calorimetry & thermal expansion theory_e

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"bmhgsfcubmrpfysgks.gh" =

ZFW[GK[

OITGBEPTW H@ PFETB O EVZ H[GIH

=. FEMP

Pfe eherly tfmt gs deghl trmhsaerre` detweeh twi di`ges ir detweeh m`nmkeht pmrts ia m di`y ms mresuot ia tebpermture `gaaerehke gs kmooe` femt. Pfus, femt gs m airb ia eherly. Gt gs eherly gh trmhsgtwfehever tebpermture `gaaerehkes exgst. Ihke gt gs trmhsaerre`, gt dekibes tfe ghterhmo eherly ia tferekegvghl di`y. Gt sfiuo` de koemroy uh`erstii` tfmt tfe wir` "femt" gs bemhghlauo ihoy ms oihl ms tfeeherly gs deghl trmhsaerre`. Pfus, expressgihs ogce "femt gh m di`y" ir "femt ia m di`y" mre bemhghloess.

M DFemt

P 8 P= 4 P4

\feh we smy tfmt m di`y gs femte` gt bemhs tfmt gts bioekuoes delgh ti bive wgtf lremter cghetgkeherly.[. . uhgt ia femt eherly gs niuoe (N). Mhitfer kibbih uhgt ia femt eherly gs kmoirge (kmo).

= kmoirge 2 0.=6 niuoes.

= kmoirge > Pfe mbiuht ia femt hee`e` ti ghkremse tfe tebpermture ia = lb ia wmter arib =0.5 ti =5.5K mt ihe mtbispfergk pressure gs = kmoirge.

=.= Bekfmhgkmo Equgvmoeht ia FemtGh emroy `mys femt wms hit rekilhgze` ms m airb ia eherly. Femt wms suppise` ti de sibetfghlhee`e` ti rmgse tfe tebpermture ia m di`y ir ti kfmhle gts pfmse. Kmoirge wms `eaghe` ms tfeuhgt ia femt. M hubder ia expergbehts were perairbe` ti sfiw tfmt tfe tebpermture bmy moside ghkremse` dy `ighl bekfmhgkmo wirc ih tfe systeb. Pfese expergbehts estmdogsfe` tfmtfemt gs equgvmoeht ti bekfmhgkmo eherly mh` bemsure` fiw bukf bekfmhgkmo eherly gsequgvmoeht ti m kmoirge. Ga bekfmhgkmo wirc \ pri`ukes tfe smbe tebpermture kfmhle ms femtF, we wrgte,

\ 2 NFwfere N gs kmooe` bekfmhgkmo equgvmoeht ia femt. N gs expresse` gh niuoe/kmoirge. Pfe vmoue ia Nlgves fiw bmhy niuoes ia bekfmhgkmo wirc gs hee`e` ti rmgse tfe tebpermture ia = l ia wmter dy=K.

Exmbpoe =. \fmt gs tfe kfmhle gh pitehtgmo eherly (gh kmoirges) ia m =: cl bmss mater =: b amoo 9[ioutgih > Kfmhle gh pitehtgmo eherly

U 2 blf 2 =: =: =:2 =::: N

2=61.0

=:::kmo Mhs.

4. [ZEKGAGK FEMP[pekgagk femt ia sudstmhke gs equmo ti femt lmgh ir reoemse` dy tfmt sudstmhke ti rmgse ir amoo gts tebpermturedy =K air m uhgt bmss ia sudstmhke.\feh m di`y gs femte`, gt lmghs femt. Ih tfe itfer fmh`, femt gs oist wfeh tfe di`y gs kiioe`. Pfe lmghir oiss ia femt gs `grektoy pripirtgihmo ti>(m) tfe bmss ia t fe di`y ] b(d) rgse ir amoo ia tebpermture ia tfe di`y ] P

8/12/2019 Calorimetry & Thermal Expansion Theory_E

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"bmhgsfcubmrpfysgks.gh" 4

ZFW[GK[

] b P ir ] 2 b s P

ir `] 2 b s P ir ] 2 b s ` P. .

wfere s gs m kihstmht mh` gs chiwh ms tfe spekgagk femt ia tfe di`y s 2Pb

] . [. . uhgt ia s gs niuoe/

cl-ceovgh mh` K.L.[. uhgt gs kmo./lb K.

[pekgagk femt ia wmter > [ 2 04:: N/clK 2 =::: kmo/clK 2 = Ckmo/clK 2 = kmo/lbK

[pekgagk femt ia stemb 2 fmoa ia spekgagk femt ia wmter 2 spekgagk femt ia gke

Exmbpoe 4. Femt requgre` ti ghkremses tfe tebpermte ia = cl wmter dy 4:K[ioutgih > femt requgre` 2 ] 2 bs

[ 2 = kmo/lbK 2 = Ckmo/clK2 = 4: 2 4: Ckmo.

4.= Femt kmpmkgty ir Pferbmo kmpmkgty >Femt kmpmkgty ia m di`y gs `eaghe` ms tfe mbiuht ia femt requgre` ti rmgse tfe tebpermture ia t f m t d i ` y d y = . G a ' b ' g s t f e b m s s m h ` ' s ' t f e s p e k g a g k f e m t i a t f e d i ` y, t f e hFemt kmpmkgty 2 b s .Uhgts ia femt kmpmkgty gh> KL[ systeb gs, kmo K=3 [G uhgt gs, NC =

4.4 Gbpirtmht Zights>

(m) \e chiw, s 2Pb

] , ga tfe sudstmhke uh erlies tfe kfmhle ia stmte wfgkf ikkurs mt

kihstmht tebpermture ( P 2 :) , tfeh s 2 ]/: 2 . Pfus tfe spekgagk femt ia m sudstmhkewfeh gt beots ir digos mt kihstmht tebpermture gs ghaghgte.

(d) Ga tfe tebpermture ia tfe sudstmhke kfmhles wgtfiut tfe trmhsaer ia femt (] 2 :) tfeh

s 2Pb

] 2 :. Pfus wfeh ogqug` gh tfe tferbis aomsc gs sfmceh, gts tebpermture

ghkremses wgtfiut tfe trmhsaer ia femt mh` fehke tfe spekgagk femt ia ogqug` gh tfe tferbisaomsc gs zeri.

(k) Pi rmgse tfe tebpermture ia smturmte` wmter vmpiurs, femt (]) gs wgtf`rmwh. Fehke,spekgagk femt ia smturmte` wmter vmpiurs gs helmtgve. (Pfgs gs air yiur ghairbmtgih ihoymh` hit gh tfe kiurse)

(`) Pfe soglft vmrgmtgih ia spekgagk femt ia wmter wgtf tebpermture gs sfiwh gh tfe lrmpf mt =mtbispfere pressure. Gts vmrgmtgih gs oess tfmh=% iver tfe ghtervmo airb : ti =::K.

4.; Teomtgih detweeh [pekgagk femt mh` \mter equgvmoeht>Gt gs tfe mbiuht ia wmter wfgkf requgres tfe smbe mbiuht ia femt air tfe smbe tebpermture rgse mstfmt ia tfe idnekt

bs P 2 b \ [ \ P b \ 2 \sbs

Gh kmoirge s\ 2 = b

\ 2 bs

b w gs mosi represeht dy \si \ 2 bs.

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"bmhgsfcubmrpfysgks.gh" ;

ZFW[GK[

4.0 Zfmse kfmhle >Femt requgre` air tfe kfmhle ia pfmse ir stmte,] 2 bO , O 2 omteht femt.

Omteht femt (O)> Pfe femt suppoge` ti m sudstmhke wfgkf kfmhles gts stmte mt kihstmhttebpermture gs kmooe` omteht femt ia tfe di`y.

Omteht femt ia Ausgih (O a )> Pfe femt suppoge` ti m sudstmhke wfgkf kfmhles gt arib siog` tiogqug` stmte mt gts beotghl pight mh` = mtb. pressure gs kmooe` omteht femt ia ausgih. Omteht femtia ausgih ia gke gs 6: ckmo/cl

Omteht femt ia vmpirgzmtgih (O v )> Pfe femt suppoge` ti m sudstmhke wfgkf kfmhles gt aribogqug` ti vmpiur stmte mt gts digoghl pight mh` = mtb. pressure gs kmooe` omteht femt ia vmpirgzmtgih.Omteht femt ia vmpirgzmtgih ia wmter gs 50: ckmo cl =.

Omteht femt ia gke > O 2 6: kmo/lb 2 6: Ckmo/cl 2 04:: 6: N/cl

Omteht femt ia stemb > O 2 50: kmo/lb 2 50: Ckmo/cl 2 04:: 50: N/cl

Pfe lgveh aglure, represehts tfe kfmhle ia stmtedy `gaaereht oghesIM siog` stmte , MD siog` + ogqug` stmte (Zfmse kfmhle)DK ogqug` stmte , K@ ogqug` + vmpiur stmte (Zfmse kfmhle)@E vmpiur stmte

] 2 bs P

soipe]P

2bs=

]P

[=

wfere bmss (b) ia sudstmhke kihstmht soipe ia P ] lrmpf gs ghverseoy pripirtgihmo ti spekgagkfemt, ga gh lgveh `gmlrmb(soipe) IM 8 (soipe) @Etfeh (s) IM ? (s) @Ewfeh ] 2 bOGa (oehltf iaMD) 8 (oehltf ia K@)

tfeh (omteht femt ia MD) 8 (omteht femt ia K@)

Exmbpoe ;. Agh` tfe mbiuht ia femt reoemse` ga = cl stemb mt 4::K gs kihverte` ghti 4:K gke.[ioutgih > Femt reoemse` ] 2 femt reoemse ti kihvert stemb mt 4:: K ghti =::K stemb + femt reoemse ti

kihvert =:: K stemb ghti =::K wmter + femt reoemse ti kihvert =:: wmter ghti :K wmter + femtreoemse ti kihvert : K wmter ghti 4:K gke.

] 2 = 4=

=:: + 50: = + = = =:: + = 6: + = 4=

4:

2 \feh twi sudstmhkes mt `gaaereht tebpermtures mre bgxe` tiletfer, tfeh exkfmhle ia femt

kihtghues ti tmce pomke tgoo tfegr tebpermtures dekibe equmo. Pfgs tebpermture gs tfeh kmooe`

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"bmhgsfcubmrpfysgks.gh" 0

ZFW[GK[

aghmo tebpermture ia bgxture. Fere, Femt tmceh dy ihe sudstmhke 2 Femt lgveh dy mhitfer sudstmhke

b = s = (P = P b ) 2 b 4 s 4 (P b P 4)

Exmbpoe 0. Mh grih doikc ia bmss 4 cl, amoo arib m feglft =: b. Mater kioog`ghl wgtf tfe lriuh` gt oises 45%eherly ti surriuh`ghls. Pfeh agh tfe tebpermture rgse ia tfe doikc. (Pmce sp. femt ia grih 0 b[ 20=

blf 20Ga idnekts M mh` D mre sepmrmteoy gh tferbmo equgogdrgub wgtf m tfgr` idnekt K , tfeh idnekts M mh` D mre ghtferbmo equgogdrgub wgtf emkf itfer.

Exmbpoe 5. Pfe tebpermture ia equmo bmsses ia tfree `gaaereht ogqug`s M, D, mh` K mre =:K =5K mh` 4:Krespektgveoy. Pfe tebpermture wfeh M mh` D mre bgxe` gs =;K mh` wfeh D mh` K mre bgxe`, gt gs=1K. \fmt wgoo de tfe tebpermture wfeh M mh` K mre bgxe`9

[ioutgih >

wfeh M mh` D mre bgxeb[ = (=; =:) 2 b [ 4 (=5 =;)

;[ = 2 4[ 4 .....(=)wfeh D mh` K mre bgxe`

[ 4 = 2 [ ; 0 ......(4)wfeh K mh`M mre bgxe`

[ =( =:) 2 [ ; (4: ) ....(;)dy usghl equmtgih (=), (4) mh` (;)

we let 2==

=0:K

Exmbpoe 1. Ga tfree `gaaereht ogqug` ia `gaaereht bmsses spekgagk femts mh` tebpermture mre bgxe` wgtf emkf itfer mh` tfeh wfmt gs tfe tebpermture bgxture mt tferbmo equgogdrgub..b =, s =, P = spekgagkmtgih air ogqug`b 4, s 4, P 4 spekgagkmtgih air ogqug`b ; , s ; , P ; spekgagkmtgih air ogqug`.

[ioutgih > Pitmo femt oist ir lmgh dy moo sudstmhke gs equmo ti zeri] 2 :

b =s =(P P =) + b 4s 4(P P 4) + b ; s ; (P P ; ) 2 :

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"bmhgsfcubmrpfysgks.gh" 5

ZFW[GK[

si P 2;;44==

;;;444===

sbsbsbPsbPsbPsb

Exmbpoe Femt requgre` ti kihvert = cl gke mt 4:K ghti = cl wmter mt =::K2 = cl gke mt 4:K ti = cl gke mt :K gke mt :K + = cl wmter

mt :K + = cl wmter mt :K ti = cl wmter mt =::K

2 = 4=

4: + = 6: + = =:: 2 =7: Ckmo. [i F 2 =7: Ckmo

Helmtgve sglh gh`gkmte tfmt =7: Ckmo femt gs wgtf `rmwh arib = cl wmter mt =::K ti kihvert gt ghti= cl gke mt 4:K

Exmbpoe 6. = cl gke mt 4:K gs bgxe` wgtf = cl stemb mt 4::K. Pfeh agh` equgogdrgub tebpermture mh` bgxturekihteht.

[ioutgih > Oet equgogdrgub tebpermture gs =:: K femt requgre` ti kihvert = cl gke mt 4:K ti = cl wmter mt=::K gs equmo ti

F = 2 = 4=

4: + = 6: + = = =:: 2 =7: Ckmofemt reoemse dy stemb ti kihvert = cl stemb mt 4::K ti = cl wmter mt =::K gs equmo ti

F 4 2 = 4=

=:: + = 50: 2 57: Ckmo

= cl gke mt 4:K 2 F = + =cl wmter mt =::K ......(=)= cl stemb mt 4::K 2 F 4 + =cl wmter mt =::K .......(4)dy m` ghl equmtgih (=) mh` (4)= cl gke mt 4:K + = cl stemb mt 4::K 2 F = + F 4 + 4 cl wmter mt =::K.Fere femt requgre` ti gke gs oess tfmh femt suppoge` dy stemb si bgxture equgogdrgub tebpermture gs=::K tfeh stemb gs hit kibpoeteoy kihverte` ghti wmter.[i bgxture fms wmter mh` stemb wfgkf gs pissgdoe ihoy mt =::Kbmss ia stemb wfgkf kihverte` ghti wmter gs equmo ti

b 250:

=::4=

==7: 2

4 Pfe rghl sfiuo` de femte` ti ghkremse gts `gmbeter arib =5.:: kb ti =5.:5 kb.Usghl 4 2 = (= + ),

2 K/=:=4kb::.=5kb:5.:

1 2 4 ms we chiwh tfmt strmgh

strmgh 2 oehltfirglghmooehltfghkfmhle

2:

[trmgh 2 2 =.4 =: 5 (5: 4:) 2 ;.1 =: 0

fere strmgh gs kibpressgve strmgh dekmuse aghmo oehltf gs sbmooer tfmh ghgtgmo oehltf.

Exmbpoe =1. M steeo wgre ia kriss-sektgihmo mrem :.5 bb 4 gs feo` detweeh twi agxe` suppirts. Ga tfe wgre gs nust

tmut mt 4:K, `eterbghe tfe tehsgih wfeh tfe tebpermtureamoos ti :K. Kieaagkgeht ia oghemr expmhsgihia steeo gs =.4 =: 5 /K mh` gts Wiuhls bi`uous gs 4.: =: == H/b 4.[ioutgih > fere aghmo oehltf gs bire tfmh irglghmo oehltf si tfmt strmgh gs tehsgoe mh` tehsgoe airke gs lgveh dy

A 2 MW t 2 :.5 =: 1 4 =:== =.4 =: 5 4: 2 40 H

5.4 Qmrgmtgih ia tgbe pergi` ia peh`uoub koikcs>Pfe tgbe represehte` dy tfe koikc fmh`s ia m peh`uoub koikc `epeh`s ih tfe hubder ia iskgoomtgihperairbe` dy peh`uoub every tgbe gt remkfes ti gts extrebe pisgtgih tfe sekih` fmh` ia tfe koikcm`vmhkes dy ihe sekih` tfmt bemhs sekih` fmh` bives dy twi sekih s wfeh ihe iskgoomtgih ghkibpoete

Oet P 2 4l

O: mt tebpermture : mh` P 2 4 lO mt tebpermture .

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"bmhgsfcubmrpfysgks.gh" 7

ZFW[GK[

PP

2OO

2

O=O

2 = +4=

Pfereaire kfmhle (oiss ir lmgh) gh tgbe per uhgt tgbe ompse` gs

PPP

24=

lmgh ir oiss gh tgbe gh `urmtgih ia 't' gh

t 24= t , ga P gs tfe kirrekt tgbe tfeh

(m) ? : , P ? P koikc dekibes amst mh` lmgh tgbe(d) 8 : , P 8 P koikc dekibes soiw mh` oiise tgbe

Exmbpoe = Pfe tgbe `gaaerehke ikkurre gh 40 fiurs (610:: sekih`s) gs lgveh dy

t 2 4=

t

24=

=.4 =: 1 4: 610:: 2 =.:0 sek. Mhs.

Pfgs gs oiss ia tgbe ms gs lremter tfmh : . Ms tfe tebpermture ghkremses, tfe tgbe pergi` mosighkremses. Pfus, tfe koikc lies soiw.

5.; Bemsurebeht ia oehltf dy betmoogk skmoe>Kmse (g)\feh idnekt gs expmh`e` ihoy

4 2

= {= +

:(

4

=)

= 2 mktumo oehltf ia idnekt mt =K 2 bemsure oehltf ia idnekt mt =K.4 2 mktumo oehltf ia idnekt mt 4K 2 bemsure oehltf ia idnekt mt 4K.: 2 oghemr expmhsgih kieaagkgeht ia idnekt.

=

4

=

4

: 4 ;

Kmse (gg)\feh ihoy bemsurebeht ghstrubeht gs expmh`e` mktumo oehltf ia idnekt wgoo hit kfmhle dutbemsure` vmoue (BQ) `ekremses.BQ 2 = { = [ ( 4 =)}

[ 2 oghemr expmhsgih kieaagkgeht ia bemsurghl ghstrubeht.mt = K BQ 2 ;

=

: 4 ; 0

: = 4 ;

==K

4 K

mt 4 K BQ 2 4.4

Kmse (ggg)Ga ditf expmh`e` sgbuotmheiusoyBQ 2 {= + ( : s ) ( 4 =)(g) Ga : 8 s , tfeh bemsure` vmoue gs bire tfeh tfe mktumo vmoue mt =K(gg) Ga : ? s , tfeh bemsure` vmoue gs oess tfeh tfe mktumo vmoue mt =K

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"bmhgsfcubmrpfysgks.gh" = :

ZFW[GK[

=

4

4

: 4 ; 0

: = 4 ;

= 5

0

=

4

=K

K

K

K

mt =K BQ 2 ;.04K BQ 2 0.=

Bemsure` vmoue 2 kmogdrmte` vmoue {= + }wfere 2 : s

i 2 kieaagkgeht ia oghemr expmhsgih ia idnekt bmtergmo, s 2 kieaagkgeht ia oghemr expmhsgih ia skmoebmtergmo

2 K 2 tebpermture mt tfe tgbe ia bemsurebeht K 2 tebpermture mt tfe tgbe ia kmogdrmtgih.

Air skmoe, true bemsurebeht 2 skmoe rem`ghl S= + ( : )RGa 8 : true bemsurebeht 8 skmoe rem`ghl

? : true bemsurebeht ? skmoe rem`ghl

Exmbpoe =6. M dmr bemsure` wgtf m Qerhger kmogper gs aiuh` ti de =6:bb oihl. Pfe tebpermture `urghl tfebemsurebeht gs =:K. Pfe bemsurebeht errir wgoo de ga tfe skmoe ia tfe Qerhger kmogper fmsdeeh lrm`umte` mt m tebpermture ia 4:K > ( 2 =.= =: -5 K -=. Mssube tfmt tfe oehltf ia tfedmr `ies hit kfmhle.)(M) =.76 =: = bb (D*) =.76 =: 4 bb (K) =.76 =: ; b b (@) =.76 =: 0 bb

[ioutgih > Prue bemsurebeht 2 skmoe rem`ghl S= + ( : )R2 =6: S= =: =.= =: 5 Rerrir 2 =6: =6: S= =.= =: 0 R 2 =.76 =: 4 bb

1. [UZETAGKGMO IT MTEMO EVZMH[GIH\feh m siog` gs femte` mh` gts mrem ghkremses, tfeh tfe tferbmo expmhsgih gs kmooe` superagkgmo ir mremoexpmhsgih. Kihsg`er m siog` pomte ia mrem M : . \feh gt gs femte`, tfe kfmhle gh mrem ia tfe pomte gs`grektoy pripirtgihmo ti tfe irglghmo mrem M : mh` tfe kfmhle gh tebpermture P.

`M 2 M: `P ir M 2 M: P O:O: @O

@O

Osgze ia idnektmt ?= 4

sgze ia idnekt

mt 4

2P M

M

: Uhgt ia gs K= ir C =.

M 2 M: (= + P)wfere M gs mrem ia tfe pomte mater femtghl,

Exmbpoe =7. M pomhe ombghm fms mrem 4b4 mt =:K tfeh wfmt gs gts mrem mt ==:K ts superagkgmo expmhsgih gs4 =: 5 //K

[ioutgih > M 2 M: ( = + ) 2 4 { = + 4 =: 5 (==: =:) }2 4 {= + 4 =: ; } Mhs.

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"bmhgsfcubmrpfysgks.gh" ==

ZFW[GK[

`Q 2 Q: `P ir Q 2 Q: P

2PQ

Q

: Uhgt ia gs K= ir C =.

Q 2 Q: (= + P) wfere Q gs tfe vioube ia tfe di`y mater femtghl

Exmbpoe 4:. Pfe vioube ia lomss vesseo gs =::: kk mt 4:K. \fmt vioube ia berkury sfiuo` de piure` ghti

gt mt tfgs tebpermture si tfmt tfe vioube ia tfe rebmghghl spmke `ies hit kfmhle wgtf tebperm-ture9 Kieaagkgeht ia kudgkmo expmhsgih ia berkury mh` lomss mre =.6 =: 0 /K mh` 7.: =: 1 /Krespektgveoy.

[ioutgih > Oet vioube ia lomss vesseo mt 4:K gs Q l mh` vioube ia berkury mt 4:K gs Q bsi vioube ia rebmghghl spmke gs 2 Q l Q bGt gs lgveh kihstmht si tfmt

Ql Q b 2 Ql Qbwfere Q i ' mh` Qb ' mre aghmo vioubes.

Ql Q b 2 Ql {= + l } Qb {= + Fl } Ql l 2 Qb Fl

Qb 2 0

1

=:6.=

=:7=:: Qb 2 5: kk.

6. TEOMPGIH DEP\EEH , MH@

(g) Air gsitripgk siog`s> > > 2 = > 4 > ; ir =

24

2;

(gg) Air hih-gsitripgk siog` 2 = + 4 mh` 2 = + 4 + ; . Fere = , 4 mh` ; mre kieaagkgeht ia oghemr expmhsgih gh V, W mh` ^ `grektgih.

Exmbpoe 4=. Ga perkehtmle kfmhle gh oehltf gs =% wgtf kfmhle gh tebpermture ia m kudig` idnekt ( 4 ; )tfeh wfmt gs perkehtmle kfmhle gh gts mrem mh` vioube.

[ioutgih > perkehtmle kfmhle gh oehltf wgtf kfmhle gh tebpermture 2 %

=:: 2 =:: 2 =

kfmhle gh mrem

% M 2 M M

=:: 2 =:: 4 ( =::)

% M 2 4 % Mhs.kfmhle gh vioube

% Q 2Q

Q =:: 2 Q =:: 2 ; ( =::)

% Q 2 ; % Mhs.

7. QMTGMPGIH IA @EH[GPW \GPF PEBZETMPUTE Ms we chiwh tfmt bmss 2 vioube `ehsgty .Bmss ia sudstmhke `ies hit kfmhle wgtf kfmhle gh tebpermture si wgtf ghkremse ia tebpermture, vioubeghkremses si `ehsgty `ekremses mh` vgke-versm.

` 2 )P=(` :

.

Air siog`s vmoues ia mre lehermooy sbmoo si we kmh wrgte ` 2 ` : (= P) (usghl dghibgmo expmhsgih).

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"bmhgsfcubmrpfysgks.gh" =4

ZFW[GK[

Hite > (g) air ogqug`s mre gh ir`er ia =: ; .(gg) Mhmbioius expmhsgih ia wmter >

Air wmter `ehsgty ghkremses arib : K ti 0 K si gs helmtgvemh` air 0 K ti fglfer tebpermture gs pisgtgve. Mt 0 K `ehsgtygs bmxgbub. Pfgs mhmbioius defmvgiur ia wmter gs `ue tipresehke ia tfree types ia bioekuoes g.e. F 4I, (F 4I) 4 mh`

(F 4I) ; fmvghl `gaaereht vioube/bmss mt `gaaereht tebpermtures.

. Pfgs mhibmoius defmvgiur ia wmter kmuses gke ti airb agrst mt tfe suramke ia m omce gh kio` wemtfer. Ms wghter mpprimkfes , tfe wmter tebpermture `ekremses ghgtgmooy mt tfe suramke. Pfe wmter tferesghcs dekmuse ia gts ghkremse `ehsgty. Kihsequehtoy , tfe suramke remkfes : : K agrst mh` tfe omcedekibes kivere` wgtf gke.Mqumtgk ogae gs mdoe ti survgve tfe kio` wghter ms tfe omce dittib rebmghsuharizeh mt m tebpermture ia mdiut 0 : K.

Exmbpoe 44. Pfe `ehsgtges ia wii` mh` dehzehe mt :K mre 66: cl/b ; mh` 7:: cl/b ; respektgveoy. Pfe kieaag-kgehts ia vioube expmhsgih mre =.4 =: ; /K air wii` mh` =.5 =: ; /K air dehzehe. Mt wfmttebpermture wgoo m pgeke ia wii` nust sghc gh dehzehe9

[ioutgih > Mt nust sghc lrmvgtmtgih airke 2 uptfrust airke bl 2 A D Q =l 2 Q 4l = 2 4

;=:4.==

66:2 ;=:5.==

7:: 2 6; K

=:. MZZMTEHP EVZMH[GIH IA M OG]UG@ GH M KIHPMGHETGhgtgmooy kihtmgher wms auoo . \feh tebpermture kfmhle dy P,

vioube ia ogqug` Q O 2 Q: (= + O P)vioube ia kihtmgher Q

K 2 Q

: (= +

K P)

[i iveraoiw vioube ia ogqug` reomtgve ti kihtmgher Q 2 QO QK Q 2 Q: ( O K) P

[i, kieaagkgeht ia mppmreht expmhsgih ia ogqug` w.r.t.kihtmgher

mppmreht 2 O K .

Gh kmse ia expmhsgih ia ogqug` + kihtmgher systeb>ga O 8 K oeveo ia ogqug` rgsega O ? K oeveo ia ogqug` amooGhkremse gh feglft ia ogqug` oeveo gh tude wfeh duodwms ghgtgmooy hit kibpoeteoy agooe`

f 2tudeia mremogqug`ia vioube

2 )P4=( M)P=(Q

[:

O:2 f : { = + ( O 4 [ ) P}

f 2 f : { = + ( O 4 [ ) P}wfere f : 2 irglghmo feglft ia ogqug` gh kihtmgher

[ 2 oghemr kieaagkgeht ia expmhsgih ia kihtmgher.

Exmbpoe 4;. M lomss vesseo ia vioube =:: kb ; gs agooe` wgtf berkury mh` gs femte` arib 45K ti Q 2 Q: ( O K) P 2 =:: {=.6 =: 0

; =.6 =: 1

} 5:Q 2 :.6< kb ; Mhs.

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"bmhgsfcubmrpfysgks.gh" = ;

ZFW[GK[

==. QMTGMPGIH IA AITKE IA DUIWMHKW \GPF PEBZETMPUTEGa di`y gs sudberle` kibpoeteoy ghsg`e tfe ogqug`Air siog`, Duiymhky airke A D 2 Q: ` O l

Q: 2 Qioube ia tfe siog` ghsg`e ogqug`,` O 2 `ehsgty ia ogqug`

Qioube ia di`y mater ghkremse gts tebpermture Q 2 Q : S= + [ R ,

@ehsgty ia di`y mater ghkremse gts tebpermture ` O 2 OO

=`

.

Duiymhky airke ia di`y mater ghkremse gts tebpermture, A D 2 Q ` O l ,D

DAA

2 O

[

==

,

ga [ ? O tfeh A D ? AD(Duiymht airke `ekremses) ir mppmreht weglft ia di`y gh ogqug` lets ghkremse`S\ A D 8 \ ADR .

Exmbpoe 40. M di y gs aoimt ghsg`e ogqug` ga we ghkremses tebpermture tfeh wfmtkfmhles ikkur gh Duiymhky airke. (Mssube di`y gs mowmys ghaoimtghl kih`gtgih)

[ioutgih > Di`y gs gh equgogdrgubsi bl 2 Dmh` lrmvgtmtgihmo airke `ies hit kfmhle wgtf kfmhle gh tebpermture. [i Duiymhky airke rebmghskihstmht.Dy ghkremsghl tebpermture `ehsgty ia ogqug `ekremses si vioube ia di`y ghsg`e tfe ogqug ghkremsesti cept tfe Duiymhke airke kihstmht air equmo ti lrmvgtmtgihmo airke)

Exmbpoe 45. Gh prevgius questgih `gskuss tfe kmse wfeh di`y bive iwhwmr`, upwmr`s mh rebmghs mt smbepisgtgih wfeh we ghkremses tebpermture.

[ioutgih > Oet a 2 armktgih ia vioube ia di y sudberle` gh ogqug .

a 2di`yia vioubetitmo

ogqug`ghsudberle`di`yia vioube

a = 2 :=

vv

mt =K

a 4 2 );=(vv

[:

4 mt 4K

air equgogdrgub bl 2 D 2 v =` =l 2 v 4` 4l.

si v 4 2 4==

``v

` 4 2 O=

=`

2 v=(= + O ) a 4 2 );=(v)=(v

s:

O=

wfere 2 4 =Kmse G > Di`y bive `iwhwmr` ga a 4 8 a =

bemhs O 8 ; [Kmse GG > Di`y bive upwmr`s ga a 4 ? a =

bemhs O ? ; [Kmse GGG > Di`y rebmghs mt smbe pisgtgih

ga a 4 2 a =bemhs O 2 ; [

=4. DGBEPMOOGK [PTGZGt twi strgp ia `gaaereht betmos mre weo e` tiletfer ti airb m dgbetmoogk strgp, wfeh femte` uhgairboy gt deh`sgh airb ia mh mrk, tfe betmo wgtf lremter kieaagkgeht ia oghemr expmhsgih oges ih kihvex sg`e. Pfe rm`gus ia mrktfus airbe` dy dgbetmo gs >

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"bmhgsfcubmrpfysgks.gh" =0

ZFW[GK[

: (= + = ) 2

4`

T

: (= + 4 ) 2

4`

T

m4

m=

`

`

:

m m4 =8

Oiwer tebpermture (mt =K)

Ih 45 K:

t

=

4

==

2

4`

T

4`

T

)(`

T=4

T

Fglfer tebpermture (mt 4K)(Iaa) ;: K

:

Dgbetmoogk strrgp

2 kfmhle gh tebpermture2 4 =

M dgbetmoogk strgp, kihsgstghl ia m strgp ia drmss mh` m strgp ia steeo weo`e` tiletfer, mt tebpermture P : gh aglure(m) mh` aglure (d). Pfe strgp deh`s ms sfiwh mt tebpermtures mdive tfe reaerehke tebpermture. Deoiw tfereaerehke tebpermture tfe strgp deh`s tfe itfer wmy. Bmhy tferbistmts ipermte ih tfgs prghkgpoe, bmcghlmh` dremcghl mh eoektrgkmo kgrkugt ms tfe tebpermture rgses mh` amoos.

=;. MZZOGKMPGIH[ IA PFETBMO EVZMH[GIH(m) M sbmoo lmp gs oeat detweeh twi grih rmgos ia tfe rmgowmy.(d) Grih rghls mre sogppe` ih tfe wii`eh wfeeos dy femtghl tfe grih rghls(k) [tipper ia m lomss dittoe nmbbe` gh gts hekc kmh de tmceh iut dy femtghl tfe hekc.

( ) Pfe peh`uoub ia m koikc gs bm`e ia ghvmr Smh mooiy ia zghk mh` kipperR.

=0. PEBZETMPUTEPebpermture bmy de `eaghe` ms tfe `elree ia fithess ir kio`hess ia m di`y. Femt eherly aoiws aribm di`y mt fglfer tebpermture ti tfmt mt oiwer tebpermture uhtgo tfegr tebpermtures dekibe equmo. Mttfgs stmle, tfe di`ges mre smg` ti de gh tferbmo equgogdrgub.

=0.= Bemsurebeht ia PebpermturePfe drmhkf ia tferbi`yhmbgks wfgkf `emos wgtf tfe bemsurebeht ia tebpermture gs kmooe`tferbibetry. M tferbibeter gs m `evgke use` ti bemsure tfe tebpermture ia m di y. Pfe sudstmhkesogce ogqug`s mh` lmses wfgkf mre use` gh tfe tferbibeter mre kmooe` tferbibetrgk sudstmhkes.

=0.4 @gaaereht [kmoes ia Pebpermture M tferbibeter kmh de lrm`umte` ghti aiooiwghl skmoes.(m) Pfe Kehtglrm`e ir Keosgus skmoe (K)(d) Pfe Amfrehfegt skmoe (A)(k) Pfe Temuber skmoe (T)( ) Ceovgh skmoe ia tebpermture (C)

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"bmhgsfcubmrpfysgks.gh" =5

ZFW[GK[

=0.; Kibpmrgsih detweeh @gaaereht Pebpermture [kmoes

Mdsioute zeri

C K A

4:.< -454.5 - 044.5

=75 -

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"bmhgsfcubmrpfysgks.gh" =1

ZFW[GK[

=0.1 Pfe kihstmht-vioube lms tferbibeterPfe stmh`mr` tferbibeter, mlmghst wfgkf moo itfer tferbibeters mre kmogdrmte`, gs dmse` ih tfepressure ia m lms gh m agxe` vioube. Aglure sfiws sukf m kihstmht vioube lms tferbibeter3 gtkihsgsts ia m lms-agooe` duod kihhekte` dy m tude ti m berkury bihibeter.

P 2 (4 Femt requgre` 2 = 4=

=:: 2 5: ckmo

Zridoeb ;. Kmokuomte femt requgre` ti rmgse tfe tebpermture ia = l ia wmter tfriulf =K 9[ioutgih > femt requgre` 2 = =: ; = = 2 = =: ; ckmo 2 = kmo

Zridoeb 0. 04: N ia eherly suppoge` ti =: l ia wmter wgoo rmgse gts tebpermture dy

[ioutgih >4:.0=:04: ;

2 =: =: ; = t 2 =: K

Zridoeb 5. Pfe rmtgi ia tfe `ehsgtges ia tfe twi di`ges gs ; > 0 mh` tfe rmtgi ia spekgagk femts gs 0 > ; . Agh` tfermtgi ia tfegr tferbmo kmpmkgtges air uhgt vioube 9

[ioutgih >4

=2

0;

,4

=

ss

2;0

rmtgi 2/b

sb

4

=2

4

=

s

s

4

=2 = > =.

8/12/2019 Calorimetry & Thermal Expansion Theory_E

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"bmhgsfcubmrpfysgks.gh" = F 2 = 4=

5: + = 50: + = = 5:

2 50: + Cghetgk eherly 24=

5 =: ; 0:: 0::

bs P 2 5 =: ; 5:: PP 2 =1: K

Tgse gh tebpermture gs =1: K

Zridoeb 7. = cl gke mt =:K gs bgxe` wgtf = cl wmter mt =::K. Pfeh agh` equgogdrgub tebpermture mh` bgxturekihteht.

[ioutgih > Femt tmceh dy = cl Gke 2 Femt lgveh dy = cl wmter

= 4=

=: + = 6: + = P 2 = (=:: P)

65 2 =:: 4P 4P 2 =5

24

=52 Femt tmceh dy gke 2 5 Ckmo + 6: Ckmo 2 65 CkmoFemt lgveh dy wmter 2 = = 5: 2 5: CkmoFemt tmceh 8 Femt lgveh si, gke wgoo hit kibpoete beot oet b l gke beot tfeh

= 4=

=: + 6: b 2 5:

6: b 2 05 b 26:05

Kihteht ia bgxture

cl6:05

=gke

cl6:05

=wmter mh` tebpermture gs :K

Zridoeb ==. M sbmoo rghl fmvghl sbmoo lmp gs sfiwh gh aglureih femtghl wfmt wgoo fmppeh ti sgze ia lmp.

[ioutgih >Lmp wgoo mosi ghkremse. Pfe remsih gs smbe ms gh mdive exmbpoe.

Zridoeb =4. Mh gsiskeoes trgmhloe gs airbe` wgtf m tfgh ri` ia oehltf = mh` kieaagkgeht ia oghemr expmhsgih =, mstfe dmse mh` twi tfgh ri s emkf ia oehltf 4 mh` kieaagkgeht ia oghemr expmhsgih 4 ms tfe twi sg`es.Ga tfe `gstmhke detweeh tfempex mh` tfe bg pight ia tfe dmse rebmgh uhkfmhle` ms tfe tebpermture

gs vmrge` sfiw tfmt4= 2 4

=4 .

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"bmhgsfcubmrpfysgks.gh" =6

ZFW[GK[

[ioutgih > 444

=

4

444

=4

4

: 2 `P`

4`P`

4=

44

44==

P4

===

2 4 4 4 4 P 4

4

4=

2 0=

4

4

=2 4

=

4.

Zridoeb =;. M kihkrete somd fms m oehltf ia =: b ih m wghter hglft wfeh tfe tebpermture gs :K. Agh` tfe oehltfia tfe somd ih m subber `my wfeh tfe tebpermture gs ;5K. Pfe kieaagkgeht ia oghemr expmhsgih ia kihkrete gs =.: =: 5 /K.

[ioutgih > t 2 =:(= + = =: 5 ;5)

2 =:.::;5 b

Zridoeb =0. M steeo ri gs kombpe` mt gts twi eh`s mh` rests ih m agxe` firgzihtmo dmse. Pfe ri gs uhstrmghe` mt4:K. Agh` tfe oihlgtu ghmo strmgh `eveoipe gh tfe ri` ga tfe tebpermture rgses ti 5:K. Kieaagkgeht ia oghemr expmhsgih ia steeo 2 =.4 =: 5 /K.

[ioutgih >:

: 2 ;.1 =: 0

Zridoeb =5. Ga ri` gs ghgtgmooy kibpresse` dy oehltf tfeh wfmt gs tfe strmgh ih tfe ri` wfeh tfe tebpermture(m) gs ghkremse` dy (d) gs `ekremse` dy .

[ioutgih> (m) [trmgh 2 + (d) [trmgh 2

Zridoeb =1. M peh`uoub koikc fmvghl kipper ri` ceeps kirrekt tgbe mt 4:K. Gt lmghs =5 sekih s per `my ga kiioe` ti :K. Kmokuomte tfe kieaagkgeht ia oghemr expmhsgih ia kipper.

[ioutgih >1:1:40

=5 2

4=

4: 2;1::=1=

2 =.< =: 5 /K

Zridoeb = t 2 = (= =.= =: 5 =:) 2 :.77767 kb

Zridoeb =6. M uhgairb siog` drmss spfere gs ritmtghl wgtf mhluomr spee` : mdiut m `gmbeter. Ga gts tebpermture gshiw ghkremse` dy =::K. \ fmt wgoo de gts hew mhluomr spee`. (Lgveh D 2 4.: =: 5 perK)

(M) ::4.:=: (D) ::4.:=

: (K*) ::0.:=: (@) ::0.:=

:

[ioutgih > : : 2 t tBr :

4: 2 Br :

4 (= + 4 P) t

t 2 ::0.:=: .

Zridoeb =7. Pfe vioube ikkupge` dy m tfgh - wmoo drmss vesseo mh` tfe vioube ia m siog` drmss spfere mre tfesmbe mh` equmo ti =,::: kb ; mt :K. Fiw bukf wgootfe vioube ia tfe vesseo mh` tfmt ia tfe spferekfmhle upih femtghl ti 4:K 9 Pfe kieaagkgeht ia oghemr expmhsgih ia drmss gs 2 =.7 =: -5.

[ioutgih > Q 2 Q: ; P 2 =.=0 kb ;=.=0 kb ; air ditf

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"bmhgsfcubmrpfysgks.gh" =7

ZFW[GK[

Zridoeb 4:. M tfgh kipper wgre ia oehltf O ghkremses gh oehltf dy =% , wfeh femte` arib tebpermture P = ti P 4.\fmt gs tfe perkehtmle kfmhle gh mrem wfeh m tfgh kipper pomte fmvghl `gbehsgihs 4O O gs femte`arib P = ti P 4 9(M) =% (D) ;% (K) 0% (@*) 4%

[ioutgih > Oa 2 O (= + t ) OOa =:: 2 (= + t) =:: 2 =%

Ma 2 4O O (= + 4 t) OO4

Ma =:: 2 (= + 4 t) =:: 2 4%

Zridoeb 4=. Pfe `ehsgty ia wmter mt :K gs :.776 l/kb ; mh` mt 0K gs =.::: l/kb ; . Kmokuomte tfe mvermlekieaagkgeht ia vioube expmhsgih ia wmter gh tfe tebpermture rmhle : ti 0K.

[ioutgih > ` t 2 t=` : = 2 0=

776.: 2 5 =: 0 / : K

Zridoeb 44. M lomss vesseo bemsures exmktoy =: kb =: kb =: kb mt :K. gt gs agooe` kibpoeteoy wgtf berkurymt tfgs tebpermture. \feh tfe tebpermture gs rmgse` ti =:K, =.1 kb ; ia berkury iveraoiws. Kmoku-omte tfe kieaagkgeht ia vioube expmhsgih ia berkury. Kieaagkgeht ia oghemr expmhsgih ia lomss 2 1.5 =: 1 /K

[ioutgih > Q 2 QFl Q Q=.1 2 =:

;

=: =:;

; 1.5 =: 1

=: O 2 (=.1 + :.=75) =: 0 2 =. B ? si, DD

AA

2 R=SR=S [

DD AA

si Mppmreht weglft ghkremsessi, \ 4 8 \ =

Zridoeb 40. Gh aglure wfgkf strgp drmss ir steeo fmve fglfer kieaagkgeht ia oghemr expmhsgih.

[ioutgih > Drmss [trgp

Zridoeb 45. Pfe upper mh` oiwer agxe` pights ia m amuoty tferbibeter mre 5K mh` =:5 K . a tfe tferbibeter rem`s 45 K , wfmt gs tfe mktumo tebpermture 9

[ioutgih >=::

: K=::

545

K 2 4: K

Zridoeb 41 Mt wfmt tebpermture gs tfe Amfrehfegt skmoe rem`ghl equmo ti twgke ia Keosgus 9

[ioutgih >=6:

;4A2

=:::K

=6:;4x4

2=::

:x

=:x =1: 2 7xx 2 =1: K

Zridoeb 4=6:

;4A2

=:::0:

A 2 =:0 A

8/12/2019 Calorimetry & Thermal Expansion Theory_E

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