" 0$a!a $i5a3a'i 2a' Q &&@ (a *4a04e
oleh !elief ;al;e. Saa3 20lai %e!7ala"a", 5a" $i5e!i 3ea"a"oleh !elief ;al;e. Saa3 20lai %e!7ala"a", 5a" $i5e!i 3ea"a"
&@@ (a *4a04e $a" 3e2%e!a30! &-&@@ (a *4a04e $a" 3e2%e!a30! &-@@C. Sela2a 2e"e2%0hC. Sela2a 2e"e2%0h%e!7ala"a", 3e2%e!a30! 0$a!a $i $ala2 5a" "ai 2e"ca%ai%e!7ala"a", 3e2%e!a30! 0$a!a $i $ala2 5a" "ai 2e"ca%ai
--@@C. ia 2a'i"482a'i"4 5a" a$a 2a''a 0$a!a Q @,11 4,C. ia 2a'i"482a'i"4 5a" a$a 2a''a 0$a!a Q @,11 4,
3e"30a" 2a''a 0$a!a 6a"4 hila"4 2elal0i !elief ;al;e %a$a3e"30a" 2a''a 0$a!a 6a"4 hila"4 2elal0i !elief ;al;e %a$a
2a'i"482a'i"4 5a" oleh a!e"a ele5iha" 3ea"a" $a"2a'i"482a'i"4 5a" oleh a!e"a ele5iha" 3ea"a" $a"3e"30a" 3ea"a" 0$a!a $i $ala2 5a" 'aa3 3e2%e!a30! 0$a!a3e"30a" 3ea"a" 0$a!a $i $ala2 5a" 'aa3 3e2%e!a30! 0$a!a
e25ali 2e"7a$i Q &-e25ali 2e"7a$i Q &-@@C.C.
& Ma''a hi$!o4e" $ala2 3a50"4 Q B l52, 3ea"a" Q -@ %'ia& Ma''a hi$!o4e" $ala2 3a50"4 Q B l52, 3ea"a" Q -@ %'ia
$a" 3e2%e!a30! Q >F , hi30"4 ;ol02e hi$!o4e" $i $ala2$a" 3e2%e!a30! Q >F , hi30"4 ;ol02e hi$!o4e" $i $ala23a50"4, 'a30a" f33a50"4, 'a30a" f3--..
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/A/ III/A/ III (ERU/AHAN(ERU/AHAN (ROSES(ROSES GAS IDEALGAS IDEAL
(a$a(a$a o"$i'i 3e!3e"30o"$i'i 3e!3e"30 3e!$a%a33e!$a%a3 5e5e!a%a5e5e!a%a 2aca22aca2 %!o'e'%!o'e'
%e!05aha" ea$aa" i'3i2e#a%e!05aha" ea$aa" i'3i2e#a 4a' i$eal4a' i$eal, 6ai30:, 6ai30:
ia 'i'3e2 *4a' 2e"6e!a% a3a0 2ele%a' %a"a', 2aaia 'i'3e2 *4a' 2e"6e!a% a3a0 2ele%a' %a"a', 2aa
3e!7a$i %e!05aha" %a$a 3ea"a" *%, 3e2%e!a30! *T $a"3e!7a$i %e!05aha" %a$a 3ea"a" *%, 3e2%e!a30! *T $a";ol02e * 'eca!a 'i20l3a".;ol02e * 'eca!a 'i20l3a".
1.1. (ROSES ISOTHERMIS?ISOTHERMAL(ROSES ISOTHERMIS?ISOTHERMAL&.&. (ROSES ISOMETRIC?ISOCHORIC(ROSES ISOMETRIC?ISOCHORIC
-.-. (ROSES ISO/ARIC(ROSES ISO/ARIC
.. (ROSES ADIA/ATIC?ISENTRO(IC(ROSES ADIA/ATIC?ISENTRO(IC
1 (ROSES ISOTHERMIS?ISOTHERMAL1 (ROSES ISOTHERMIS?ISOTHERMAL
-
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((e!05aha" ea$aa"e!05aha" ea$aa" 4a' %a$a4a' %a$a 3e2%e!a30! o"'3a"3e2%e!a30! o"'3a"
Ga' $i2a'0 Ga' $i2a'0 a" ea" e $ala2 'ili"$e! 3o!a.$ala2 'ili"$e! 3o!a.
Kea$aa" 4a'Kea$aa" 4a' $i!05ah $a!i ea$aa" 1 e$i!05ah $a!i ea$aa" 1 eea$aa"ea$aa" & $e"4a" 2e"ea" 3o!a.& $e"4a" 2e"ea" 3o!a.
Te2%e!a30!Te2%e!a30! 4a' $i7a4a o"'3a" $e"4a"4a' $i7a4a o"'3a" $e"4a"
ca!aca!a 2e"$i"4i"a"2e"$i"4i"a"??2e2a"a'a" 'ili"$e!2e2a"a'a" 'ili"$e!..
(e!'a2aa" 4a' i$eal, % ; Q R T(e!'a2aa" 4a' i$eal, % ; Q R T
U"30 T o"'3a", 2aa % ; Q o"'3a"U"30 T o"'3a", 2aa % ; Q o"'3a"
%%11 ;;11 Q %Q %&& ;;&&
1
2
2
1
v
v
p
p=A3a0,A3a0,
4a'4a'
Dia4!a2 %=;Dia4!a2 %=;((
;;
;;11;;&&
11
&&
TQo"'3a"TQo"'3a"
%%11
%%&&
&& 11
1
2
2
1
p
p
v
v=→
1. (ROSES ISOTHERMIS?ISOTHERMAL1. (ROSES ISOTHERMIS?ISOTHERMAL
& (ROSES ISOMETRIC?ISOCHORIC& (ROSES ISOMETRIC?ISOCHORIC
-
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K K ea$aa" 4a' $i!05ah $a!i ea$aa" 1 eea$aa" 4a' $i!05ah $a!i ea$aa" 1 e
ea$aa" & $e"4a" 2e2a"a'a" 'ili"$e!,ea$aa" & $e"4a" 2e2a"a'a" 'ili"$e!,3o!a $i3aha" '0%a6a3o!a $i3aha" '0%a6a 3i$a 3i$a 5e!4e!a5e!4e!a
'ehi"44a ;ol02e 4a' $ala2 'ili"$e! 3e3a%'ehi"44a ;ol02e 4a' $ala2 'ili"$e! 3e3a%
o"'3a"o"'3a" $a" 3ea"a" "ai.$a" 3ea"a" "ai.
(e!'a2aa" 4a' i$eal, % ; Q R T(e!'a2aa" 4a' i$eal, % ; Q R T
U"30 ; o"'3a", 2aa:U"30 ; o"'3a", 2aa:
" v
%
&
== C: o"'3a"C: o"'3a"
((e!05aha" ea$aa"e!05aha" ea$aa" 4a' %a$a4a' %a$a ;ol02e o"'3a";ol02e o"'3a"..
&. (ROSES ISOMETRIC?ISOCHORIC&. (ROSES ISOMETRIC?ISOCHORIC
Dia4!a2 %8;Dia4!a2 %8;
11
&&((&&
((11
Q o"'3a" Q o"'3a"
((
@@
4a'4a'
2
1
2
1
1
2
1
2
2
2
1
1
&
&
p
p
&
&
p
p
&
p
&
p=→=→=a$i,a$i,
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((e!05aha" ea$aa"e!05aha" ea$aa" 4a' %a$a4a' %a$a 3ea"a" o"'3a"3ea"a" o"'3a"..
Kea$aa" 4a' $i!05ah $a!i ea$aa" 1 eKea$aa" 4a' $i!05ah $a!i ea$aa" 1 eea$aa" & $e"4a" 2e2a"a'a" 'ili"$e!,ea$aa" & $e"4a" 2e2a"a'a" 'ili"$e!,
3o!a $i50a3 5e5a' 5e!4e!a 'ehi"44a3o!a $i50a3 5e5a' 5e!4e!a 'ehi"44a
3ea"a" 4a' $ala2 'ili"$e!3ea"a" 4a' $ala2 'ili"$e! $i7a4a$i7a4a o"'3a"o"'3a"..
(e!'a2aa" 4a' i$eal(e!'a2aa" 4a' i$eal % ; Q R T% ; Q R T
U"30 % o"'3a", 2aa:U"30 % o"'3a", 2aa:
"
p
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Dia4!a2 %8;Dia4!a2 %8;
11 &&((11 QQ ((&&
11
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2
1
2
1
1
2
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2
2
2
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1
&
&
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v
&
&
v
v
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v=→=→=a$i,a$i,
DIAGRAM UNTUK (ROSES
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pp
vv
IsothermisIsothermis
IsobaricIsobaric
IsometricIsometric
Permukaan p - v - T gas idealPermukaan p - v - T gas ideal
DIAGRAM % = ; UNTUK (ROSESDIAGRAM % = ; UNTUK (ROSES
ISOTHERMIS, ISOMETRIC DAN ISO/ARICISOTHERMIS, ISOMETRIC DAN ISO/ARIC
2
22
1
11
&
v p
&
v p=
2
1
22
11
&
&
v p
v p=
Ga50"4a" a"3a!a %!o'e'Ga50"4a" a"3a!a %!o'e'i'o3he!2al $a" i'o5a!ici'o3he!2al $a" i'o5a!ic
2e"4ha'ila" %e!'a2aa"2e"4ha'ila" %e!'a2aa"
'e'0ai $e"4a" h002'e'0ai $e"4a" h002
/OYLE = GAY LUSSAC,/OYLE = GAY LUSSAC,
6ai30:6ai30:
TA/EL DIAGRAM (ROSES UNTUK GAS IDEALTA/EL DIAGRAM (ROSES UNTUK GAS IDEAL
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e"i'e"i'
$ia4!a2$ia4!a2
I'o3he!2alI'o3he!2al I'o2e3!icI'o2e3!ic i'o5a!ici'o5a!ic
Dia4!a2Dia4!a2
% 8 ;% 8 ;
Dia4!a2Dia4!a2
% = T% = T
Dia4!a2Dia4!a2
; 8 T; 8 T
1
2
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v
p
p
= 21
2
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2
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TA/EL DIAGRAM (ROSES UNTUK GAS IDEALTA/EL DIAGRAM (ROSES UNTUK GAS IDEAL
CONTOH SOAL: (ERU/AHAN (ROSES GASCONTOH SOAL: (ERU/AHAN (ROSES GAS
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CONTOH SOAL: (ERU/AHAN (ROSES GASCONTOH SOAL: (ERU/AHAN (ROSES GAS
o'i4e",Oo'i4e",O&&
Q & 2 Q & 2
TT11 Q @Q @@@CC
Sili"$e!Sili"$e!
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2 Q 2 Q
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Q & 2 Q & 2--, T, T11 Q @C &P- Q -1- K Q @C &P- Q -1- K
((11 Q B@ a3a Q B@ *1,@1 < 1@Q B@ a3a Q B@ *1,@1 < 1@>> Q B@,B *1@ Q B@,B *1@>> N?2 N?2
molekg
m
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& %v O
−===
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5 43,0
106,60
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1. Sili"$e! 3e!3030%, ;ol02e Q & 2 5e!i'i o'i4e", 3e2%e!a30!1. Sili"$e! 3e!3030%, ;ol02e Q & 2 5e!i'i o'i4e", 3e2%e!a30!
a#al Q @C $a" 3ea"a" Q B@ a3a. Hi30"4 702lah 2ole $a"a#al Q @C $a" 3ea"a" Q B@ a3a. Hi30"4 702lah 2ole $a"
2a''a O2a''a O&& $ala2 'ili"$e!. ia 3e2%e!a30! o'i4e" $i"aia"$ala2 'ili"$e!. ia 3e2%e!a30! o'i4e" $i"aia"2e"7a$i @@C, hi30"4 3ea"a" ahi! o'i4e" $i 'ili"$e!.2e"7a$i @@C, hi30"4 3ea"a" ahi! o'i4e" $i 'ili"$e!.
Da!i %e!'a2aa" 4a' i$eal %e! 'a30a" 2ole,Da!i %e!'a2aa" 4a' i$eal %e! 'a30a" 2ole,
(( ; Q R ; Q R @@ TT
ol02e '%e'ifi 2ola!:ol02e '%e'ifi 2ola!:
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02lah 2ole,02lah 2ole, molekg v
V n −=== 65,4
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Ma''a o'i4e", 2 Q " */M OMa''a o'i4e", 2 Q " */M O&& Q ,B> *-& Q 1 4 Q ,B> *-& Q 1 4
Te2%e!a30! $i"aia" 2e"7a$i, TTe2%e!a30! $i"aia" 2e"7a$i, T&& Q @@Q @@C.C.
TT&& Q @@ C &P- Q BP- K Q @@ C &P- Q BP- K
Sili"$e! o"$i'i 3e!3030%, 'ehi"44a %!o'e' 5e!la"4'0"4Sili"$e! o"$i'i 3e!3030%, 'ehi"44a %!o'e' 5e!la"4'0"4
%a$a ;ol02e o"'3a" *i'o2e3!ic.%a$a ;ol02e o"'3a" *i'o2e3!ic.
( )ata
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(ENYELESAIAN:(ENYELESAIAN:
(!o'e' 1 = &: i'o2e3!ic, & = -: i'o3he!2al, - = 1: i'o5a!ic(!o'e' 1 = &: i'o2e3!ic, & = -: i'o3he!2al, - = 1: i'o5a!ic
&. Ga' i$eal l52 2ole, % Q >@ a3a $a" Q -@ f3&. Ga' i$eal l52 2ole, % Q >@ a3a $a" Q -@ f3--, $i%a"a'a", $i%a"a'a"%a$a %!o'e' i'o2e3!ic 'ehi"44a 3ea"a" "ai 2e"7a$i & ali%a$a %!o'e' i'o2e3!ic 'ehi"44a 3ea"a" "ai 2e"7a$i & ali3ea"a" a#al. Ke20$ia" 4a' $ie'%a"'ia" 'eca!a i'o3he!2al3ea"a" a#al. Ke20$ia" 4a' $ie'%a"'ia" 'eca!a i'o3he!2al
'ehi"44a e25ali e 3ea"a" a#al, 'ela"703"6a 4a' $io2%!e'i'ehi"44a e25ali e 3ea"a" a#al, 'ela"703"6a 4a' $io2%!e'i'eca!a i'o5a!ic $a" e25ali e ;ol02e a#al. Ga25a!a"'eca!a i'o5a!ic $a" e25ali e ;ol02e a#al. Ga25a!a"$ia4!a2 % 8 ; $a" % = T 'e!3a ; = T. Hi30"4 3e2%e!a30! ahi!$ia4!a2 % 8 ; $a" % = T 'e!3a ; = T. Hi30"4 3e2%e!a30! ahi!%a$a %!o'e' i'o2e3!ic%a$a %!o'e' i'o2e3!ic
%%
;;
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%%11 Q %Q %--
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Dia4!a2 ; 8TDia4!a2 ; 8T
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1 a32 Q 1,P l5?i"1 a32 Q 1,P l5?i" Q 1,P *1 5?f3 Q 1,P *1 5?f322
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(!o'e': 1 = & a$alah i'o2e3!ic, (!o'e': 1 = & a$alah i'o2e3!ic, 11 Q Q &&
$a" %$a" %&& Q & %Q & %11
1
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-
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(ENYELESAIAN:(ENYELESAIAN:
TT11 Q 1&@Q 1&@F Q 1&@ B@R Q >@RF Q 1&@ B@R Q >@R
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/ila ;ol02e 0$a!a 5e!3a25ah $a!i 1>@ f3/ila ;ol02e 0$a!a 5e!3a25ah $a!i 1>@ f3-- 2e"7a$i &>@ f32e"7a$i &>@ f3--
$a" 3e2%e!a30! a#al Q 1&@F, hi30"4 3e2%e!a30! ahi!$a" 3e2%e!a30! a#al Q 1&@F, hi30"4 3e2%e!a30! ahi!
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U$ $ l ili $ 1 i 3 U$a!a $ala2 'ili"$e! 1 2e2%0"6ai 3ea"a" %e"400!a"
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11
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Tea"a" a5'ol03, %Tea"a" a5'ol03, %11 Q > 1 Q B 4?c2Q > 1 Q B 4?c2
(!o'e' 3e2%e!a30! o"'3a", 2aa:(!o'e' 3e2%e!a30! o"'3a", 2aa:
%%11 11 Q %Q %&& &&
33
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. U$a!a $ala2 'ili"$e! 1, 2e2%0"6ai 3ea"a" %e"400!a". U$a!a $ala2 'ili"$e! 1, 2e2%0"6ai 3ea"a" %e"400!a"
%%11 Q > 4?c2 $a" $i5ia!a" 5e!e'%a"'i $i 'ili"$e! & $e"4a"Q > 4?c2 $a" $i5ia!a" 5e!e'%a"'i $i 'ili"$e! & $e"4a"
;ol02e - ;ol02e - 11. Hi30"4 3ea"a" ahi! %a$a 'ili"$e! &, 7ia. Hi30"4 3ea"a" ahi! %a$a 'ili"$e! &, 7ia
%!o'e' 5e!la"4'0"4 %a$a 3e2%e!a30! o"'3a".%!o'e' 5e!la"4'0"4 %a$a 3e2%e!a30! o"'3a".
TUGAS *TUGAS *HOME WORKHOME WORK
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>@@ c2>@@ c2--
-@ c2-@ c2
$ Q > 22$ Q > 22
B c2B c2
TUGAS *TUGAS * HOME WORK HOME WORK
1. ol02e 5ola *1. ol02e 5ola *bulbbulb Q >@@ c2 %a$a o"$i'i a#al Q >@@ c2 %a$a o"$i'i a#al
5ola $a" a%ile! 5e!i'i 0$a!a 3ea"a" Q PB@ 22 H4.5ola $a" a%ile! 5e!i'i 0$a!a 3ea"a" Q PB@ 22 H4.
Sela"703"6a ai! !a'a $i2a'0a" $a!i 5a#ah 5olaSela"703"6a ai! !a'a $i2a'0a" $a!i 5a#ah 5ola
'ehi"44a 2e"40!0"4 0$a!a %a$a 070"4 %i%a a%ile!'ehi"44a 2e"40!0"4 0$a!a %a$a 070"4 %i%a a%ile!
'e%a"7a"4 B c2. ia %!o'e' 5e!la"4'0"4 %a$a'e%a"7a"4 B c2. ia %!o'e' 5e!la"4'0"4 %a$a
3e2%e!a30! o"'3a", hi30"4 3ea"a" 0$a!a 6a"43e2%e!a30! o"'3a", hi30"4 3ea"a" 0$a!a 6a"4
3e!0!0"4 %a$a a%ile! 5a4ia" a3a'.3e!0!0"4 %a$a a%ile! 5a4ia" a3a'.
&. Sili"$e! %i'3o", %a"7a"4 la"4ah, < Q & f3,&. Sili"$e! %i'3o", %a"7a"4 la"4ah, < Q & f3,
$ia2e3e! Q & i". (i'3o" $i3ea" 'ehi"44a$ia2e3e! Q & i". (i'3o" $i3ea" 'ehi"44a
4a6a %a$a 4a' "ai $a!i @ 2e"7a$i 1@@ N.4a6a %a$a 4a' "ai $a!i @ 2e"7a$i 1@@ N.
ia 3ea"a" 0$a!a l0a! 1 5a! $a" %!o'e'ia 3ea"a" 0$a!a l0a! 1 5a! $a" %!o'e'i'o3he!2al, hi30"4 %a"7a"4 %e"ea"a"i'o3he!2al, hi30"4 %a"7a"4 %e"ea"a"
%i'3o" *
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CAM(URAN GASCAM(URAN GAS
Ko2%o'i'i ca2%0!a" 5e5e!a%a 4a' $a%a3 $i3e"30a"Ko2%o'i'i ca2%0!a" 5e5e!a%a 4a' $a%a3 $i3e"30a"
5e!$a'a!a" 2a''a a3a0 ;ol02e"6a. (e!'e"3a'e o2%o"e"5e!$a'a!a" 2a''a a3a0 ;ol02e"6a. (e!'e"3a'e o2%o"e"
4a' *4 5e!$a'a!a" 2a''a a$alah:4a' *4 5e!$a'a!a" 2a''a a$alah:
m
m g
m
m g
m
m g
m
m g nn ==== ;;;
33
22
11
Ke3e!a"4a":Ke3e!a"4a":
2211 2 2"" Q 2a''a o2%o"e" 2a'i"482a'i"4 4a'Q 2a''a o2%o"e" 2a'i"482a'i"4 4a'
2 Q 2a''a 3o3al ca2%0!a" 4a'2 Q 2a''a 3o3al ca2%0!a" 4a'
To3al o2%o"e" 4a'To3al o2%o"e" 4a' 4411 4 4&& 4 4-- . 4. 4""Q 1Q 1
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V mmakam
V #ari ρ ρ
=→=→
ii
iiiii
i r %
%r
BM
BM
V
V
m
m g ====
ρ
ρ
(e!'e"3a'e o2%o"e" 4a'(e!'e"3a'e o2%o"e" 4a'
V
V
r V
V
r V
V
r V
V
r n
n ==== ;;; 3
3
2
2
1
1
(e!'e"3a'e o2%o"e" 4a' *! 5e!$a'a!a" ;ol02e:(e!'e"3a'e o2%o"e" 4a' *! 5e!$a'a!a" ;ol02e:
CONTOH SOAL: CAM(URAN GASCONTOH SOAL: CAM(URAN GAS
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CONTOH SOAL: CAM(URAN GASCONTOH SOAL: CAM(URAN GAS
1. (e!'e"3a'e o2%o"e" 4a' 50a"4 $a!i Ge"e!a3o!: H1. (e!'e"3a'e o2%o"e" 4a' 50a"4 $a!i Ge"e!a3o!: H&& Q 1V,Q 1V,
CO Q &V, COCO Q &V, CO&& Q BV $a" NQ BV $a" N&& Q >&V. Te"30a" V 2a''aQ >&V. Te"30a" V 2a''a
2a'i"482a'i"4 o2%o"e" 4a', 3e"30a" 3ea"a" %a!'ial2a'i"482a'i"4 o2%o"e" 4a', 3e"30a" 3ea"a" %a!'ial2a'i"482a'i"4 4a' 7ia 3ea"a" 4a' ca2%0!a" Q PB@ 22 H42a'i"482a'i"4 4a' 7ia 3ea"a" 4a' ca2%0!a" Q PB@ 22 H4
(ENYELESAIAN:(ENYELESAIAN:
/e!a3 2ole0l */M ca2%0!a" 4a'/e!a3 2ole0l */M ca2%0!a" 4a'
Q *@,1 & *@,& & *@,@B *@,>& & Q &Q *@,1 & *@,& & *@,@B *@,>& & Q &
307,1
4,22
24
* m
kg
v
BM total === ρ
De"'i36 ca2%0!a" 4a':De"'i36 ca2%0!a" 4a':
(e!'e"3a'e *V 2a''a 2a'i"482a'i"4 o2%o"e" 4a':(e!'e"3a'e *V 2a''a 2a'i"482a'i"4 o2%o"e" 4a':
%5,1015,0)18,0(24
22
22 ==== H
total
H H r
BM
BM g
28"OBM
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%6,27276,0)24,0(24
28==== "O
total
"O"O r
BM
BM g
%9,10109,0)06,0(24
442
22 ==== "Ototal
"O"O r BM
BM
g
%606,0)52,0(24
282
22 ==== N
total
N N r
BM
BM g
Tea"a" %a!'ial 2a'i"482a'i"4 o2%o"e" 4a',Tea"a" %a!'ial 2a'i"482a'i"4 o2%o"e" 4a',
Hg mm pr p H H 8,136760)18,0(22 ===
Hg mm pr p "O"O 4,182760)24,0( === Hg mm pr p "O"O 6,45760)06,0(22 ===
Hg mm pr p N N 2,395760)52,0(22 ===
& K 3 $i i $ i >V $ *R & &P ? K& K 3 $i i $ i >V $ *R & &P ? K
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&. Ko2%o"e" 4a' 3e!$i!i $a!i >V 0$a!a *R Q &,&P 42?4 K&. Ko2%o"e" 4a' 3e!$i!i $a!i >V 0$a!a *R Q &,&P 42?4 K
$a" >V 4a' a%i *R Q P-,> 42?4 K. Te"30a" o"'3a"3a *R$a" >V 4a' a%i *R Q P-,> 42?4 K. Te"30a" o"'3a"3a *R
$a" $e"'i36 *$a" $e"'i36 * $a!i 4a' ca2%0!a" 'e!3a o2%o'i'i ;ol02e $a!i 4a' ca2%0!a" 'e!3a o2%o'i'i ;ol02e
2a'i"482a'i"4 o2%o"e" 4a'.2a'i"482a'i"4 o2%o"e" 4a'.
(ENYELESAIAN:(ENYELESAIAN:
Ko"'3a"3a 4a' ca2%0!a":Ko"'3a"3a 4a' ca2%0!a":
$ kg kgm % 47,315,73)05,0(77,29)95,0( =+=
molekg kg
% % BM
total
total −=== 9,26
47,318480
/e!a3 2ole0l ca2%0!a" 4a':/e!a3 2ole0l ca2%0!a" 4a':
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(e!'e"3a'e *V ;ol02e 2a'i"482a'i"4 4a':(e!'e"3a'e *V ;ol02e 2a'i"482a'i"4 4a':
3
2,14,22
9,26
* m
kg
v
BM total total
=== ρ
De"'i36 4a' ca2%0!a":De"'i36 4a' ca2%0!a":
( ) %5,88885,047,31
27,2995,0 ====
total
u#arau#arau#ara %
% g r
( ) %5,11115,047,31
5,7305,0 ====
total
api
apiapi
%
% g r
/A/ I HUKUM TERMODINAMIKA I/A/ I HUKUM TERMODINAMIKA I
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Ko"'e% e"e!4i 2ea"i Ko"'e% e"e!4i 2ea"i E"e!4i?e!7a, e"e!4i i"e3iE"e!4i?e!7a, e"e!4i i"e3i
$a" e"e!4i %o3e"'ial$a" e"e!4i %o3e"'ial
'i'3e2'i'3e2
li"3a'a"li"3a'a"
Ma''a 'i'3e2 *2 5e!4e!aMa''a 'i'3e2 *2 5e!4e!a
$e"4a" ece%a3a" Q $'?$3.$e"4a" ece%a3a" Q $'?$3.
Ma''a $ie"ai 4a6a F $a" 4a6a FMa''a $ie"ai 4a6a F $a" 4a6a F
3e!'e503 $i0!aia" 2e"7a$i 4a6a3e!'e503 $i0!aia" 2e"7a$i 4a6aFF'' 'e%a"7a"4 li"3a'a" $a" 4a6a'e%a"7a"4 li"3a'a" $a" 4a6a
"o!2al F"o!2al F"" 3e4a l0!0' li"3a'a".3e4a l0!0' li"3a'a".
Da!i h002 Ne#3o" II 3e"3a"4 4e!aa", 4a6a a$alahDa!i h002 Ne#3o" II 3e"3a"4 4e!aa", 4a6a a$alah%e!alia" 2a''a 'i'3e2 $e"4a" %e!ce%a3a""6a.%e!alia" 2a''a 'i'3e2 $e"4a" %e!ce%a3a""6a.
F Q 2 aF Q 2 a
=
#t
#V m F s
/A/ I HUKUM TERMODINAMIKA I/A/ I HUKUM TERMODINAMIKA I
#V#s#V#V
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'i'3e2'i'3e2
li"3a'a"li"3a'a" ∫ ∫ =2
1
2
1
s
s
s
V
V
#s F #V V m
( )2
1
2
22
12
1V V m#V V m
V
V −=∫ E"e!4i i"e3i, EE"e!4i i"e3i, E QQ 2 2
&&
(e!05aha" e"e!4i i"e3i,(e!05aha" e"e!4i i"e3i, WWEE QQ 2 * 2 *&&&& 8 8 11
&&
E"e!4i i"e3i $i%e"4a!0hi oleh fa3o! ece%a3a" $a!i 'i'3e2.E"e!4i i"e3i $i%e"4a!0hi oleh fa3o! ece%a3a" $a!i 'i'3e2.ENERGI KINETIK ENERGI KINETIK
=
=
=
#s
#V V m
#t
#s
#s
#V m
#t
#V m F s FF'' $' Q 2 $$' Q 2 $
ENERGI (OTENSIALENERGI (OTENSIAL
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99&&
9911
99
2 42 4
R R
502i502i
( ) ∫ ∫ −=−2
1
2
1
2
1
2
221
(
(
(
(
#( g m#( %V V m
( )122
1
( ( mg #( g m
(
(
−=
∫ ( ) ( ) ∫ =−+−
2
1
12
2
1
2
22
1 (
(
#( % ( ( g mV V m
E"e!4i %o3e'ial *4!a;i3a'i, EE"e!4i %o3e'ial *4!a;i3a'i, E%% QQ 2 4 92 4 9
(e!05aha" e"e!4i %o3e"'ial,(e!05aha" e"e!4i %o3e"'ial, WWEE%% QQ 2 4 *92 4 *9&& = 9 = 911
E"e!4i %o3e"'ial $i%e"4a!0hi oleh fa3o! e3i"44ia" a3a0E"e!4i %o3e"'ial $i%e"4a!0hi oleh fa3o! e3i"44ia" a3a0
ele;a'i $a!i 'i'3e2.ele;a'i $a!i 'i'3e2.
7 i 7 iK 7 $ l h li 3 $ 7 li 3
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$$
((
11 &&
$'$'
11
&&
F'F'
F'F'
Dia4!a2 % 8 , e!7a 4a'Dia4!a2 % 8 , e!7a 4a'$ala2 Sili"$e!$ala2 Sili"$e!
Ke!7a a$alah %e!alia" a"3a!a 4a6a $e"4a" 7a!a li"3a'a""6a.Ke!7a a$alah %e!alia" a"3a!a 4a6a $e"4a" 7a!a li"3a'a""6a.
F: 4a6a *NJ l5, $': li"3a'a" *2J f3 F: 4a6a *NJ l5, $': li"3a'a" *2J f3
F Q A %F Q A % %: 3ea"a" %a$a %i'3o".%: 3ea"a" %a$a %i'3o".
a$i, $+ Q % A $'. 'e$a"4a"a$i, $+ Q % A $'. 'e$a"4a"
A $' Q $A $' Q $
$ : %e!5e$aa" ;ol02e$ : %e!5e$aa" ;ol02e
Ke!7a, $+ Q F $'Ke!7a, $+ Q F $'
Sa30a" e!7a: *N2 J o0le J Sa30a" e!7a: *N2 J o0le J
Ke!7a 3o3al, $+ Q % $Ke!7a 3o3al, $+ Q % $
∫ =2
1
V
V
#V pW
CONTOH SOAL: (ERU/AHAN ENERGICONTOH SOAL: (ERU/AHAN ENERGI
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CONTOH SOAL: (ERU/AHAN ENERGICONTOH SOAL: (ERU/AHAN ENERGI
Si'3e2 2e2%0"6ai 2a''a, 2 Q 1 4 5e!4e!a $e"4a" e"aia"Si'3e2 2e2%0"6ai 2a''a, 2 Q 1 4 5e!4e!a $e"4a" e"aia"
ece%a3a" $a!i 1> 2?' 2e"7a$i -@ 2?' %a$a ele;a'i $a!i 1> 2 eece%a3a" $a!i 1> 2?' 2e"7a$i -@ 2?' %a$a ele;a'i $a!i 1> 2 e
> 2. Te"30a" %e!05aha" e"e!4i i"e3i $a" %o3e"'ial.> 2. Te"30a" %e!05aha" e"e!4i i"e3i $a" %o3e"'ial.(ENYELESAIAN:(ENYELESAIAN:
(e!05aha" e"e!4i i"e3i,(e!05aha" e"e!4i i"e3i, WWEE QQ 2 * 2 *&&&& 8 8 11
&&
WWEE QQ *1 4 X*-@ 2?' *1 4 X*-@ 2?'&& = *1> 2?' = *1> 2?'&& Q --P Q @,--P Q --P Q @,--P
(e!05aha" e"e!4i %o3e"'ial,(e!05aha" e"e!4i %o3e"'ial, WWEE%% QQ 2 4 *92 4 *9&& = 9 = 911
WWEE%% QQ *I 4 *,1 2?'*I 4 *,1 2?'&& *1> 2 = > 2 Q ,1 Q @,@1 *1> 2 = > 2 Q ,1 Q @,@1
Kece%a3a", Kece%a3a", 11 Q 1> 2?' $a" Q 1> 2?' $a" && Q -@ 2?'Q -@ 2?'
Ke3i"44ia"?ele;a'i, 9Ke3i"44ia"?ele;a'i, 911 Q 1> 2 $a" 9Q 1> 2 $a" 9&& Q > 2Q > 2
(e!ce%a3a" 4!a;i3a'i 502i, 4 Q ,1 2?'(e!ce%a3a" 4!a;i3a'i 502i, 4 Q ,1 2?'&&
(a$a 3e!2o$i"a2ia 3e"i, %e!05aha" e"e!4i 3o3al %a$a 'i'3e2(a$a 3e!2o$i"a2ia 3e"i, %e!05aha" e"e!4i 3o3al %a$a 'i'3e2
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(a$a 3e!2o$i"a2ia 3e"i, %e!05aha" e"e!4i 3o3al %a$a 'i'3e2(a$a 3e!2o$i"a2ia 3e"i, %e!05aha" e"e!4i 3o3al %a$a 'i'3e2
$a%a3 $ila'ifia'ia" 3e!$i!i $a!i:$a%a3 $ila'ifia'ia" 3e!$i!i $a!i:
1.1. E"e!4i i"e3i, %e"4a!0h $a!i fa3o! ece%a3a" *E"e!4i i"e3i, %e"4a!0h $a!i fa3o! ece%a3a" *WWEE ,,
&.&. E"e!4i %o3e"'ial, %e"4a!0h $a!i fa3o! e3i"44ia" *E"e!4i %o3e"'ial, %e"4a!0h $a!i fa3o! e3i"44ia" *WWEE%%,,
-.-. E"e!4i $ala2 *i"3e!"al e"e!46, fa3o! ea$aa" 'i'3e2 *E"e!4i $ala2 *i"3e!"al e"e!46, fa3o! ea$aa" 'i'3e2 *WWU.U.
(e!05aha" e"e!4i 3o3al %a$a 'i'3e2 a$alah:(e!05aha" e"e!4i 3o3al %a$a 'i'3e2 a$alah:
EE&& = E = E11 Q *EQ *E&& 8 E8 E11 *E *E%&%& 8 E8 E%1%1 *U *U&& = U = U11
**WWEE Q *Q *WWEE * *WWEE%% * *WWUU
H002 3e!2o$i"a2ia IH002 3e!2o$i"a2ia I
ia $iia $i5e!ia" 'e702lah %a"a' ecil $ %a$a '5e!ia" 'e702lah %a"a' ecil $ %a$a '0a0a30 'i'3e230 'i'3e2
*4a',*4a', 2aa2aa 4a'4a' 3e!'e503 5e!e'%a"'i $a" 2ela0a" e!7a3e!'e503 5e!e'%a"'i $a" 2ela0a" e!7a
l0a! 6a"4 ecil 'e5e'a! $+.l0a! 6a"4 ecil 'e5e'a! $+.
4a'4a'
&&11$$
$+$+
$U$U
DDi'a2%i"4 i30 %e2a"a'a" 3e!ha$a%i'a2%i"4 i30 %e2a"a'a" 3e!ha$a% 4a'4a' 704a 2e"i250la":704a 2e"i250la":
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4a'4a'
&&11$$
$+$+
$U$U
DDi'a2%i"4 i30, %e2a"a'a" 3e!ha$a%i'a2%i"4 i30, %e2a"a'a" 3e!ha$a% 4a'4a' 704a 2e"i250la": 704a 2e"i250la":
1.1. (e!05aha" e"e!4i i"e3i *(e!05aha" e"e!4i i"e3i *WWEE ,,
&.&. (e!05aha" E"e!4i %o3e"'ial *(e!05aha" E"e!4i %o3e"'ial *WWEE%%,,
-.-. (e!05aha" E"e!4i $ala2 *(e!05aha" E"e!4i $ala2 *WWU.U.
Defi"i'i h002 3e!2o$i"a2ia I: 702lah e"e!4i 6a"4Defi"i'i h002 3e!2o$i"a2ia I: 702lah e"e!4i 6a"4
3e!a"$0"4 %a'a 'i'3e2 *E Q 702lah e"e!4i %a"a' 6a"43e!a"$0"4 %a'a 'i'3e2 *E Q 702lah e"e!4i %a"a' 6a"4
$i3!a"'fe! e 'i'3e2 * = e"e!4i 6a"4 $i3!a"'fe! el0a!$i3!a"'fe! e 'i'3e2 * = e"e!4i 6a"4 $i3!a"'fe! el0a!
'i'3e2 5e!0%a e!7a *+.'i'3e2 5e!0%a e!7a *+.
Seca!a 2a3e2a3ia $a%a3 $i30li':Seca!a 2a3e2a3ia $a%a3 $i30li':
EE&& = E = E11 Q = +Q = +
**WWEE * *WWEE%% * *WWU Q = +U Q = +
ia 'i'3e2 a$alah 3e!3030%, 2aa *ia 'i'3e2 a$alah 3e!3030%, 2aa *WWEE Q @, *Q @, *WWEE%% Q @Q @
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**WWEE * *WWEE%% * *WWU Q = +U Q = +
a$i h002 3e!2o$i"a2ia I 2e"7a$i: U Q = +a$i h002 3e!2o$i"a2ia I 2e"7a$i: U Q = +
Q U + Q U + $ Q $U $+$ Q $U $+
KETENTUAN:KETENTUAN:
1.1. (a"a' * 2a'0 e 'i'3e2, 5e!3a"$a %o'i3if.(a"a' * 2a'0 e 'i'3e2, 5e!3a"$a %o'i3if.&.&. (a"a' * el0a! $a!i 'i'3e2, 5e!3a"$a "e4a3if.(a"a' * el0a! $a!i 'i'3e2, 5e!3a"$a "e4a3if.
-.-. Si'3e2 2ela0a" e!7a l0a! *+, + 5e!3a"$a %o'i3if.Si'3e2 2ela0a" e!7a l0a! *+, + 5e!3a"$a %o'i3if.
.. Si'3e2 $ie"ai e!7a l0a! *+, + 5e!3a"$a "e4a3if.Si'3e2 $ie"ai e!7a l0a! *+, + 5e!3a"$a "e4a3if.
>.>. (e!05aha" e"e!4i $ala2 *(e!05aha" e"e!4i $ala2 *WWU Q UU Q U&& = U = U11 30!0", 7ia 30!0", 7ia %a"a'%a"a'
* 2a'0 'i'3e2 $a" 2ela0a" e!7a l0a! *+.* 2a'0 'i'3e2 $a" 2ela0a" e!7a l0a! *+.
B.B. (e!05aha" e"e!4i $ala2 *(e!05aha" e"e!4i $ala2 *WWU Q UU Q U&& = U = U11 "ai, 7ia "ai, 7ia 'i'3e2'i'3e2
$ie"ai e!7a l0a! *+ $a" %a"a' * el0a! $a!i 'i'3e2.$ie"ai e!7a l0a! *+ $a" %a"a' * el0a! $a!i 'i'3e2.
CONTOH SOAL:CONTOH SOAL:
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CONTOH SOAL:
4 4a' 3e!$a%a3 $ala2 'ili"$e! 3o!a, h050"4a" a"3a!a 4 4a' 3e!$a%a3 $ala2 'ili"$e! 3o!a, h050"4a" a"3a!a
3ea"a" $a" ;ol02e a$alah: %3ea"a" $a" ;ol02e a$alah: %1,>1,> Q o"'3a". Tea"a" $a"Q o"'3a". Tea"a" $a"
;ol02e a#al - 5a! a5'ol03 $a" @,1 2;ol02e a#al - 5a! a5'ol03 $a" @,1 2--
. ol02e ahi! 2e"7a$i. ol02e ahi! 2e"7a$i@,& 2@,& 2-- $a" %e!05aha" e"e!4i $ala2,$a" %e!05aha" e"e!4i $ala2, WWU Q 8 - ?4. Te"30a"U Q 8 - ?4. Te"30a"
%a"a' 6a"4 $i3!a"'fe! e 'i'3e2.%a"a' 6a"4 $i3!a"'fe! e 'i'3e2.
11 Q @,1 2Q @,1 2-- $a" $a" && Q @,& 2Q @,& 2
--, 7a$i %!o'e', 7a$i %!o'e'
5e!la"4'0"4 e'%a"'i5e!la"4'0"4 e'%a"'i
(ENYELESAIAN:(ENYELESAIAN:
∫ =2
1
V
V
#V pW
Ke!7a 6a"4 $iha'ila":Ke!7a 6a"4 $iha'ila":WW0 Q 00 Q 0&& = 0 = 011 Q 8 -?4Q 8 -?4
++
%%1,>1,> QQ
o"'3a"o"'3a" A!ea Q e!7aA!ea Q e!7a
%%1,>1,> QQ
o"'3a"o"'3a"
%1 >1 > 3o"'3a"5,15,1 VpVp =
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%%1,>1,> Q o"'3a"Q o"'3a" 2211 V pV p =
2
5
5,15,1
2
1
12
1006,106,12,0
1,03
m
N xbar
V
V p p
==
=
=
((11 Q - 5a! Q - < 1@Q - 5a! Q - < 1@>> N?2N?2&&
((11 Q 1,@B 5a! Q 1,@B < 1@Q 1,@B 5a! Q 1,@B < 1@>> N?2N?2&&
( ) ( )k)
m
N x xW 6,1717600
15,1
2,01006,11,01032
55
==−
−−=
Ke!7a 6a"4 $ila0a" 'i'3e2 *a$ia5a3i:Ke!7a 6a"4 $ila0a" 'i'3e2 *a$ia5a3i:
A!ea Q e!7aA!ea Q e!7a
%%1,>1,> QQ
o"'3a"o"'3a"
)(1
12211 V pV p
k W −
−=
(e!'a2aa" h002 3e!2o$i"a2ia I:(e!'a2aa" h002 3e!2o$i"a2ia I:
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**WWEE * *WWEE%% * *WWU Q = +U Q = +
Ka!e"a %!o'e' 5e!la"4'0"4 $e"4a" 'i'3e2 3e!3030%, 2aa:Ka!e"a %!o'e' 5e!la"4'0"4 $e"4a" 'i'3e2 3e!3030%, 2aa:
**WWEE * *WWEE%% * *WWU Q = +U Q = + 2 *02 *0&& = 0 = 011 Q 8 + Q 8 +
(e!'a2aa" h002 3e!2o$i"a2ia I:(e!'a2aa" h002 3e!2o$i"a2ia I:
2 *02 *0&& = 0 = 011 Q 8 + Q 8 +
Q 2 *0 Q 2 *0&& = 0 = 011 + +
(a"a' 6a"4 $i3!a"'fe! e 'i'3e2:(a"a' 6a"4 $i3!a"'fe! e 'i'3e2:
Q *8 - 1P,B Q >,B Q *8 - 1P,B Q >,B (a"a' 5e!3a"$a %o'i3if, 5e!a!3i %a"a' 2a'0 e 'i'3e2.(a"a' 5e!3a"$a %o'i3if, 5e!a!3i %a"a' 2a'0 e 'i'3e2.
EKIALEN (ANAS * DENGAN KERA *+EKIALEN (ANAS * DENGAN KERA *+
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* * * *
E"e!4i 2ea"i a3a0 e!7a $a%a3 2e"4ha'ila" %a"a', 'e5a4aiE"e!4i 2ea"i a3a0 e!7a $a%a3 2e"4ha'ila" %a"a', 'e5a4ai
co"3oh $0a 50ah 5a30 $i4e'ea" $a%a3 2e"4ha'ila" a%i.co"3oh $0a 50ah 5a30 $i4e'ea" $a%a3 2e"4ha'ila" a%i.
Se5ali"6a, e"e!4i %a"a' $a%a3 2e"4ha'ila" e!7a, 'e5a4aiSe5ali"6a, e"e!4i %a"a' $a%a3 2e"4ha'ila" e!7a, 'e5a4ai
co"3oh 2e'i" 0a% $a%a3 5e!4e!a oleh %a"a' ha'il $a!i %!o'e'co"3oh 2e'i" 0a% $a%a3 5e!4e!a oleh %a"a' ha'il $a!i %!o'e'
%e25aa!a".%e25aa!a".
Sa30a" 702lah %a"a': cal a3a0 cal.Sa30a" 702lah %a"a': cal a3a0 cal.
Sa30a" e!7a a3a0 e"e!4i: 42 a3a0 N2Sa30a" e!7a a3a0 e"e!4i: 42 a3a0 N2
1 cal a$alah 702lah %a"a' 6a"4 $i5030ha" 0"301 cal a$alah 702lah %a"a' 6a"4 $i5030ha" 0"30
2e"aia" 3e2%e!a30! 1 4 ai! 'e5e'a! 12e"aia" 3e2%e!a30! 1 4 ai! 'e5e'a! 1CC
(a"a' $a" e!7a $a%a3 ei;ale" $a" $io";e!'i 'a30 'a2a(a"a' $a" e!7a $a%a3 ei;ale" $a" $io";e!'i 'a30 'a2a
lai", 6ai30:lai", 6ai30:
Q A + Q A +
Q A + Q A +
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: 702lah %a"a' *cal 6a"4 $io";e!'i 2e"7a$i e!7a.: 702lah %a"a' *cal 6a"4 $io";e!'i 2e"7a$i e!7a.
+: e!7a a3a0 e"e!4i *42 6a"4 $i$a%a3 $a!i %a"a' .+: e!7a a3a0 e"e!4i *42 6a"4 $i$a%a3 $a!i %a"a' .A: oefi'ie" %!o%o!'io"alA: oefi'ie" %!o%o!'io"al
H050"4a" a"3a!a %a"a' $e"4a" e"e!4i 2ea"i $i'e503H050"4a" a"3a!a %a"a' $e"4a" e"e!4i 2ea"i $i'e503
HUKUM KONSERASI ENERGI, 2e"6a3aa" 5ah#a e"e!4iHUKUM KONSERASI ENERGI, 2e"6a3aa" 5ah#a e"e!4i
3i$a $a%a3 $ihila"4a", 3e3a%i ha"6a $a%a3 $io";e!'i e3i$a $a%a3 $ihila"4a", 3e3a%i ha"6a $a%a3 $io";e!'i e$ala2 5e"30 e"e!4i lai".$ala2 5e"30 e"e!4i lai".
W
* A =
Q A + Q A +
Da!i e'%e!i2e":Da!i e'%e!i2e":
==
kgm
k!al
W
* A
427
1
a$i: 1 cal Q &P 42a$i: 1 cal Q &P 42
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a$i: 1 cal Q &P 42a$i: 1 cal &P 42
Seca!a i$eal, 'e3ia% e!7a 2ea"i 'e5e'a! 1 42 2e"4ha'ila"Seca!a i$eal, 'e3ia% e!7a 2ea"i 'e5e'a! 1 42 2e"4ha'ila"%a"a' 'e5e'a! 1?&P cal $a" 'e5ali"6a 'e3ia% 1 cal %a"a'%a"a' 'e5e'a! 1?&P cal $a" 'e5ali"6a 'e3ia% 1 cal %a"a'
$a%a3 2e"4ha'ila" e!7a 2ea"i 'e5e'a! &P 42.$a%a3 2e"4ha'ila" e!7a 2ea"i 'e5e'a! &P 42.
(a$a i"$0'3!i, 'e!i"4 $i40"aa" 'a30a" TENAGA KUDA(a$a i"$0'3!i, 'e!i"4 $i40"aa" 'a30a" TENAGA KUDA
*% a3a0 *HORSE (O+ER*% a3a0 *HORSE (O+ER h%h%
1 h% Q P> 42?'1 h% Q P> 42?'
1 h% 8 h! Q P> *B@ *B@ Q &P@.@@@ 421 h% 8 h! Q P> *B@ *B@ Q &P@.@@@ 42
h!: ho0! a3a0 7a2.h!: ho0! a3a0 7a2.
k!al hr hp 632427
000.2701 ==−
Se$a"4a" 'a30a" e"e!4i li'3!i *#h, 6ai30 $a6a 'e3ia% #Se$a"4a" 'a30a" e"e!4i li'3!i *#h, 6ai30 $a6a 'e3ia% #
-
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Se$a"4a" 'a30a" e"e!4i li'3!i *#h, 6ai30 $a6a 'e3ia% #Se$a"4a" 'a30a" e"e!4i li'3!i *#h, 6ai30 $a6a 'e3ia% #
$ala2 #a30 1 7a2.$ala2 #a30 1 7a2.
1 N2?' Q 1 #a331 N2?' Q 1 #a33
1 h% Q P> 42?' Q P> *,1 2?'1 h% Q P> 42?' Q P> *,1 2?' Q P-B #a33 Q P-B #a33
1 h% Q @,1 h% Q @,P-B #P-B #
1 # Q 1,-B h% Q 1@& 42?'1 # Q 1,-B h% Q 1@& 42?'
a$i , 1 #h Q 1@& < B@ < B@a$i , 1 #h Q 1@& < B@ < B@
Q -BP.&@@ 42 Q 1,-B h% 8 h!.Q -BP.&@@ 42 Q 1,-B h% 8 h!.
k!al k+h 860427
200.3671 ==
KONERSI DARI HORSE(O+ER MENADI KILO+ATTKONERSI DARI HORSE(O+ER MENADI KILO+ATT
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Da6a 0$a a3a0 3e"a4a 0$a a$alah 0"i3 %e"400!a" $a6aDa6a 0$a a3a0 3e"a4a 0$a a$alah 0"i3 %e"400!a" $a6a
6a"4 'e3a!a $e"4a" P-B hi"44a PB #a33.6a"4 'e3a!a $e"4a" P-B hi"44a PB #a33.
Defi"i'i $a6a 0$a 5e!;a!ia'i 3e!4a"30"4 a%lia'i"6a:Defi"i'i $a6a 0$a 5e!;a!ia'i 3e!4a"30"4 a%lia'i"6a:
Da6a 0$a 2ea"i'?hi$!oli *Da6a 0$a 2ea"i'?hi$!oli *mechanical horsepower mechanical horsepower
a$alah "ilai 6a"4 5e'a!"6a 'e3a!a >>@ ai8%o0"$ %e! $e3ia$alah "ilai 6a"4 5e'a!"6a 'e3a!a >>@ ai8%o0"$ %e! $e3i
*f38l5?' a3a0 'e3a!a $e"4a" PB #a33.*f38l5?' a3a0 'e3a!a $e"4a" PB #a33.
U"30 2o3o! li'3!i, 'a30 $a6a 0$a 'e3a!a $e"4a" PB #a33.U"30 2o3o! li'3!i, 'a30 $a6a 0$a 'e3a!a $e"4a" PB #a33.
A"4a 6a"4 3e!30li' %a$a la5el 2e!0%aa" $a6a o03%03,A"4a 6a"4 3e!30li' %a$a la5el 2e!0%aa" $a6a o03%03,
50a" $a6a i"%03.50a" $a6a i"%03.
Da6a 0$a 2e3!i *Da6a 0$a 2e3!i *metric horsepower metric horsepower a$alah "ilai 6a"4 a$alah "ilai 6a"45e'a!"6a 'e3a!a $e"4a" P> *42?', a3a0 'e3a!a $e"4a"5e'a!"6a 'e3a!a $e"4a" P> *42?', a3a0 'e3a!a $e"4a"
P-B #a33.P-B #a33.
CONTOH SOAL:CONTOH SOAL:
1 D l 7i 5 i $ P@ l?1 D l 7i 5 i $ P@ l?
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(ENYELESAIAN:(ENYELESAIAN:Me'i" 0a%Me'i" 0a%
1>@ h%1>@ h%
1.@@ 4?h!1.@@ 4?h!
02lah %a"a' 6a"4 $io";e!'i02lah %a"a' 6a"4 $io";e!'i
2e"7a$i e!7a 'e3ia% 7a2:2e"7a$i e!7a 'e3ia% 7a2:
Q P@ *1.@@ Q .@@@ cal Q P@ *1.@@ Q .@@@ cal
Ke!7a 2e'i" 0a% $ala2 #a30 6a"4 'a2a: + Q 1>@ h% 8 h!Ke!7a 2e'i" 0a% $ala2 #a30 6a"4 'a2a: + Q 1>@ h% 8 h!
+ Q 1>@ < P> < B@ < B@ Q @.>@@.@@@ 42+ Q 1>@ < P> < B@ < B@ Q @.>@@.@@@ 42
1. Dala2 07i co5a 2e'i", 0a% 2e"4a"$0"4 %a"a' P@ cal?4.1. Dala2 07i co5a 2e'i", 0a% 2e"4a"$0"4 %a"a' P@ cal?4.
Me'i" 0a% 2e"4ha'ila" e!7a 1>@ h% $a" 2e"4o"'02'iMe'i" 0a% 2e"4ha'ila" e!7a 1>@ h% $a" 2e"4o"'02'i
0a% 'e5e'a! 1.@@ 4?h!. Te"30a" ei;ale" %a"a' $a" e!7a0a% 'e5e'a! 1.@@ 4?h!. Te"30a" ei;ale" %a"a' $a" e!7a
$ala2 07i co5a 2e'i" 0a% 3e!'e503.$ala2 07i co5a 2e'i" 0a% 3e!'e503.
Ei;ale" %a"a' $e"4a" e!7a:Ei;ale" %a"a' $e"4a" e!7a:k!al kgm
*W
A413
000.98000.500.401 ===
Ha'il"6a: 1 cal ha"6a 2e"4ha'ila" e!7a 1- 42,Ha'il"6a: 1 cal ha"6a 2e"4ha'ila" e!7a 1- 42,
a!e"a 3e!$a%a3 %a"a' 6a"4 hila"4 oleh !a$ia'i.a!e"a 3e!$a%a3 %a"a' 6a"4 hila"4 oleh !a$ia'i.
&. (e25a"4i3 3e"a4a li'3!i 2e"4o"'02'i 5aha" 5aa!&. (e25a"4i3 3e"a4a li'3!i 2e"4o"'02'i 5aha" 5aa!
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/a305a!a &@ 3o" Q &@.@@@ 4/a305a!a &@ 3o" Q &@.@@@ 4
(ENYELESAIAN:(ENYELESAIAN:
02lah %a"a' 6a"4 $io";e!'i 2e"7a$i e"e!4i li'3!i02lah %a"a' 6a"4 $io";e!'i 2e"7a$i e"e!4i li'3!i
'e3ia% B 7a2 $a" efi'ie"'i &@V:'e3ia% B 7a2 $a" efi'ie"'i &@V:
Q &@.@@@ < P@@@ < @,& Q &.@@@.@@@ cal Q &@.@@@ < P@@@ < @,& Q &.@@@.@@@ cal
kWh*
W 560.32
860
000.000.28
860
=== 1 +h Q B@ cal1 +h Q B@ cal
5a305a!a &@ 3o" 'e3ia% B 7a2, 1 4 5a305a!a 2e"4ha'ila"5a305a!a &@ 3o" 'e3ia% B 7a2, 1 4 5a305a!a 2e"4ha'ila"
%a"a' P.@@@ cal. Te"30a" $a6a li'3!i 6a"4 $iha'ila" 7ia%a"a' P.@@@ cal. Te"30a" $a6a li'3!i 6a"4 $iha'ila" 7ia
ha"6a &@ V %a"a' 6a"4 $io";e!'i 2e"7a$i e"e!4i li'3!i.ha"6a &@ V %a"a' 6a"4 $io";e!'i 2e"7a$i e"e!4i li'3!i.
Ra3a8!a3a e"e!4i li'3!i 6a"4 $i5a"4i3a" 'e3ia% 7a2:Ra3a8!a3a e"e!4i li'3!i 6a"4 $i5a"4i3a" 'e3ia% 7a2:
kW h
k+h N 420.5
6
560.32==
KERA?ENERGI *+KERA?ENERGI *+
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$$
((
11 &&
$'$'
11
&&
FF
FF
Dia4!a2 % 8 ;, e!7a 4a'Dia4!a2 % 8 ;, e!7a 4a'
$ala2 Sili"$e!$ala2 Sili"$e!
Ke!7a a$alah %e!alia" a"3a!a 4a6a $e"4a" 7a!a li"3a'a""6a.Ke!7a a$alah %e!alia" a"3a!a 4a6a $e"4a" 7a!a li"3a'a""6a.
F: 4a6a *NJ l5, $': li"3a'a" *2J f3 F: 4a6a *NJ l5, $': li"3a'a" *2J f3
F Q A %F Q A % %: 3ea"a" %a$a %i'3o".%: 3ea"a" %a$a %i'3o".
a$i, $+ Q % A $'. 'e$a"4a"a$i, $+ Q % A $'. 'e$a"4a"A $' Q $A $' Q $
$ : %e!5e$aa" ;ol02e$ : %e!5e$aa" ;ol02e
Ke!7a, $+ Q F $'Ke!7a, $+ Q F $'
Sa30a" e!7a: *N2 J o0leSa30a" e!7a: *N2 J o0le
Ke!7a 3o3al, $+ Q % $Ke!7a 3o3al, $+ Q % $
Ke!7a 'e3ia% 'a30a" 2a''a, $# Q % $;Ke!7a 'e3ia% 'a30a" 2a''a, $# Q % $; ?4 J ?4?4 J ?4
ENERGI?KERA TERGANTUNG (ADA ENIS (ROSESENERGI?KERA TERGANTUNG (ADA ENIS (ROSES
-
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(a$a $ia4!a2 % = ;, 'i'3e2 *4a' 5e!05ah(a$a $ia4!a2 % = ;, 'i'3e2 *4a' 5e!05ah
$a!i ea$aa" a e ea$aa" 5 2elal0i & 7e"i'$a!i ea$aa" a e ea$aa" 5 2elal0i & 7e"i'
%!o'e' 5e!5e$a, 6ai30 %!o'e' I $a" II. Ke!7a%!o'e' 5e!5e$a, 6ai30 %!o'e' I $a" II. Ke!7a
6a"4 $iha'ila" a3a0 $i3e!i2a 'i'3e2 *4a'6a"4 $iha'ila" a3a0 $i3e!i2a 'i'3e2 *4a'
a$alah l0a'a" a"3a!a li"3a'a" %!o'e'a$alah l0a'a" a"3a!a li"3a'a" %!o'e'
3e!ha$a% '0250 ;.3e!ha$a% '0250 ;.
(a$a $ia4!a2 % = ;, 'i'3e2 *4a' 5e!05ah $a!i ea$aa" a e(a$a $ia4!a2 % = ;, 'i'3e2 *4a' 5e!05ah $a!i ea$aa" a e
ea$aa" 5, %!o'e' I 2e2%0"6ai l0a'a": a = I = 5 = & = 1 = aea$aa" 5, %!o'e' I 2e2%0"6ai l0a'a": a = I = 5 = & = 1 = a
le5ih 5e'a! $a!i %!o'e' II 6a"4 2e2%0"6ai l0a'a": a = II =le5ih 5e'a! $a!i %!o'e' II 6a"4 2e2%0"6ai l0a'a": a = II =
5 = & = 1 = a. a$i e!7a 6a"4 $iha'ila" a3a0 $i3e!i2a5 = & = 1 = a. a$i e!7a 6a"4 $iha'ila" a3a0 $i3e!i2a'i'3e2 *4a' 'a"4a3 3e!4a"30"4 %a$a 7e"i' %!o'e'"6a.'i'3e2 *4a' 'a"4a3 3e!4a"30"4 %a$a 7e"i' %!o'e'"6a.
ENERGI?KERA TERGANTUNG (ADA ENIS (ROSESENERGI?KERA TERGANTUNG (ADA ENIS (ROSES
%%
;;
IIII 55
aa II
&&11
KERA (ADA (ERU/AHAN (ROSES GASKERA (ADA (ERU/AHAN (ROSES GAS
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1. Ke!7a %!o'e' 3e2%e!a30! o"'3a" *1. Ke!7a %!o'e' 3e2%e!a30! o"'3a" *isothermalisothermal
Si'3e2 5e!05ah $a!i ea$aa" 1 e ea$aa" &Si'3e2 5e!05ah $a!i ea$aa" 1 e ea$aa" &%a$a%a$a 3e2%e!a30! o"'3a"3e2%e!a30! o"'3a",, TT11 Q TQ T&&
(!o'e' i'o3e!2i', %(!o'e' i'o3e!2i', %11 ;;11 Q %Q %&& ;;&& 1
2
2
1
v
v
p
p=→
(e!'a2aa" 4a' i$eal 'e3ia% 'a30a" 2a''a:(e!'a2aa" 4a' i$eal 'e3ia% 'a30a" 2a''a:
v
& % p =→
% ; Q R T% ; Q R T
((
;;
((11
((&&
;;&&;;11
11
&&
T Q CT Q C
Ke!7a 'i'3e2 %e! 'a30a" 2a''a: $# Q % $;Ke!7a 'i'3e2 %e! 'a30a" 2a''a: $# Q % $;
1
2
ln
2
1v
v
& %v
#v
& %+
v
v == ∫
((a$i e!7a 'i'3e2 %e! 'a30a" 2a''a:a$i e!7a 'i'3e2 %e! 'a30a" 2a''a:
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92
2
1ln p
p& %+ =→
1
2
112
1
11 lnln v
v
v p p
p
v p+ ==⇒
% ; Q R T
;;
((11
((&&
;;&&;;11
11
&&
T Q CT Q C
a$i