2do Taller Termodinamica Aplicada Diego Romero

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

W]CMCNK = XKM]E HBHFKX KWWK, GBÂXEF,  GbedkGE Nksâ ]k`erk OþóezXWB]FBOD R E]BHXXKO.  Qrkleskr> Hcrfks Meffk. Drupk> 3. 33-1:-=1=1. 33-1:-=1=1. Wer`kgboã`bhc cpfbhcgc, Uobversbgcg gef Ctfãotbhk, Ctfãotbhk-Quertk Hkfk`mbc.

Hbhfk Kttk Ef hbhfk Kttk se cpfbhc c `ktkres ge hk`mustbøo boteroc que trcmcnco hko uoc `ezhfc ge cbre y uo hk`mustbmfe vkfãtbf hk`k dcskfboc, dcs, k cfhkjkf, y huyc hk`mustbøo se bobhbc hko uoc hjbspc efâhtrbhc. Xus etcpcs sko fcs sbdubeotes> cgbcmãtbhc> fc `ezhfc ge cbre y dcskfboc se hk`prb`e sbo boterhc`mbcr hcfkr hko ef 3. Hk`presbøo cgbcmãtbhc> exterbkr exte rbkr.. Fc trcoslkr trcoslkr`chb `chbøo øo es pkr tcotk bseotrøp bseotrøpbhc. bhc. Fc pksbhbøo pksbhbøo que cfhcozc cfhcozc ef pbstøo pbstøo se (Q@X).. Ef trcmcnk recfbzcgk pkr fc `ezhfc eo estc etcpc es geok`boc geok `boc puotk `uertk `uertk superbkr superbkr (Q@X) oedctbvk, yc que âstc se hk`prb`e. Expfksbøo> fc munà =. Expfksbøo> munàcc se ch chtb tbvc vc,, scft scftcc uoc uoc hj hjbs bspc pc y fc `ezh `ezhfc fc se eo eohb hbeo eoge ge.. Gurc Gurcot otee es estc tc trcoslkr`chbøo fc presbøo cu`eotc c vkfu`eo hkostcote. cgbcmãtbhc> fc `ezhfc se expcoge cgbcmãtbhc`eote. Gurcote este prkhesk, fc eoerdàc 8. Expcosbøo cgbcmãtbhc> quà`bhc fbmercgc gurcote fc hk`mustbøo se trcoslkr`c eo eoerdàc `ehãobhc, yc que ef trcmcnk gurcote estc trcoslkr`chbøo es pksbtbvk. Eolrbc`beotk bsøhkrk bsøhkrk> gurc 7. Eolrbc`beotk gurcot otee estc estc etcp etcpcc fc pr pres esbø bøo o gb gbs` s`bo bouy uyee y fc `ezh `ezhfc fc se eo eolr lràc àc fbmerãogkse hcfkr cf exterbkr.

Lbdurc 3> Enehuhbøo gef hbhfk ge Kttk bgecf.

3

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Lbdurc => Gbcdrc`c Q vs v ge uo hbhfk ge Kttk

Lbdurc 8> Gbcdrc`c W vs s pcrc hbhfk

bgecf.

Kttk bgecf.

Qcrc fc hk`presbøo, hk`k es uo prkhesk cgbcmãtbhk, pcrc fc presbøo se kmtbeoe>  I 

 I 

 Q3 \ 3 0 Q= \ =

Gkoge I es fc refchbøo eotre fks hcfkres espehàlbhks c presbøo hkostcote (H Q) y c vkfu`eo hkostcote (Hv), es gehbr> H  Q  I 0 H \  Xe scme que

\ `cx \ `bo

es fc refchbøo ge hk`presbøo (r) pkr fk tcotk se puege jcffcr Q = hk`k>  Q=0 Q3 r I 

Qcrc fc te`percturc se kmtbeoe>  I ∝3

W 3 \ 3

 I ∝ 3

0W = \ =

Qkr eoge gespencogk W== se kmtbeoe> W =0W 3 r

 I ∝ 3

Qcrc fc hk`mustbøo hk`k ef vkfu`eo per`coehe hkostcote, se tbeoe> Seotrcgc0 ( u8∝u= ) 0H v ( W 8∝W = )

Qkr eoge> ˒ 0  ` S ˒ H v ( W 8∝W = )

=

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Qcrc ef eolrbc`beotk hk`k es c vkfu`eo hkostcote, se tbeoe> Sscfbgc0( u 7∝ u3 )0H \  (W 7∝W 3 ) Eotkohes pcrc ef hbhfk ge Kttk bgecf fc elbhbeohbc târ`bhc se puege exprescr hk`k> W 7 ∝W 3 S scfbgc δter 03∝ ⇝δ ter03 ∝ W 8∝W = S eotrcgc Eo târ`boks ge fc te`percturc. δter 03∝

 3  I ∝ 3

r

Eo târ`boks ge fc refchbøo ge hk`presbøo. Ene`pfk prkpuestk> 2.78Uo 2.78 Uo `ktkr ge dcskfboc ge huctrk hbfbogrks y huctrk tbe`pks, ge 3.< F, kperc eo hbhfk ge Kttk hko uoc refchbøo ge hk`presbøo ge 33. Ef cbre estã c 311 iQc y 84 ±H cf bobhbk gef prkhesk ge hk`presbøo, y fc presbøo `ãxb`c eo ef hbhfk es ge : @Qc. Fks prkhesks ge hk`presbøo y expcosbøo puegeo `kgefcrse hk`k pkfbtrøpbhks, hko uoc hkostcote pkfbtrøpbhc ge 3.8. Uscogk hcfkres espehàlbhks hkostcotes c :51 I, geter`boe> C) Fc te`percturc te`percturc cf lbocf lbocf gef prkhesk ge expcosbøo. expcosbøo. M) Fc prkguh prkguhhbøo hbøo oetc ge trcmcnk trcmcnk y fc elbhbeohb elbhbeohbcc târ`bhc. H) Fc presbø presbøo o `egbc `egbc elehtbvc elehtbvc.. G) Ef oþ`erk ge revkfuhbk revkfuhbkoes oes pkr `boutk `boutk gef `ktkr `ktkr pcrc uoc prkguhhbø prkguhhbøo o ge pkteohb pkteohbcc oetc ge 51 iT.. iT E) Ef hkosu`k hkosu`k espehàlbhk espehàlbhk ge hk`mustbm hk`mustbmfe, fe, eo d/iTj, gelbobgk gelbobgk hk` hk`k k fc refchbøo refchbøo ge fc `csc ge hk`mustbmfe hkosu`bgk cf trcmcnk oetk prkguhbgk. Fc refchb refchbøo øo cbrecbre-hk` hk`mus mustbm tbmfe fe,, gelbob gelbobgc gc hk`k hk`k fc hcotb hcotbgc gcg g ge cbre cbre gb gbvbg vbgbg bgcc eotre eotre fc hc hcotb otbgc gcg g ge hk`mustbmfe cg`btbgk, es 3 ef cbre hk`k uo dcs bgecf, ef H Q y H\ sko hkostcotes, ge fc tcmfc C-= gef Heodef se kmtbeoeo fcs hkostcotes gef cbre c :51I y se kmtbeoe pkr boterpkfchbøo que>

8

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Hkostcote ge dcs, ] (iN/id I)

Hp (iN/id I)

Hv (iN/id I)

i

Q(iQc)

W(±H)

1,=:4

3.33

1.:=8

3.8:74=73:

311

84

Xe cocfbzco fks prkhesks> Qrkhesk 3-=> hk`presbøo bseotrøpbhc. Ge fc ehuchbøo ehuchbøo ge te`percturc te`percturc pcrc prkhesks cgbcmãtbhks se gespenc fc te`percturc te`percturc pcrc ef estcgk =, ge fc ehuchbøo ge presbkoes pcrc prkhesks cgbcmãtbhks se kmtbeoe fc presbøo pcrc ef estcgk gks. Hko estks gctks se kmtbeoe ef trcmcnk pkr uobgcg ge `csc eo târ`boks ge fc ehuchbøo>  ] ( W m∝ W e ) T em 0 3∝ i  Hkokhb Hko khbeo eogk gk qu que, e, se sedþo dþo ef ener enerhbh hbhbk bk y ge ch chuer uergk gk c fc eh ehuch uchbøo bøo ge fc refchb refchbøo øo ge hk`pr hk`presb esbkoe koess v3 v7 0 033, se kmtbeoe> v= v8 W =0 W 80==55, W 70312:, 8  ` v =01,1:3 id  Q@E 02:3,4 iQc

δW 0

Ge chuergk hko fcs espehblbhchbkoes gef enerhbhbk, ef vkfu`eo gef `ktkr es 3,

5

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

W  h c  C 0 ` 0 ` ∝ ` 01,11133 es uo prkhesk ge hk`presbøo cgbcmãtbhc reversbmfe (bseotrøpbhc), es gehbr sbo boterhc`mbk ge hcfkr hko ef exterbkr y hko uo trcmcnk recfbzcgk cf sbste`c pcrc hk`prb`brfk. se kmtbeoe hk`k uo prkhesk ge cgbhbøo ge hcfkr c presbøo hkostcote. Ge =. Hk`mustbøo (=-8)> se jehjk, este es ef þobhk prkhesk eo ef que fks hbhfks Kttk y Gbâsef gblbereo. 8. Expco pcosb sbøo øo (8-7 (8-7))> fc `ezhfc se expcoge cgbcmãtbhc`eote. Gurcote este prkhesk, fc eoerdàc quà`bhc fbmercgc gurcote fc hk`mustbøo se hkovberte eo eoerdàc `ehãobhc pkrque ef trcmcnk gurcote estc hkoversbøo es pksbtbvk. 7. Eolrbc`beotk (7-3)> estc etcpc es uo prkhesk bskhørbhk (eshcpe) es gehbr c vkfu`eo hkostcote. Gesge fc presbøo lbocf ge expcosbøo jcstc fc presbøo bobhbcf ge hk`presbøo.

<

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Lbdurc  Gbcdrc`c W vs s pcrc hbhfk  Gbâsef bgecf.

Lbdurc 5> Gbcdrc`c Q vs v pcrc hbhfk  Gbâsef bgecf. bgecf.

Qcrc fc hk`presbøo, hk`k es uo prkhesk cgbcmãtbhk, pcrc fc presbøo se kmtbeoe>  I 

 I 

 Q3 \  3 3 0 Q= \ =

Gkoge I es fc refchbøo eotre fks hcfkres espehàlbhks c presbøo hkostcote (H Q) y c vkfu`eo hkostcote (Hv), es gehbr> H  Q  I 0 H \  \ `cx Xe scme que es fc refchbøo ge hk`presbøo (r) se puege jcffcr fc Q = hk`k> \ `bo  I 

 Q=0 Q3 r

Qcrc fc te`percturc se kmtbeoe>  I ∝3

W 3 \ 3

 I ∝ 3

0W = \ =

Qkr eoge gespencogk W= se kmtbeoe> W =0W 3 r

Qcrc fc hk`mustbøo se tbeoe>

4

 I ∝ 3

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Seotrcgc0 Q = ( v 8∝v = ) + ( u8∝u= ) 0( j8 ∝j= )0H  Q ( W 8∝W = )

Qkr eoge> ˒ 0  ` S ˒ ( j8 ∝j= ) 0` ˒ H  Q ( W 8∝W =)

Cge`ãs se gelboe uoc ouevc hcotbgcg, fc refchbøo ge hkrte ge cg`bsbøo r h, hk`k fc refchbøo ge fks vkfþ`eoes eotre ef hbfbogrk cotes y gespuâs ge fc hk`mustbøo> v8 rh0 v= Qcrc ef eshcpe se kmtbeoe> Qkr eoge>

S scfbgc0 ( u 7∝ u3 )0H v ( W 7 ∝ W 3) ˒ scfbgc 0  ˒ S ` H v ( W 7 ∝W 3 )

Fuedk pcrc fc elbhbeohbc târ`bhc se tbeoe> δter 0

T oetk S eotrcgc

Qerk T oetk 0S eotrcgc∝Sscfbgc, pkr eoge se kmtbeoe>   S scfbgc S eotrcgc∝S scfbgc δter 0 ⇝ δ03∝ Seotrcgc S eotrcgc ]e`pfczcogk fcs ehuchbkoes ge hk`mustbøo y ge eshcpe eo fc ge fc elbhbeohbc târ`bhc, se kmtbeoe> ∝

δter 03∝ H v ( W 7 W 3 ) H  Q ( W 8 ∝W = )

Gkoge se puege exprescr cf hkhbeote

H v H  Q

hk`k ef boversk ge fcs refchbkoes ge fks hcfkres espehblbhks es

gehbr> H v

0

 3

H   QQ  I 

Qkr fk que fc elbhbeohbc târ`bhc quegc exprescgc hk`k

δter 03∝

  ( W  ∝W  ) 7

i  W  ∝W 

( :

3

8

=

)

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

R pcrc fc elbhbeohbc târ`bhc eo târ`boks ge fcs refchbkoes ge hkrte ge cg`bsbøo se tbeoe>

δter 03∝

r

Y ( ) P  I 

r h ∝3

3  I ∝ 3

i  r h ∝3

Ene`pfk prkpuestk> 2. W =0878,35 I ∔==

1,7

⇝

W =033:3,5 I 

Qrkhesk =-8 Es uo prkhesk c presbøo hkostcote pkr fk que se puege jcffcr fc te`percturc pkr `egbk ge> v= W = v =0W 8 v 8 ⇝ W 80W = ⇝ W 80W = r h v8 Qkr eoge se kmtbeoe W8> W 8033:5,5 I ∔3,: ⇝ W 80 =387 I 

Qrkhesk 8-7 Qkr ser uo prkhesk cgbcmãtbhk bseotrøpbhk, pcrc jcffcr fc te`percturc 7 se usc> 2

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC ∝3

 I ∝3 0 7

W 7 \ 

 I ∝ 3 ⇝ 8

W 8 \ 

 I 

( )

8 W 7 0W 8 \  \ 7

Qerk v80 3.: v=  y v70 v3 pkr eoge re`pfczcogk eo fc ehuchbøo se kmtbeoe> W 70W 8

( ) 3.: v =

v3

 I ∝3 ⇝

W 7 0 W 8

(  )

 I ∝3

3.:

r

Qkr eoge re`pfczcogk fks gctks se kmtbeoe>

(  )

3,: W 70=387 I  ==

1,7 ⇝

W 704:7 I 

Uscogk fc ehuchbøo ge dcses bgecfes se kmtbeoe fc `csc, pkr eoge>  Q3 v 3   ( 24 iQc ) ( 1,11= `8) ∝8 id `0 ⇝ `0 ⇝ ` 03,217: x 31 8 W 3 ] iQc` ( 878,35 ) 1,=2 ∝8

(

Seot 0`H  Q ( W 8∝ W = ) ⇝ S eot 0 ( 3,217: x 31 id ) 3,182

 )

  iN  ( =387 ∝33:3,5 ) I  idI 

Seot 03,::5 iN  ∝8

(

Sscf 0`H \  ( W 7 ∝W 3) ⇝ S scf 0( 3,217: x 31 id ) 1,478

)

  iN  ( 4:7 ∝878,35 ) I  idI 

1, w oetk0Seot ∝Sscf ⇝ woetk03,::5 iN ∝ 1, Enehuhbøo gef hbhfk ge Xtbrfbod  

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Lbdurc 2> Gbcdrc`c W vs s ge Lbdurc :> Gbcdrc`c Q vs v

hbhfk Xtbrfbod

hbhfk Xtbrfbod

Qcrc fcs `cqubocs târ`bhcs fc elbhbeohbc târ`bhc se gelboe hk`k> T oetk δter 0 S cmsrmbgk Xe scme que skfk se prkguhe trcmcnk eo fc expcosbøo y fc hk`presbøo pkr fk que T oetk se gelboe hk`k>  v v3 + o]W  F fo 8 T oetk 0o]W  J  fo v7 v=

()

( )

Gkoge fk Gkoge fkss hkhbe hkhbeote otess ge fks fks vkfþ`e vkfþ`eoes oes es fc refchb refchbøo øo ge hk`pr hk`presb esbøo øo y pk pkrr eoge eoge cpfbh cpfbhco cogk gk fc fcss prkpbegcges gef fkdcrbt`k, se kmtbeoe> T oetk 0o] ( W  J ∝ W  F ) fo ( r ) Eo este sbste`c sbste`c skfk se cmskrme cmskrme hcfkr hcfkr pcrc pcrc fc expcosbø expcosbøo o bsktâr`bhc bsktâr`bhc y ef hcfeotc` hcfeotc`beot beotk k c vkfu`eo vkfu`eo hkostcote pkr eoge se kmtbeoe> Scmskrmbgk0oH \  (W  J ∝W  F ) + o]W  J  fo ( r )

3=

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC

Eo fc prãhtbhc ge este sbste`c es hk`þo uscr redeoercgkres, redeoercgkres, estks per`bteo ef cf`cheoc`beotk ge hcfkr hegbgk pkr ef dcs gurcote ef eolrbc`beotk gef prkhesk pcrc fuedk gevkfverfk cf sbste`c gurcote ef prkhesk ge hcfeotc`beotk, cuoque eo fc tekràc pkr trctcrse ge prkhesks bskhørbhks fcs hcotbgcges eo ef `kgufk sko bducfes, ef redeoercgkr ok es perlehtk pkr eoge pcrte ge fc eoerdàc es pergbgc, gelbobeogk su S gevueftk se kmtbeoe> elbhbeohbc hk`k δ] 0 Shegbgk S cmskrmbgk0( 3∝δ] ) oH \  (W  J ∝W  F ) + o]W  J  fo ( r ) Qkr eoge se kmtbeoe fc elbhbeohbc târ`bhc hk`k> o] ( W  J ∝W  F ) fo ( r ) δter 0 (3 ∝δ] ) oH \  ( W  J ∝W  F ) +o]W  J  fo ( r ) Eotre `ãs se cherque c fc bgecfbgcg pkr eoge se cfhcozc fc `ãxb`c elbhbeohbc târ`bhc teørbhc es gehbr fc gef hbhfk ge Hcrokt, pkr eoge se kmtbeoe> W  F δter 03∝ W  J   J  Ene`pfk prkpuestk> 2.:3 Uo hbhfk Xtbrfbod hko cbre estãogcr kperc hko uoc presbøo `ãxb`c ge 8

Xe

csu`e

que

Etcpc Etcpc =

Q (ipc)

Etcpc Etcpc 3 8 Enehuhbøo gef Hbhfk ge Erbhssko

Lbdurc 3=> Gbcdrc`c W vs s Lbdurc 33> Gbcdrc`c Q vs v

Hbhfk ge Erbhssko

Hbhfk ge Erbhssko

Fc elbhbeohbc târ`bhc estã gelbobgc pkr fc ehuchbøo> δter 03∝

  S Xcfbgc S Eotrcgc

35

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC R ef hcfkr hcfkr pcrc este hbhfk hbhfk estã estã ge gete ter`b r`bocg ocgk k pk pkrr S0WΗs , fc gblereohbc ge eotrkpbc eo uo prkhesk bsktâr`bhk estc gcgk pkr>  Q W e ∝ ]fo e  Ηs 0H  Q fo  Q b W b

( ) ( ) ( )

Gkoge ef hkhbeote ge te`percturcs es 3 pkr eoge se hcohefc ge fc ehuchbøo y se kmtbeoe>  Qe  Ηs 0∝ ]fo  Qb Qkr eoge fcs ehuchbkoes pcrc fc eotrcgc y scfbgc ge hcfkr se kmtbeoeo respehtbvc`eote>

( ( ))

 ]fo S eot 0W  J   J   ]fo  J  ( s =∝ s3 ) 0W  J 

 Q3  Q=

0 ]W  J   J  fo

(  )  Q3  Q=

 y

( (  ))

S scf0W  J  ( s 7∝ s8 ) 0W f  ]fo

 Q 7  Q8

]e`pfczcogk eo fc ehuchbøo ge fc elbhbeohbc târ`bhc se kmtbeoe>

δter 03∝

S scf S eot 

 ]W  J  fo ⇝

(  ) ( ) (  )

0 ]W  J  fo

δter 03∝  ]W  J  fo

 Q 7  Q8

 Q7  Q8

 Q3  Q=

Qerk Q7 0 Q3 y Q8 0 Q==, pkr eoge se kmtbeoe> δter 03∝

W  F

W  J  Ene`pfk prkpuestk> 2.44 Uo hbhfk Erbhssko kperc eotre gepøsbtks ge eoerdàc târ`bhc c Etcpcs W ( I) Toetk  (iT)

3-= 211

8-7 =:1 511

Qcrc gescrrkffcr este enerhbhbk jcy que teoer eo hueotc fcs ehuchbkoes c uscr, eo este hcsk skfk se uscrc fcs ehuchbkoes ge elbhbeohbc târ`bhc, eo fcs hucfes fc gelbobhbøo estã gcgc pkr>

3<

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC  F oetk δt 0 T  03∝ W  W  J  Seotrcgc Uscogk estc ehuchbøo ge elbhbeohbc târ`bhc gcgc pkr uo hbhfk reversbmfe, se kmtbeoe>

δt 03∝

 W  F

03∝

=:1 I   01.//fcpfche.us.es/wbib/bogex.pjp/Hbhfk[Gbesef Gepcrtc`eotk ge Làsbhc cpfbhcgc BBB. (s. l.-m). Hbhfk Kttk. Uobversbgcg ge Xevbffc. ]ehupercgk 8 ge cdkstk ge =1=1, ge jttp>//fcpfche.us.es/wbib/bogex.pjp/Hbhfk[Kttk Gepcrtc`eotk ge Làsbhc cpfbhcgc BBB. (s. l.-h). Hbhfk Kttk. Uobversbgcg ge Xevbffc. ]ehupercgk 8 ge cdkstk ge =1=1, ge jttp>//fcpfche.us.es/wbib/bogex.pjp/Hbhfk[Kttk Gepcrtc`eotk ge Làsbhc cpfbhcgc BBB. (s. l.). Hcsk ge hbhfk Erbhssko. Uobversbgcg ge Xevbffc. ]ehupercgk 8 ge cdkstk ge =1=1, ge 34

 

UOB\E]XBGCG GEF C CWFÃOWBHK WFÃOWBHK LCHUFWCG GE BODEOBE]ÀC Q]KD]C@C GE BODEOBE]ÀC SUÀ@BHC jttp>//fcpfche.us.es/wbib/bogex.pjp/Hcsk[ge[hbhfk[Erbhssko#]epreseotchb.H8.M8o[dr.H8.C3lbh c

3: