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Laword/settings.xmlPK-!J؊Nword/webSettings.xmlPK-!6)!9;word/styles.xmlPK-!L *word/numbering.xmlPK-!X=edocProps/core.xmlPK-!f B`word/fontTable.xmlPK-!ZdocProps/app.xmlPKKKV Lud@Kg2!Microsoft Office Word dokumentum MSWordDocWord.Document.129q`Lud@Kg24vMicrosoft Office Word dokumentumC:\Documents and Settings\Keszei Ernoe\Local Settings\Temporary Internet Files\Content.Outlook\ETGXKZV5\Problems.docITEM000ODS`ITEM000FMT ITEM000FMT#3 FA5A5Ole #3Rich Text Format>^tnOlePres000.uITEM000FMTRich Text Format8Cn      !"#$%&'()*+,-./0123456789:;<DEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~>^t v&" WMFC| l5V>^ EMF!h   WRp@GaramonddRO`2d\̞H$O`2d\ q.1\d "r.1  X'9Garamodt$X\-'1̝̝z%1"dv% % % Rp@GaramonddRO`2d\̞H$O`2d\ q.1\d #r.1  X'9Garamod2-'1̝̝z%1#dv% % %  % % %  TKbt@@O LW`Problem 2.')#?#TdLbt@@LOLWT/a. )$% % % THft@@O*LWThe energy of a particular gaseous system 9/&&/&)&/%/%&-%)%"&/-""%"&GTV ft@@O LW`was found=%"/-/.TTW u ft@@W OLWP Tv ft@@v OLWto obey the following equation/./&&/&/.=/)&--%//TT ft@@ OLWP TT "ft@@ OLWPu-Tl#ft@@#OLWXnder /.& Th{t@@LWpcertain conditions&&%/&//../"TT|ht@@|LWP:TTht@@LWP ) !WF(GDIC!b K!b     @  !% %     Rp@Garamond!%wQ4:\'X'%p!1g|$fL%5 !UV!=5 !25 !50$e   sf wpde |`|]||dv% ( % % 0 % K( % % " % ( " " FGDIC" % % % TTt@@mLWP ) T  /t@@#LWThe system is taken through a cycle9/&"&!&G"%+&///-(/%&&&'TT '/t@@ LWP T(/t@@(LW(represented by the contin&/&"&/&./&.&&///TT /t@@LWPu-T  /t@@ LWtous straight line in/-""%)//&.TT  /t@@ LWP T` 1 /t@@ LWTthe/&TT2 M /t@@2 LWP TTN r /t@@N LWPfTxl J /t@@l LW\igure),)-&TTK f /t@@K LWP Tg /t@@g  LW`beginning /&)///( T&" WMFC `0t@@LWTand%/.TT0t@@LWP Tx0t@@LW\ending &/./)T0t@@LWhat the point A%/&.//>TX0t@@LWP. T0t@@ LW`Calculate9%&-%&TT0#t@@LWP )Rp@Garamond< RO`2$O`2 q.1 $r.1  X'9Garamod;4:.1̜-'1z%10$dv% % % Rp@"Arial<  RO`2 $O`2 q.1 &r.1X3.* ArialԜ ~2̜-'1z%10 &dv% % %  % % % TXt@@LWPa), % % % TT+t@@LWP J% % % Tx,t@@,2LWthe internal energies at the points A, B, C and D;/&/&/%&/%)&"%/&.//">9:%/.GTTt@@LWP )!W"  % % % TXdt@@MLWPb)3 % % % TT+at@@MLWP C% % % T, dt@@,M?LWthe value of heat and work for all four processes of the cycle;/&+%-&//&%%/.=.+/%/,//&&""%"./&%&&&TT  dt@@ MLWP )!W"  % % % TXet@@LWPc)+ % % % TT^+t@@LWP K% % % TX,et@@,WLWand the value of heat and work, while the system undergoes the process between C and B %/.*/&*+%-&*/*/&%*%/-*=/+*=/&*/&*"%"&G*,/.&)/&"*/&*//&%""*/&<&&/*:*%/.*8!W" Rp@GaramonddRO`2d\̞H$O`2d\ q.1\d 'r.1  X'9Garamod2\-'1̝̝z%1'dv% % %  % % % T, 2t@@,LWtalongside the dashed%//)".&/&.$"/&.TT #2t@@ LWP T$2t@@$ LW`hyperbola /&/&./%% % % TT2t@@LWPh&% % % TT2t@@LWP TT 2t@@,LWthat is described by the following equation:/%".%"&/&./&/%//=/)&--%./TT  2t@@ LWP )!W"  !WF(GDICZci!b K!b    ` \e  f!% %     Rp@Garamond!%w !%w:2w!%w ҹ! 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LPRnTTcQ(?+?<LPnTTQ 4(?+?LPUTTQ(?+?LPnTT 4(?+?LPVTX>n(?+?aLPRnTTL{n(?+?5LPSRp "Systemd|eA|H]| v5 !Sn!5 !m5 !=5 !35 !25 !$edfe |`|]||dv% ( % % 0 % K( ( ( % % " % ( " " FGDIC" % % % TT  nt@@ WLWP ) T|5}t@@fLW\Prove th4/+&/T6}t@@6fLWe validity of the statement.&+%.%//%"%&G&/TT}t@@fLWP TT}t@@fLWP(TTW}t@@fLWPC:TXP}t@@Xf LWhheck whether /&&+=/&/&TQ }t@@Qf LWdthe equation/&&--%//TT & }t@@ fLWP T'  }t@@' fLW|meets all those requiremG&&"%/."&&,-&GT }t@@ fLWlents concerning &/"&//&&/.( T~d t@@BLWthe entropy that are imposed by the postulates of thermodynamics)./&&/./&/%%&G/."&-/&/&/."-%&"//&G..&/%G&"TTe ~z t@@e LWP TT{ ~ t@@{ LWP ) TDLt@@5)LW                                         \\\[\\[\\[[\\\[\\[\\[[\\\[\\[\\[[\\\[\\[[TTLt@@5LWP )Rp@GaramondpԛTRO`2ԛ̘<$O`2ԛ̘ q.1̘ԛ ,(r.1  X'9Garamod41-'1<<z%1d,(dv% % % % % %  % % % T|[#t@@LW\Problem .')#?TT$[Ft@@$LWP3#TTG[ot@@GLWP/)TTp[t@@pLWPa$TX[t@@LWP. % % % TTMt@@LWPT9TMIt@@ LW`here are t/&&%&TIM=t@@J LWhwo containers=/&//%/&"TT>MQt@@>LWP,TTRMkt@@RLWP T kM t@@l#LWA and B, having the same volume of >%/.9/%+/)/&"%G&+/-G&/TT M t@@ LWP2+TT M t@@ LWP TT M9 t@@ LWPmG% % % TT: UT t@@: LWP3% % % TU Mt@@U LW, and they are both filled %.&" WMFC ./&&%&///&- Tt@@LWwith a monatomic ideal ga=/%G//%/G&.&%)%T(t@@LWs. The containers are separated"9/&&//%/&"%&"&/%%&.TT)Gt@@)LWP TH t@@HLWlfrom each other/G&%&///&TT  t@@ LWP T t@@ LWby a rigid and adiabatic wall/&%(.%/.%.%/%&=%TXt@@LWP;  Tt@@jjLW and a wall disallowing the transport of every possible extensive quantities separates the containers from %/. % =% ."%/=/) /% %/"/. / &+&& /.""/& %*&/"+& --%.&! "&/%%%! /& &/.%/&! /F Tt@@LWptheir environment/&&/+/.G&/T7 t@@6LW. The container A holds 3 moles, the container B holds9/&&//%/&>//."+G/&"/&&//%/&9//-"TT8 P t@@8 LWP TQ  t@@Q LWt5 moles of the gas. +G/&"//&)%"TT E t@@ LWPC:TF t@@F  LWdontainer A //%/&> TL Ot@@8ULWinitially has a temperature of 600 K and the total energy in the composite system is /%&/%"%&G/%%-&.+++D%/./&/%&/&)&//&&/G./"&"&"%G"TT  Ot@@ 8LWP3+Tl S Ot@@ 8LWX5 kJ.*+TTT | Ot@@T 8LWP ) % % % TXPt@@LWPa), % % % TTI+t@@LWP J% % % Td,P t@@,YLWCalculate the internal energies of the two subsystems and the temperature of container B.:%&-%&/&/&/%&/&)&"//&=/"-."&"&F"%../&&G/%%-&.&//%.&9TT P t@@ LWP )!W"  % % % TXt@@LWPb)3 % % % TT+t@@LWP C% % % TD,t@@,)LWCalculate the pressure in the two contain:%&-%&/&/&"",&//&=/&//%/TdKt@@LWTers.&"TTLtt@@LLWP )!W"  % % % TXt@@nLWPc)+ % % % TT+t@@nLWP K% % % Td+t@@,nYLWWhat would be the temperature of the system, if we would let the wall separating the two Q/%+=/-.+/%+/&*&G/%%-&+.+/&+"%"&G++=%+=/-.+&+/&+=%*"&/%%/)+/&*=.!W"  T,t@@,LWcontainers be diathermal?&//%/&"/&.%/&G%"TTt@@LWP T t@@8LWHow would the pressure change in each of the containers?E/==/-./&.&!"-&&/%.)&/&%&///&&/.%/&!!TT  t@@ LWP )!W"  % % % TXSt@@<LWPd)3 % % % TT+Pt@@<LWP C% % % T(+ St@@,<OLWWhat would be the pressure in the two containers, if we would let the wall sepaQ&WMFC /% =/-. /& /& .&!"-& / /& =/ &/.%/&" =& =/-. & /& =% "&/%T St@@ <LWlrating them be %/) /&G .%!W"  T,Tt@@,^LWflexible? How would this affect the tempreature measured in the two subsystems, and how would &*/&"E/==/-./"$&&/&&G.&%-&G&%!-%.//&</",/"%"&F"%..//==/--!W"  T$,Z!t@@, $LWthe volume of the containers change?/&+/-G&./&&/.%/&!&/%/)&"TT[!t@@[ LWP )!W"  % % % TX"t@@qLWPe)+ % % % TT+t@@qLWP K% % % T|+"t@@,q]LWWhat would be the common temperature and pressure of the two subsystems, if we would let the Q/%=/-./&/&&/GG./&G/&%-&%/./%"",&//&=/"-."&!&G"=%=/-.&/&!W"  % % % T+t@@,LWpwall be diatherma=%/&.%/&G%TXt@@LWPl % % % T`Ct@@LWTand%'%% % % TT;Qt@@;LWP TRt@@RLWflexible at the same time?&*.&%/&"%G&G&!TTt@@LWP )!W"  TDVt@@?)LW                                         \\\[\\[\\[[\\\[\\[\\[[\\\[\\[\\[[\\\[\\[[TTVt@@?LWP )% %    .@Garamond---@Garamond------ 2   Problem 2 2 8 /a. ---J2 M* The energy of a particular gaseous system  2 U  was found  2   82  to obey the following equation  2 X   2 ] u2 e nder e&2 ! certain conditions 2 !l : 2 !o  , ,--.  @Garamond- .Garamond- 2 Bp. 2 BlJ 2 Bg  2 BY10 2 B&5Garamond- 2 ;E2Symbol- 2 BN+ 2 B= Garamond- 2 B-PV 2 B U "System------'"System-'''--- 2 Bw  @2 a# The system is taken through a cycle   2 a  22 a (represented by the contin 2 a u)2 a ous straight line in 2 a  2 a the 2 a   2 a f2 a igure),  2 a@  2 aE  beginning 2 s and 2 s  2 s ending  2 sF at the point A 2 s . 2 s  Calculatei  2 s  @Garamond---@"Arial------2  a)--- 2 &   ---V2 32 the internal energies at the points A, B, C and D;     2 X  , '---2  b) --- 2 '   ---j2 3? the value of heat and work for all four processes of the cycle;  2   , '---2  c)--- 2 &   ---2 3W and the value of heat and work, while the system undergoes the process between C and B       , '@Garamond------)2 3 alongside the dashed 2   2  hyperbola --- 2  h--- 2   M2 , that is described by the following equation:  2   , ', ,--.  @Garamond- .- 1M- 0eGaramond- 2 f; 2 \4 2 2dm 2 IkPa 2 F  2 ?4 2 ;. 2 40Garamond-  2 G3Symbol-  2 Q- 2 #= Garamond-  2 7V 2 P "System-  ---   --'-'''--- 2 l  ------2 # d) --- 2 #'   ---[2 #35 and a parametric equation of all the adiabats in the r --- 2 #f P 2 #n  2 #v V --- 2 #  2 # plane. 2 #  , ', ,--.  @Garamond-- - %- -  - - %"0- -  - - -- 88CBBCBC- - - -  - - -- ;8- - - -  Garamond- "System-- -Garamond- . 2 0.4?--- -- ;8- -- - -- -- ;8- -- - - -- -Garamond- . 2 0.1B--- -- $MMLLM- -- - Garamond----Garamond- . 2 ]k -----Garamond- . 2 ]P -----Garamond- . 2 ]a-Garamond----Garamond- . 2 FP--- -- $- -- - Garamond----Garamond- . 2 !3%-----Garamond- . 2 )d%-----Garamond- . 2 )m&-----Garamond- . 2 V%--- -- ;8BAABBBAABBBAABBBAABBAABBA- -- - -- -- ;8- -- - -- -- ;8- -- - - -- -Garamond- . 2 2--- -- 8BAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABBBAABB- -- - - -- -Garamond- . 2 >5-- -- -Garamond- . 2 8-Garamond----Garamond- . 2 A-----Garamond- . 2 B-----Garamond- . 2 DC-----Garamond- . 2 D--- -- 8 #!CAAAAAAAAAAAAAAAAACCCCCCCCCCCCCCCCCDBBBBBBBBBBBBBAACCCCCCCCCCCCDDDFDDDDDDDDCCCCCCCCDDDDEEEEEEEEEFFFIHHGGGGGFFFFFFFEGGGGGGHHHHHIIIIMLLLLKKKKJJJJIIKKKKKLLLLMMMMMSRRRQQPPPOOONNOPPPQQQRRRSSSZYYYXXWWVVUUUVVWWWXXYYZZZcbbaa``_^^]]\\]]^^__``abbcclkkkjiihggfeeffgghiijkkllvvuutsrrqpooppqqrsttuvv~~}|{zzz{{|}~- -- - Garamond----Garamond- . 2 Qh----   --'-'''--- 2 ,  I2 D)  2 D|  ---2 V Problem   2 V2 22 V8 /b2 VF . ---2 VM  Later on, in  2 V  Chapter 10,n  2 V  2 V by the i2 V  ncorporati2 VS on ofe 2 Vu  2 Vz quan)2 V tum consdierations,  2 V  we shall  2 VH statee 2 Vd  2 Vi that e---@2 i# the following equation (namely, the   2 i  ---2 i Sackur 2 i 2 i Tetrodei --- 2 i-  2 i0 equation 2 id ) 2 ii  &2 im is fundamental for  2 i  ,2 i a monatomic ideal gas:   2 ig  , ,--.  @Garamond- .- - {/(- HQluGaramond- 2 . 2 3 2 4 2 ln 2 m3 2 m5 2 I2 2 I3 2 lnGaramond- 2 2Garamond-  2 ,2 2 (3Symbol- 2  2  2  2  2 d 2 d 2 d 2 d 2  2  2  2  2  2  2 x+ 2 <+ 2 2 2 2 2 2 2 2 2  2  2  2  2 ! 2 ! 2 ! 2   2   2   2 =Garamond-  2 h 2 m Garamond- 2 Garamond-  2 SRn  2 n 2 U 2 n 2 V 2 Rn  2 S"System- ---  --'-'''--- 2   2  Prove th 52 4 e validity of the statement.  2    2  ( 2  C 2   heck whether  2 =  the equation 2   /2  meets all those requirem  #2 ! ents concerning n2 B the entropy that are imposed by the postulates of thermodynamics).    2    2   I2 )  2 |  @Garamond---------2  Problem   2 1 3 2 7 / 2 > a2 D . --- 2 L T 2 U  here are t2   wo containers  2  , 2   @2 # A and B, having the same volume of     2  2 2    2  m --- 2  3---42  , and they are both filled .12  with a monatomic ideal gad   :2  s. The containers are separated  2 b  "2 g from each other  2   72  by a rigid and adiabatic walle 2 | ; 2 &j and a wall disallowing the transport of every possible extensive quantities separates the containers from    %2 8 their environment \2 8m6 . The container A holds 3 moles, the container B holds     2 8  )2 8 5 moles of the gas.   2 86 C 2 8?  ontainer A  2 KU initially has a temperature of 600 K and the total energy in the composite system is      2 K 32 K 5 kJ.e 2 K  ---2 ] a)--- 2 ]&   ---2 ]3Y Calculate the internal energies of the two subsystems and the temperature of container B.      2 ]K  , '---2 p b) --- 2 p'   ---I2 p3) Calculate the pressure in the two contain  2 p( ers. 2 p<  , '---2  c)--- 2 &   ---2 3Y What would be the temperature of the system, if we would let the wall separating the two        , '12 3 containers be diathermal?  2   _2 8 How would the pressure change in each of the containers?    2 /  , '---2  d) --- 2 '   ---2 3O What would be the pressure in the two containers, if we would let the wall sepa     "2 & rating them be  , '2 3^ flexible? 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\insrsid13120051 The system is taken through a cycle (represented by the continuous straight line in the figure), beginning and ending at the point A. 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The containers are separated from each other by a rigid and adiabatic wall; and a wall disallowing the transport of every possible extensive quantities separates the containers from their environment. The container A holds 3 moles, the container B holds 5 moles of the gas. C ontainer A initially has a temperature of 600 K and the total energy in the composite system is 35 kJ. \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 a)\tab}}\pard \ltrpar\qj \fi-360\li720\ri0\widctlpar \jclisttab\tx720\wrapdefault\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0\pararsid13120051 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 Calculate the internal energies of the two subsystems and the temperature of container B. \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 b)\tab}Calculate the pressure in the two containers. \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 c)\tab} What would be the temperature of the system, if we would let the wall separating the two containers be diathermal? How would the pressure change in each of the containers? \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 d)\tab}What would be the pressure in the two containers, if we would let the wall sepa rating them be flexible? 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\ltrch\fcs0 \i\insrsid13120051 b}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 , and }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 c}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 positive real constants. Show how you can use this equation in order to calculate the thermodynamic quantities }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 T}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 p}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\f434\insrsid13120051 \'ec}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 F}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 and }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 C}{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\sub\insrsid13120051 V}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 of the system. \par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 5/a}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 We are consuming electric energy from t he power company that we use to provide heating to our appartement having a temperature of 25 \'b0C in an environment of \endash 2 \'b0C . Show that at which factor we can improve our cost-benefit ratio if we use the energy to drive a reverse Carnot engine rather than to produce Joule heat. \par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 5/b}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 The so-called air-standard }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051\charrsid1123785 Otto cycle}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 is a rough approximation model of the gasoline engines of cars. In an Otto cycle the working fluid (which we would now consider as a monatom ic ideal gas) is \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 a)\tab}}\pard \ltrpar\qj \fi-360\li720\ri0\widctlpar \jclisttab\tx720\wrapdefault\aspalpha\aspnum\faauto\ls3\adjustright\rin0\lin720\itap0\pararsid13120051 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 first compressed adiabatically; \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 b)\tab}then it is heated at constant volume; \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 c)\tab}then it is expanded adiabatically; \par {\listtext\pard\plain\ltrpar \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \b\f39\fs22\lang1038\langfe1038\langnp1038\langfenp1038\insrsid13120051 \hich\af39\dbch\af0\loch\f39 d)\tab}and finally it is cooled down isochorically to the initial state. \par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par Illustrate the operation of the Otto cycle by plotting its }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051\charrsid13640175 P\endash V}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 and }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051\charrsid13640175 T\endash S}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 diagrams. 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\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{ \rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 6/a}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 By using a pycnometer, we have measured the density of 60 and 82.5 g/dm}{\rtlch\fcs1 \af0 \ltrch\fcs0 \super\insrsid13120051 3}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 aqueous NaCl solutions at 25 \'b0C. The measured densities were 1.0315 and 1.0463 g/cm}{\rtlch\fcs1 \af0 \ltrch\fcs0 \super\insrsid13120051 3}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 , respectively. Calculate the partial molar volume of NaCl and of water in the solution! \par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 6/b}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 We have to gas containers, one containing 1 g of protiu m, the other 1 g of deuterium. If we open the valve separating the containers, the two gases would be mixed. Calculate the change of entropy! \par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 6/c}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 We have a thermodynamic system containing two components, A and B, }{\pard\plain \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \f39\fs22\lang1038\langfe1038\cgrid\langnp1038\langfenp1038\insrsid13120051 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\emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 7/a}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 The equilibrium vapor pressure over a single component fluid was found to be 0.2 atm at 300 K. Assuming that the vapor can be treated as an ideal gas, and that its density is much less than the density of th e fluid, estimate the temperature at which the equilibrium vapor pressure would be doubled. The heat of vaporization is 40 kJ/mol. \par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 7/b}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 . }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 Sketch the phase diagram of methanol at the vicinity of its triple point (}{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 T = }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 175.610 K, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \i\insrsid13120051 p}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 = 0.0002 Pa by making use of the 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\b\fs18\insrsid13120051\charrsid9648051 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 The melting points of}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 the}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 pure }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 compounds A and B}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 are 1}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 20}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 K and 1}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 50}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 K}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 , respectively}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 . The two substances}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 undergo a chemical reaction in both solid and liquid phases, to}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 form a compound }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 AB:}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 \par }\pard \ltrpar\qc \li0\ri0\sb120\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 {\pard\plain \ltrpar \qc \li0\ri0\sb120\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \f39\fs22\lang1038\langfe1038\cgrid\langnp1038\langfenp1038\insrsid13120051\charrsid9648051 {\object\objemb\objw1240\objh260{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000 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{\pict{\*\picprop\shplid1043{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}} {\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}} {\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}} \picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2187\pich459\picwgoal1240\pichgoal260\wmetafile8\bliptag1005112271\blipupi-2205{\*\blipuid 3be8cbcfc7b0d39031813963a6145809} 010009000003e200000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02 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\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13120051 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 The melting point of the }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 AB compound}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 is }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 140}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 K. The reacting system has two eutectic points at atmospheric pressure, one at the absolute mole fraction of }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 A}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 of 0.25 (1}{ \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 10}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 K) and another at 0.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 8}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 0 (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 90}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051\charrsid9648051 K). 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At the given temperature, the vapor pressure of pure A and B are 120.1 kPa and 89.0 kPa, respectively. Prove that the solution is ideal and calculate the composition of the vapor as boiling begins. \par \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 8/a}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 .}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid9648051 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 The equilibrium constant of a particular chemical reaction was found to obey the following formula in the close vicinity of }{\pard\plain \ltrpar \qj 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\emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13120051 \par }{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051 Problem 8/b}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid15751010 .}{\rtlch\fcs1 \af0\afs18 \ltrch\fcs0 \b\fs18\insrsid13120051\charrsid9648051 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \insrsid13120051 The equilibrium constant of a particular chemical reaction gets doubled if we elevate the temperature from 200 K to 300 K. 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