MAT MATA KULI ULIAH
: TERM ERMODI ODINAMI NAMIKA KA KEB KEBUMI UMIAN
DOSEN
: Dr. Imran Hilman
TUGAS KE -
:2
KELOMPOK
:1
Soal: Termodinamika modinamika.. Halaman 49-50, (Zeman!" Mar! . #$ Di%%man Ri&'ar( H. 1)*+. Kalor dan Ter
Ban(,n. ITB
2./ 2./
Per Peram amaan aan !ea(a !ea(aan an 'am0i 'am0ira ran n a a n"a%a n"a%a 0a(a %e!an %e!anan an e(an e(an mem0,n" mem0,n"ai ai en%, en%,! ! P 3
Rθ 415B6$ (enan R %e%a0an (an B 7,ni (ari θ a8a. T,n8,!!an a'9a :
a
2. 2.
β=
θ .
κ 3
1
p .
( )
dB dθ v +2 B
v +B + θ
1
1 1 + BR θ / Pv 2
l;a l;am m "an "an !em !em,a ,aia ian n ;l, ;l,mn mn"a "a <$= <$= > 1= 1=-< K -1 (an !e%ermam0a%an i;%ermn"a 1$2 > 1=-11 Pa a(a 0a(a %e!anan 1 > 1=< Pa (an %em0era%,r 2==?. l;am ini (ilin!,ni e&ara 0a ;le' inar %eal "an !em,aian (an !e%ermam0a%ann"a (a0a% (iaai!an.
a era0a!a' era0a!a' %e!anan %e!anan a!'ir 8i!a %em0era%,r %em0era%,r (inai!!an (inai!!an /2 /2=? @ . 8i!a len!,nan 0en,%,0 (a0a% mena'an %e!anan ma!im,m 1$2 > 1=* Pa$ era0a!a' %em0era%,r %er%ini i%em i%,@ 2.< 2.<
S,a% S,a%, , al;! al;! l;am l;am "an "an am amaa e0er e0er%i %i (ala (alam m ;al ;al 2. 0a(a 0a(a %e!a %e!ana nan n 1 > 1=< Pa$ ;l,m < li%er$ (an %em0era%,r 2==? menalami !enai!an %em0era%,r 12 (era8a% (an 0er%ama'an ;l,m =$< &m/. Hi%,nla' %e!anan a!'irn"a.
2.+ 2.+
a Un!a0 Un!a0!an !an !em,a !em,aia ian n ;l,m ;l,m (an !e%e !e%erm rmam am0a% 0a%an an i;% i;%erm erm$$ n"a% n"a%a!a a!an n (alam (alam !era0a !era0a%a %an n
ρ (an %,r,nan 0arialn"a.
aar!an 0eramaan
dV βd θ V 3
2.C
κ dP.
Kem,aian %ermal (an !e%ermam0a%an &airan ;!ien (ieri!an (alam %ael eri!,% ini. Gamar!an ra7i! "an mem0erli'a%!an aaimana
4 ∂ P / ∂θ ¿ v
eran%,n 0a(a
%em0era%,r.
θ , K
+=
+<
C=
C<
*=
*<
)=
β $1=-/$
/$*
/$+=
/$C<
/$)=
$=C
$//
$+=
K -1 κ $ 1=-)
=$)<
1$=+
1$2=
1$/<
1$<
1$C*
2$=+
Pa-1
2.*
Kem,aian (an !e%ermam0a%an air (ieri!an (alam %ael eri!,% ini. Gamarla' ra7i! "an men,n8,!!an aaimana 4 ∂ P / ∂θ ¿ v
eran%,n 0a(a %em0era%,r. i!a air
(i0er%a'an!an 0a(a ;l,m %e%a0 (an %em0era%,rn"a %er, (inai!!an$ a0a!a' %e!anann"a %er, er%ama' %an0a a%a @ %$ =?
2.)
β $ 1=-/$ K -1
= =$=C
<= =$+
1== =$C<
1<= 1$=2
2== 1$/<
2<= 1$*=
/== 2$)=
κ $ 1=-) Pa-1
=$<1
=$
=$)
=$+2
=$*<
1$<=
/$=<
Pa(a %em0era%,r !ri%i 4
∂ P / ∂θ ¿ T 3 =. T,n8,!!an a'9a 0a(a %i%i! !ri%i$ !em,aian
;l,m (an !e%ermam0a%an men8a(i %a! er'ina.
Jawaban:
P 3 R θ 4 1 5
2./
B θ a8a. V $ B a(ala' ,ni
B R θ ( 1 + ) V V = P v + B ) V P
R θ (
¿
V =
Men&ari
R θV + R θB VP
FFFFF.4i
∂θ ∂ V /¿
¿
∂V ∂ ∂RθB / VP = R θV / VP + ∂θ ∂ θ ∂θ
[
∂ Rθ / p ∂ Rθ / p B ∂ B / V Rθ + . + . 3 ∂θ ∂θ V ∂θ P R P
¿ +
[
R B 1 Rθ ∂ B . + . + P V V P ∂ θ
[
1 ¿ R + R + . Rθ + ∂ B
P
[
P V P
∂θ
]
R 1 Rθ ∂ B + . + =¿ P V P ∂ θ
[
]
R B θ ∂ B =¿ 1 + + . P V V ∂θ
]
]
]
β =
1 ∂ B
V ∂ θ $ e'ina: 1
β =
([
])
([
])
Rθ + RθB R B θ ∂ B 1 + + . VP P V V ∂ θ
VP R B θ ∂ B 1 + + . β = V V ∂ θ R θ ( V + B ) P
β =
β =
[
V B θ ∂ B 1 + + . θ ( V + B ) V V ∂θ
1
θ
Un%,!
V + B + θ + V + B
∂B ∂θ
∂B ∂θ
]
[
B −V −1 − k = P ( V + B ) V
]
V + B k = P ( V + B ) 1
k = P
2.
Di!:
β =¿
5,0 x 10−5 K −1
κ =1,2 x 10−11 Pa
Pi 3 1 > 1=< Pa
θ 3 2==? Di%: a P7 8i!a
θ
a9a:
θ (inai!!an 8a(i /2=?
%er%ini 8i!a P ma! 1$2 > 1=* Pa
β θf −θi ¿ a P7 Pi 3 κ 4 5,0 x 10 −5 K −1 . ( 305−293 ) K
3
κ =1,2 x 10−11 Pa
3 + > 1=-61$2 > 1=-11 3 < > 1=C Pa P7 3 < > 1=C Pa 5 1 > 1=< Pa 3 <== > 1=< Pa 5 1 > 1=< Pa 3 <=1 > 1=< Pa 3 <$=1 > 1=C Pa a(i$ %e!anan a!'irn"a a(ala' <$=1 > 1=C Pa
.
β P7 Pi 3 κ 4 θf −θi ¿
1$2 > 1=* 1 > 1=<
3 <>1=-< 6 1$2 > 1=-11 . Δ θ
12== > 1=< 1 > 1=< 3 <>1=-< 6 1$2 > 1=-11 . Δ θ
11)) > 1=<
3 $1C > 1=+ .
Δθ
Δ θ 3 11)) > 1=< 6 1$C > 1=< Δ θ 3 2*$C<=?
∂ P=
2.<
∂ P=
β 1 ∂ θ− . ∂ V κ κ . V
5 × 10
5
−
−11 .12
1,2 × 10 −5
∂ P=
5 × 10 .12 1,2 × 10
−11
2.+
5 × 10
−
−11 =
1,2 × 10
−4
11
1,2 × 10 .5
.5 × 10
−4
−4
∂ P=
1
1 × 10
− 11
1,2 × 10
5 1,2
−7
7
× 10 = 4,16 × 10
4a
4 Un%,! men&ari
dV = β ( θ V
κ dP (a0a% (i0er;le' (ari 0eramaan 0er,a'an
%e!anan in7ini%eimal "an (i,n!a0!an (alam !,an%i%a 7ii "ai%,:
( )
dP =
∂P ∂θ
θ 5 (
( )
θ 5 (
( )
∂P ∂V
(
(
Se'ina:
( )
dP =
∂P ∂θ
β (P 3 κ ( θ -
∂P ∂V
1
kV (
Ki%a !ali!an !e(,a r,a (enan ! aar ! 0a(a r,a eela' !anan ia 'ilan:
(P k 3
(
β 1 d θ − dV k κ kV
k 3
(
1
V
(P k 3
(
dV V
(P
(P 3
−dV V
(
)
β d θ −
β d θ −
dV
)
)
)
β dV d θ – k V
= k dP− β dθ
Ki%a !ali!an (enan nea%ie 4- (i !e(,a r,a:
dV =−k dP + β dθ V
dV = β dθ −k dP V
2.C
β 3.48 = 6 K 0.95 = 3,66 x 10 β 3.60 = 6 K 1.06 = 3,40 x 10 β 3.75 = 6 K 1.20 = 3,13 x 10 β 3.90 = 6 K 1.35 = 2,89 x 10
β κ
θ (K)
x 106 3.66
60
3.4
65
3.14
70
2.89
75
2.64
80
2.44
85
2.23
90
β 4.07 = 6 K 1.54 = 2,64 x 10 β 4.33 = 6 K 1.78 = 2,44 x 10 β 4.60 = 6 K 2.06 = 2,23 x 10
Grafik (/ ) bergantung pada temperatur 4
3.66
3.4
3.14
2.89
3
β/k x 106
2.64
2.44
2.23
2
1
0 55
60
65
70
75
80
85
(K)
β κ
2.*
β −0.07 = K 0.51 = -0,14
θ (oC)
x 106 -0.14
0
1.04
50
1.53
100
1.64
150
1.59
200
1.2
250
0 95
300
90
95
β 0.46 = K 0.44 = 1,04 β 0.75 = K 0.49 = 1,53 β 1.02 = K 0.62 = 1,64 β 1.35 = K 0.85 = 1,59 β 1.80 = K 1.50 = 1,2 β 2.90 = K 3.05
= 0,95
Grafik (/ ) bergantung pada temperatur 2 1.53
1.64 1.59
1.5
1.2
1.04
0.95
1
β/k x 106
0.5 -0.14 0 0
50
100
150
200
250
-0.5
(oC)
2.)
( ) δP δV
T
3=
Ki%a (a0a% menin8a,n"a (ari 0eramaan:
300
350
dV V 3 ( (P
Ini ar%in"a ear nilai
Karena
( ) δP δV
( ) δP δV
3
T
dV V .
dV V 3 ( (P$ ma!a
T
3 ( (P 3 =. Denan (emi!ian ear nilai ( 3 (P.
Se&ara ma%ema%i (a0a% (i,!%i!an eaai eri!,%:
( ) δP δV
( ) δP δV
( ) δP δV
T
3 ( ( P
∞
∫ β dθ
∞
3
T
3 4 ∞ − a ¿ – κ ( ∞ −b )
a
∫ κ dP
T
b
Se'ina ear nilai 4 ∞ - a 3 4 ∞ −b ¿ .
