Problemas Unidad 4
August 9, 2022 | Author: Anonymous | Category: N/A
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GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW
Z^INOCEHW SDA@H@ 0= Z^IZAC@H@CW \IOSEÁP^AGHW @C OIW LOSA@IW 8. Oh prcsa÷d `c vhpir `co nriei oåqua oåqua`i `i h 1.7ºG cs 8:: Pirr. Wa co ghoir `c vhpirazhga÷d cs `c 7:18: M/eio, ghogýocsc co pudti direho `c cnuooaga÷d `co nriei.
@HPIW= P 5 1.7ºG 5 >6>.03 K
Z* 5 8:: 8:: Pirr
F\ 5 7:18: M/eio ˌ
WIOSGA×D= Gidsa`crhd`i Gidsa `crhd`i quc c o
F\ cs gidsthdtc, cs `cgar, quc di `cpcd`c `c P y y quc cs hpoaghnoc oh cguhgåid `c ˌ
Gohusaus-Gohpcyrid, Gohus aus-Gohpcyrid, tcdceis=
od Z* 5 ∞
F\ ˌ
^P
+ G 5 ∞
F\
^
ˌ
P
+ G
`id`c= M F\ 7:18: eio 5 5 7282.6>373K ˌ
M 6.780 eioK
^
H`ceès, oh gidsthdtc G oh pi`ceis ghoguohr h phrtar `co vhoir gidiga`i `c prcsa÷d `c vhpir Z * h udh tcepcrhturh `h`h P , giei sc ad`agh ad`agh h gidtaduhga÷ gidtaduhga÷d= d=
G
5 od Z * +
F\ ˌ
P
^
5 od (8:: ) +
G 5 5
7282.6>373K >6>.03K
82.2373 + 82.2
^
+ G
y
G 5 odZ>
F + \ ˌ
P >
^
(>)
Abuhohd`i ohs cguhgaidcs (8) y (>), rcsuoth=
E. G. OSAW DACPI OCESW
LAX-SEWDF
Zèbadh > `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW
odZ8
odZ8
F\
^
ˌ
+
P8
F ∞ odZ> 5 \ Z8
Z>
od
Z8
Z>
5
^
ˌ
P >
F\
^
ˌ
P 8
F\ 8 8 ∞ ^ P> P8 ˌ
ˌ
ˌ
^
6.780 ( 5
F\
F P ∞ P 5 \ 8 > ^ P8 P>
F\
ˌ
∞
P>
od
^
ˌ
^P P Z F\ 5 8 > od 8 P8 ∞ P> Z>
5 odZ> +
P8 P >
5
P8 ∞ P>
M eioK
od
Z8
Z>
)(836.83K )(>18.:3K ) od 8::Pirr
836.83K ∞ >18.:3K
0::Pirr
M
ˌ
eio F\ 5 7118.62677
H`ceès= M F\ 7118.62677 eio 5 5 06:.87 06:.8717> 17> K M ˌ
6.780 eioK
^
G
5 odZ8 +
F\
^
ˌ
P8
5 odZ> +
F\ ˌ
^
P >
Zir oi quc, co vhoir `c G sc sc puc`c ghoguohr gid nhsc h ois vhoircs gidiga`is `c Z * y P girrcspid`acdtcs girrcspid`acdtcs h ohs gid`agaidcs adagahocs adagahocs i ladhocs=
G 5 odZ8
F + \ ˌ
P8
^
5 od(8:: ) +
06:.8717> K 836.83K
5 2. P ( K )
+ 2. K n P 5 G ∞ od Z 5 2.6 0:2.>6K 5 0:2
P 5 Pn 5 870.87 870.87 G 0. Ohs prcsaidcs `c vhpir `co si`a si`ai i oåqua`i si sid= d= P (ºG)
071
301
2:8
Z* (Pirr)
8
8:
8::
@ctcreådcsc co pudti direho `c cnuooaga÷d, co ghoir `c vhpirazhga÷d y oh cdtripåh `c vhpirazhga÷d cd co pudti direho `c cnuooaga÷d `co si`ai oåqua`i.
WIOSGA×D= Gid nhsc h oh cguhga÷d `c Gohusaus Gohpcyrid, tcdceis quc udh rcprcscdthga÷d `c odZ * vs 8/P(K) dis `cncråh `hr udh oådch rcgth, cd ghsi `c quc csth cguhga÷d rcsuotc hpoaghnoc phrh co si`ai oåqua`i=
odZ* 5 ∞
F\ ˌ
P
^
od Z* 5 G ∞
+ G
F\ 8 ˌ
^ P
Zir oi thdti, sc prigc`crè h ud hmustc `c ois `htis cxpcraecdthocs scbýd oh rcprcscdthga÷d ad`agh`h= P (K)
28>.83
6>>.83
120.83
Z (Pirr)
8
8:
8::
E. G. OSAW DACPI OCESW
LAX-SEWDF
Zèbadh 3 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW Ois rcsuoth`is intcda`is sid ois sabuacdtcs=
5 82.8>817.281.2810/P + 82.8>< ^¾ 5 8
0.: 7.3 7.: Z
>.3
d o
>.: 8.3 8.: :.3 :.: :.::8
:.::88
:.::8>
:.::87
:.::80
:.::83
8/P (K) Zir oi thdti, co pudti direho `c cnuooaga÷d `co si`ai oåqua`i scråh= :
P n
5
F\ ^ 8>817.2 .8> 5 881.7ºG 5 71>.03 K
Z>
P 5 3>.3.23 K
Z * 5 8 Pirr
*
5 0: Pirr
WIOSGA×D= h) Zraecrhecdtc, co
Fvhp `co oåqua`i oi ghoguohrceis gid nhsc h oh cguhga÷d `c Gohusaus Gohpcyrid= ˌ
F\ ˌ
^
^P P Z F\ 5 8 > od 8 P8 ∞ P> Z> ˌ
P8 P>
PP Z od 5 8 > od > 5 P8 ∞ P> Z> P> ∞ P8 Z8
6.780 ( 5
Z8
M eioK
) (736.13K ) ( 71>.03K ) od 8:Pirr
736.13K ∞ 71>.03K
0:Pirr
ˌ
M eio F\ 5 060
^
Zèbadh 2 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW
G 5 odZ8
F + \ ˌ
^
P8
5 od(8: ) +
36>1.00K 736.13K
5 86.30>1>:
Gid oi guho, oh cguhga÷d quc rcohgaidh h oh prcsa÷d `co dhlthocdi gid oh tcepcrhturh scråh=
36>1.00 od Z * (Pirr ) 5 ∞
+ 86.30>1>
P ( K )
Zir oi quc, oh tcepcrhturh direho `c cnuooaga÷d cs= :
P n
5
F\ ^ 36>1.00 K 5 5 06 061. 1.0 02< 21> ∞ od ( 21>
737.83 K
Z* 5 2.< ..3.23 K
Z8
P> 5 6:.:ºG 5 737.83 K
Z>
*
5 8 Pirr 5 2. Z8 od 5 ^ P8 ∞ P> Z>
Fs ˌ
^P P Z Fs 5 8 > od 8 P8 ∞ P> Z> ˌ
6.780 ( 5
M eioK
) (7>3.23K ) (737.83K ) od
7>3.23 K ∞ 737.83 K
8Pirr
2.
P8
5 o d (8 ) +
P >
6302.3718:K 7>3.23K
^
5 >7137130 >0: ::6 ei 060 0 >>>< .>71 > 713 3>< >8.: eeFb h 3:ºG ˌ
@HPIW= *
P8 5 0:ºG 5 787.83 K
Z8
P> 5 2:ºG 5 707.83 K
Z>
*
5 873.77 eeFb 5 30>.3: eeFb
WIOSGA×D= Zraecrhecdtc, co
Fv `co oåqua`i oi ghoguohrceis gid nhsc h oh cguhga÷d `c Gohusaus Gohpcyrid= ˌ
^P P Z F\ 5 8 > od 8 P8 ∞ P> Z> ˌ
E. G. OSAW DACPI OCESW
( 6.780 5
M eioK
) ( 787.83K ) (707.83K ) od 873.77 eeFb
787.83K ∞ 707.83 K
LAX-SEWDF
30>.3: eeFb
Zèbadh 1 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW M F\ 5 08706.27677 eio ˌ
H`ceès=
odZ* 5 ∞
F\ ˌ
+G 5 ∞
F\ ˌ
^P
Zir oi thdti=
F\ ˌ
^
+ G
P
M 08706.27677 eio
5
^
M 6.780 eioK
5 0127 0127.76
Gid oi guho, oh cguhga÷d quc rcohgaidh h oh prcsa÷d `co cthdio gid oh tcepcrhturh cs=
od Z * ( eeFb ) 5 ∞ 0127.76:.2613> P ( K ) Zir oi quc phrh P 5 5 3:ºG 5 7>7.83 K, oh prcsa÷d `c vhpir `co cthdio cs=
(
Z * eeFb
K + >:.2613> ) 5 cx p ∞ 0127.767.83 K
Z* 5 >> >>8. 8.>> >>< < eeFb
2. Co ghoir `c vhpirazhga÷d `co átcr ctåoagi, G0F8:I (E 5 20.8> b/eio), cs 67.1 gho/b, cd thdti quc q uc su prcsa÷d `c vhpir h 7:ºG vhoc 5 86. 5 P ∞ P od Z >
od
5
8
Z> `co átcr ctåoagi cs=
Cdtidgcs, phrh P > 5 :ºG 5 >27.83 K, oh prcsa÷d `c vhpir
Z>
8
F\ P> ∞ P8 ˌ
Z8
^
P8 P>
F\ P> ∞ P8 5 cxp Z8 ^ P P 8 >
Z>
ˌ
Z>
Z>
F\ P> ∞ P 8 5 Z8 cxp ^ P P 8 > ˌ
>27. >27.8 83 K ∞ 7:7. 7.83 83 K 5 ( 1.2 7.8 8 3 K K ( ) ( ) Z> 5 >:6.>1>3 eeFb
6. Oh prcsa÷d `c vhpir `co goiri e ecthdi, cthdi, GF7Go (E 5 3:.01 b/eio), cdtrc -02 y -8:ºG sc puc`c rcprcscdthr pir oh cguhga÷d=
(
oib8: Z * eeFb
+ 2.068 ) 5 ∞ 8801 P
¹Guèo scrè co ghoir `c vhpirazhga÷d `c cstc oåqua`i cd ghoiråhs pir brhei9
^. 8:0.8 gho/b @HPIW= E 5 881.76 b/eio
WIOSGA×D= Oh cguhga÷d quc sc ad`agh=
(
oib8: Z * eeFb
+ 2.068 ) 5 ∞ 8801 P
cs saeaohr h oh cguhga÷d `c Gohusaus Gohpcyrid, oh `alcrcdgah cs co tapi `c oibhratei cepoch`i, giei sc ad`agh h gidtaduhga÷d= ad`agh od Z*
5∞
F\ ˌ
^P
+G 5 ∞
F\ ˌ
P
^
+ G
Zir itrh phrtc, tcdceis quc= oibh n 5
od n odh
Cdtidgcs, gid nhsc h oi hdtcrair, oh cguhga÷d pripucsth oh pi`ceis csgranar `c oh sabuacdtc ehdcrh=
E. G. OSAW DACPI OCESW
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Zèbadh 88 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW
oib8: Z
5
od Z
od8:
5∞
8801 P
+ 2.068
Zir oi thdti= od Z
( eeFb ) 5 (od8: ) ∞ 8801 + 2.068 P
od Z
>>32 K ) ^ 5 ( >3:: gho/eio. Ghoguoc co pudti `c cnuooaga÷d direho `co oåqua`i.
@HPIW= P 8 5 8>:ºG 5 717.83 K
Z8 5 2>3 eeFb
F\ 5 6>:: gho/eio ˌ
Z> 5 2) cepochrceis oh cguhga÷d `c GohusausGohpcyrid=
^P P Z F\ 5 8 > od 8 P8 ∞ P> Z> ˌ
^P P Z 5 8 > od > P> ∞ P8 Z8
I nacd=
F\ ˌ
^
P8 P >
5
P8 ∞ P>
od 8 P>
E. G. OSAW DACPI OCESW
Z8
Z>
∞
P8 ∞ P>
8 P8
5
P8 P> ^
F\ ˌ
5
^
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Z8
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Zèbadh 8> `c 07
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5
8 P8
+
^
F\
od
ˌ
P > 5
Z8
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5
8
+
717.8 3 K
gho 8.162 eioK gho 6>:: eio
od
2>3eeFb 276 K 710.1> K 5 8>8.22ºG 8>8.22º G
8:. Co pudti `c cnuooaga÷d direho `co G8 egihooK )Pn: 5 (>8 egihooK ) (0>1.7 K ) 5 1:83.7 eghioo ˌ
Zir oi quc= gho F\ : 1:83.7 eio 5 5 0372.8080> K gho ˌ
^
8.162 eioK
Zir itrh phrtc, gid nhsc h oh cguhga÷d `c Gohusaus Gohpcyrid, tcdceis quc= od Z*
Zhrh P 5
5∞
F\ ˌ
^P
+G 5 ∞
F\
^
ˌ
P
+ G
:
P n 5 0>1.7 K tcdceis quc Z* 5 Z : 5 2:>:83 P 0>1.7K Zir oi quc, oh cguhga÷d quc rcohgaidh h oh prcsa÷d `c vhpir Z * gid P phrh phrh co G:>:83
H phrtar `c oh cguhga÷d hdtcrair pi`ceis cvho cvhouhr uhr oh prcsa÷d `c vhpi vhpirr h guhoquacr guhoquacr P , cd co ghsi cd co guho P 5 8::ºG 5 727.83 K, rcsuoth=
0372.8080> K
727.83 K
Z* 5 c x p ∞
E. G. OSAW DACPI OCESW
+ 82.>:>:83 5 830.17>:3 e eFb
LAX-SEWDF
Zèbadh 87 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW 88. Co GGo0 tacdc ohs sabuacdtcs prcsaidcs `c vhpir h ohs tcepcrhturhs ad`agh`hs= ad`agh`hs= P(ºG)
7:
3:
2:
8::
Z* (eeFb)
80>.7
780.0
8.8
807.83
707.83
727.83
Z* (eeFb)
80>.7
780.0
8.8
80
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7.: >.6
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E. G. OSAW DACPI OCESW
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8.
Nchttac y Ehrpoc [M. He. Gfce. Wig., Wig., 2>, 803: (813:)U `acrid oh sabuacdtc cguhga÷d phrh oh prcsa÷d `c vhpir `co 8-nutcdi giei ludga÷d `c oh tcepcrhturh cdtrc -23 y 8>3 ºG=
(
oib8: Z * hte
∞ 8
F\ csthråh `h`h pir oh sabuacdtc cguhga÷d= ˌ
>
F
^P
ˌ
\
odZ ` `P
5
(8)
Zi Zirr oi th thdt dti, i, praec praecri ri sc tcd`r tcd`rè è quc quc cv cvhou houhr hr oh `cra `cravh` vh`h h` od Z `P y pistcra pistcraire irecdtc cdtc sust sustatua atuarr cd oh cgu cguhga÷ hga÷d d (8) phrh intcdcr oh cguhga÷d quc dis pcreath ghoguohr co
F\
ˌ
cd lu ludga÷ dga÷d d `c P , giei sc eucstrh h
gidtaduhga÷d=
(
oib8: Z * hte
od Z 8707.38< 5 3.0230 ∞ ∞ 8 ∞ 763.2823 8:∞3 (8 ) P
` od Z `P
5
7:17 :17.331 .3311 180 >
P
3 ∞ 763 763.28 .2823 23 8:∞
(>)
Wustatuycd`i Wustatuycd` i oh cguhga÷d (>) cd oh cguhga÷d (8), rcsuoth=
F\ 5 ^P >
` odZ
ˌ
E. G. OSAW DACPI OCESW
`P
7:17.331180 ∞3 5 ^P > ∞ 763. 763.282 2823 3 8: > P
LAX-SEWDF
Zèbadh 83 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW
F\ ˌ
^
∞3 > 5 7:1 7:17.3 7.3311 31180 80 ∞ 76 763.2 3.2823 823 8: P
I nacd, nacd, c cd du uda` da`h`c h`css `c `coo WA, oh cg cguhg uhga÷d a÷d quc` quc`hråh hråh `c oh sabuacd sabuacdtc tc lir lireh eh== ∞3 > F\ 5 ^ ( 7:17 7:17.3 .331 3118 180 0 ∞ 763.2 763.282 823 3 8: 8: P ) ˌ
∞7 kM ∞3 > F\ 5 ( 6.78 .78 0 8: eio 7:17.3 .33 31180 ∞ 7 76 63.28 .2823 8: P ) ( K ) eio K ) ( ˌ
kM F\ ( eio ) 5 >3.28 281 1632 ∞ 7.> .>:< : ,
P (K )
ˌ
n) Zhrh P 5 7:: K, co ghoi ghoirr ei eiohr ohr ohtcd ohtcdtc tc `c vhp vhpira irazhg zhga÷d a÷d scr scråh åh cdtid cdtidgc gcs= s= ∞3 > kM F\ 5 >3.28 .281632 1632 ∞ 7.> 7.> ::
ˌ
>
kM
ˌ
F 5 >>.677K
LAX-SEWDF
Zèbadh 8 s÷oa`i cs 2.
^. Z> P> ∞ P8 Z8 P8 P>
Wusatuycd`i Wusatuycd `i `htis=
^P P Z Fs 5 8 > od 8 P8 ∞ P> Z> ˌ
(8.162 5
gho eioK
) (82:.83K )(810.
od Z `
ˌ
`P
Zir oi thdti, praecri sc tcd`rè quc cvhouhr oh `cravh`h
(8)
pistcrairecdtc ecdtc sustatuar cd oh c cguhg guhga÷d a÷d ` odZ `P y pistcrair
(8) phr phrh h intcdc intcdcrr oh cgu cguhga hga÷d ÷d qu quc c dis pcreath ghog ghoguoh uohrr co
FW
ˌ
cd ludg ludga÷d a÷d `c P , giei sc eucstrh h
gidtaduhga÷d=
(
oib8: Z * hte
E. G. OSAW DACPI OCESW
+ 8.0:3oib ) 5 ∞ 8>10 P
8:
LAX-SEWDF
P
∞ :.::38P + 0 .6::
Zèbadh 82 `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW od Z
5∞
od8:
od Z
od Z ` od Z
5
`P
` od Z `P
8>10 P
odP + 8.0:3 ∞ :.::38P + 0.6:: od8:
8>10 odP 5 (od 8: ) ∞ + 8.0:3 ∞ :.::38P + 0.6:: od8: P
5 ∞ >121.30388 + 8.0:3odP ∞ 882.0786 8: ∞0 P + 88.:3>0:6 P
∞ >121.30388 + 8.0: ∞0 0:3 3odP ∞ 882.0 2.0786 8: P + 88 88..:3> 3>0 0:6 `P P `
5 ∞>121.30388
` od Z `P
8 + 8.0:3 ` odP ∞ 88 2.0786 8:∞0 `P P `P `
`P `P
+ :
8 8 5 ∞>121.30388 ∞ > + 8.0:3 ∞ 882.0786 8:∞0 ( 8) P P
` od Z `P
5
>121.30388 P
>
+
8.0:3 P
∞0 882.07 .0786 86 8: ∞ 882
(>)
Wustatuycd`i Wustatuycd` i oh cguhga÷d (>) cd oh cguhga÷d (8) sc intacdc=
5 ^P > ` odZ `P
FW ˌ
FW ˌ
^
882.078 0786 6 8:∞0 5 ^P > > 121.3>0388 + 8.0:3 ∞ 882. P P
∞0 > >121.3 .303 0388 88 + 8.0: 8.0:3 3P ∞ 882 82.0 .078 786 6 8: P 5 >121
Cd uda`h`cs uda`h`cs WA, oh cg cguhga÷d uhga÷d quc`hråh= quc`hråh= ∞0 > >121 21.3 .303 038 88 + 8.0: 8.0:3 3P ∞ 882.0 82.078 786 6 8: P ) FW 5 ^ ( >1
ˌ
F 5 ( 6.780 ˌ
W
M eioK
.0: :3P ∞ 882.07 .0786 8: ) (>121.30388 + 88.0
∞0 > M ) 5 >022 228. 8.1 176 76:0 :00 0 + 88. 8. 8 t 8
Wustatuycd`i Wustatuycd` i `htis, rcsuoth=
:.6:: b 5 ( :.:8::> Ziasc ) :.116>1ge b ge 7
>
7
>.>3ead 8.3> 8. ead d 3> ea
5 :.: .:88 886 66< 6 ( ∞ e ) b 1 v
`id`c=
v 5
` t
Zir oi thdti=
5
> r > ( ∞ e ) b
` t
1 >
5
> r > ( ∞ e ) b t > ( :.> ge ) ( 2.1:
5
1`
b ge 7
∞ 8.8:
b ge7
) ( 16:.
) ( 33 s )
1 (8:: ge )
b 5 7>.< >... ge y udh `cdsa`h` `c 8.8: b/ge 7 ghc gid udh vcoiga`h` gidsthdtc h trhvás `c ud oåqua`i guyh `cdsa`h` cs 8.:: b/ge7 y su vasgisa`h` `c 8.:: piasc. ¹Gid quá vcoiga`h` `csgacd`c oh cslcrh9
@HPIW= r 5 5 3Ò8: -> ge
5 8.8: b/ge 7
E. G. OSAW DACPI OCESW
LAX-SEWDF
Zèbadh >: `c 07
GS^WI @C PC^EI@ADÈEAGH= Z^INOCEHW ^CWSCOPIW e 5 8.:: b/ge7
5 8.:: pia piasc sc (b/ge s)
WIOSGA×D= Hsueacd`i Hsueacd `i quc cs hpoa hpoaghnoc ghnoc oh Ocy `c Wtikcs, Wtikcs, tcdceis=
> r > ( ∞ e ) b
5
1 v Zir oi guho, oh vcoiga`h` `c `csgcdsi `c oh cslcrh cd co oåqua`i scrè=
v 5
>r
>
( ∞ e ) b > (3 8: 5 1
∞>
>
ge
v
) (8.8: ∞ 8.:: ) (16:.
b ges
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