Gas Mixtures
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Thermodynamics II Section 3 Class 2006/2
Exercises No.
2
Chapter
Gas Mixtres
Topic
!ll
Start "ate
20/##/2006
Exchan$e "ate
2%/##/2006
S&mit "ate
'/#2/2006
Ex.no..
10, 13, 15, 16, 30, 34, 36, 37 46, 48, 49, 50, 55, 57, 58, 62
Exercises No.
กล ม ตรวจ
Grop No.
#st
2nd
3rd
'th
(th
#
10
34
36
48
55
6
2
13
30
37
49
57
%
3
15
16
46
50
58
)
'
15
16
37
50
62
#
(
10
34
36
48
55
2
6
13
30
37
49
57
3
%
10
34
36
48
58
'
)
13
30
37
49
62
(
Cengel, Y.A., and Bles, M.A.,!"#$M%&Y'AM(C) *An #ngineering A++ra- , A++ra- , 5t- #d.
Gas Mixtures
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Cengel, Y.A., and Bles, M.A.,!"#$M%&Y'AM(C) *An #ngineering A++ra , 5t #ditin in )( unit,MGra/"ill, 2006. Source:
re+ared * Ass.r.)ai ri+re,-&.
rles designated a C are ne+t uestins, and students are enuraged t anser t-e all. rles it- a C&/##) in are sled using ##). rles it- a +uter/##) in are +re-ensie in nature, and are intended t e sled it- a +uter, +reeral using t-e ##) stare.
Composition o* Gas Mixtres 13-1C What is the a++arent gas nstant for a gas mixture? Can it be larger than the largest gas onstant in the mixture? 13-2C Consi!er a mixture of t"o gases# Can the a$$arent molar mass of this mixture be !etermine! b% sim$l% ta&ing the arithmeti a'erage of the molar masses of the in!i'i!ual gases When "ill this be the ase? 13-3C What is the a++arent lar ass for a gas mixture? (oes the mass of e'er% moleule in the mixture e)ual the a$$rent molar mass? 13-4C Consi!er a mixture of se'eral gases of i!ential masses# Will all the mass frations be i!ential? *o" about the mole frations? 13-5C +he sum of the mole frations for an i!eal-gas mixture is e)ual to 1# ,s this also true for a real-gas mixture? 13-6C What are mass an! mole frations? 13-7C sing the !efinitions of mass an! mole frations. !eri'e a relation bet"een them# 13-8C /omebo!% laims that the mass an! mole frations for a mixture of C2 an! 20 gases are i!ential# ,s this true? Wh%? 13-9C Consi!er a mixture of t"o gases A an! B. /ho" that "hen the mass frations A an! B are &no"n. the mole fration an be !etermine! from ## ## 13-10 +he om$osition of moist air is gi'en on a molar basis to be 78 $erent 2. 20 $erent 02. an! 2 $erent "ater 'a$or# (etermine the mass frations of the onstituents of air# 13-11 gas mixture has the follo"ing om$osition on a mole basis 60 $erent 2 an! 40 $erent C2. (etermine the gra'imetri anal%sis of the mixture. its molar mass. an! gas onstant# 13-12 e$eat rob# 13-11 b% re$laing 2 b% 02# 13-13 gas mixture onsists of 5 &g of 0 2. 8 &g of 2# an! 10 &g of C2. (etermine a: the mass fration of eah om$onent. : the mole fration of eah om$onent. an! : the a'erage molar mass an! gas onstant of the mixture# 13-14 (etermine the mole frations of a gas mixture that onsists of 75 $erent C*4 an! 25 $erent C2 b% mass# lso. !etermine the gas onstant of the mixture#
Gas Mixtures
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13-15 gas mixture onsists of 8 &mol of * 2 an! 2 &mol of 2# (etermine the mass of eah gas an! the a$$arent gas onstant of the mixture# Ansers* 16 &g. 56 &g. 1#155 &&g # 13-16 gas mixture onsists of 20 $erent 2. 30 $erent 2# an! 50 $erent C2 on mass basis# (etermine the 'olumetri anal%sis of the mixture an! the a$ $arent gas onstant#
P-v- T
+eha,ior o* Gas Mixtres
13-17C ,s a mixture of i!eal gases also an i!eal gas? :i'e an exam$le# 13-18C ;x$ress (alton
Gas Mixtures
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13-34 0#3-m3 rigi! tan& ontains 0#6 &g of 2 an! 0#4 &g of 02 at 300 # (etermine the $artial $ressure of eah gas an! the total $ressure of the mixture# Ansers* 178#1 &a# 103#9 &a. 282#0 &a 13-35 gas mixture at 350 an! 300 &a has the follo"ing 'olumetri anal%sis 65 $erent 2. 20 $erent 02. an! 15 $erent C2# (etermine the mass fration an! $artial $ressure of eah gas# 13-36 rigi! tan& that ontains 1 &g of 2 at 25=C an! 300 &a is onnete! to another rigi! tan& that ontains 3 &g of 2 at 25=C an! 500 &a# +he 'al'e onneting the t"o tan&s is o$ene!. an! the t"o gases are allo"e! to mix# ,f the final mixture tem$erature is 25=C. !etermine the 'olume of eah tan& an! the final mixture $ressure# Ansers* 0#295 m 0#465 m3. 422 &a 13-37 'olume of 0#3 m3 of 2 at 200 an! 8 >a is mixe! "ith 0#5 m3 of 2 at the same tem$erature an! $ressure. forming a mixture at 200 an! 8 >a# (etermine the 'olume of the mixture. using a: the i!eal-gas e)uation of state. : a%a# 'al'e is no" o$ene!. an! 3 &mol 2 gas is allo"e! to enter the tan& at 190 an! 8 >a# +he final mixture tem$erature is 200 # (etermine the $ressure of the mixture. using a: the i!eal-gas e)uation of state an! : the om$ressibilit% hart an! (alton
properties o* Gas Mixtres 13-40C ,s the total internal energ% of an i!eal-gas mixture e)ual to the sum of the internal energies of eah in!i'i!ual gas in the mixture? ns"er the same )uestion for a real-gas mixture# 13-41C ,s the s$eifi internal energ% of a gas mixture e)ual to the sum of the s$eifi internal energies of eah in!i'i!ual gas in the mixture? 13-42C ns"er rob# 13-40C an! 13-41C for entro$%# 13-43C ,s the total internal energ% hange of an i!eal-gas mixture e)ual to the sum of the internal energ% hanges of eah in!i'i!ual gas in the mixture? ns"er the same )uestion for a real-gas mixture# 13-44C When e'aluating the entro$% hange of the om$onents of an i!eal-gas mixture. !o "e ha'e to use the $artial $ressure of eah om$onent or the total $ressure of the mixture? 13-45C /u$$ose "e "ant to !etermine the enthal$% hange of a real-gas mixture un!ergoing a $roess# +he ethal$% hange of eah in!i'i!ual gas is !etermine! b% using the generaliAe! enthal$% hart. an! the enthal$% hange of the mixture is !etermine! b% summing them# ,s this an exat a$$roah? ;x$lain# # 13-46 $roess re)uires a mixture that is 21 $erent ox%gen. 78 $erent nitrogen. an! 1 $erent argon b% 'olume# ll three gases are su$$lie! from se$arate tan&s to an a!iabati. onstant $ressure mixing hamber at 200 &a but at !ifferent tem$eratures# +he ox%gen enters at 10=C. the nitrogen at 60=C. an! the argon at 200=C# (etermine the total entro$% hange for the mixing $roess $er unit mass of mixture#
Gas Mixtures
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13-47 mixture that is 15 $erent arbon !ioxi!e. 5 $erent arbon monoxi!e. 10 $erent ox%gen. an! 70 $erent nitrogen b% 'olume un!ergoes an a!iabati om$ression $roess ha'ing a om$ression ratio of 81# ,f the initial state of the mixture is 300 an! 100 &a. !etermine the ma&eu$ of the mixture on a mass basis an! the internal energ% hange $er unit mass of mixture# 13-48 ro$ane an! air are su$$lie! to an internal ombustion engine suh that the air-fuel ratio is 161 "hen the $ressure is 95 &a an! the tem$erature is 30=C# +he om$ression ratio of the engine is 9#5 1# ,f the om$ression $roess is isentro$i. !etermine the re)uire! "or& in$ut for this om $ression $roess. in &&g of mixture# 13-49 n insulate! rigi! tan& is !i'i!e! into t"o om$artments b% a $artition# ne om$artment ontains 2#5 &mol of C2 at 27=C an! 200 &a. an! the other om$artment ontains 7#5 &mol of *2 gas at 40=C an! 400 &a# o" the $artition is remo'e!. an! the t"o gases are allo"e! to mix# (etermine a: the mixture tem$erature an! : the mixture $ressure after e)uilibrium has been establishe!# ssume onstant s$eifi heats at room tem$erature for both gases# 13-50 0#9-m3 rigi! tan& is !i'i!e! into t"o e)ual om$artments b% a $artition# ne om$artment ontains Ne at 20=C an! 100 &a. an! the other om$artment ontains !r at 50=C an! 200 &a# o" the $artition is remo'e!. an! the t"o gases are allo"e! to mix# *eat is lost to the surroun!ing air !uring this $roess in the amount of 15 &# (etermine a: the final mixture tem$erature an! : the final mixture $ressure# Ansers* a: 16#2=C. : 138#9 &a 13-51 e$eat rob# 13-50 for a heat loss of 8 &# 13-52 ;thane C2*6@ at 20=C an! 200 &a an! methane C*4@ at 45=C an! 200 &a enter an a!iabati mixing hamber# +he mass flo" rate of ethane is 9 &gs. "hih is t"ie the mass flo" rate of methane# (etermine a: the mixture tem$erature an! : the rate of entro$% generation !uring tills $roess. in &W# +a&e ! B 25=C# 13-53 eonsi!er rob# 13-52# sing ;;/ or other@ soft"are. !etermine the effet of the mass fration of methane in the mixture on the mixture tem$erature an! the rate of exerg% !estrution# +he total mass flo" rate is maintaine! onstant at 13#5 &gs. an! the mass fration of methane is 'arie! from 0 to 1# lot the mixture tem$erature an! the rate of exerg% !estrution against the mass fration. an! !isuss the results# 13-54 n e)uimolar mixture of helium an! argon gases is to be use! as the "or&ing flui! in a lose!-loo$ gas-turbine %le# +he mixture enters the turbine at 2#5 >a an! 1300 an! ex$an!s isentro$iall% to a $ressure of 200 &a# (etermine the "or& out$ut of the turbine $er unit mass of the mixture# 13-55 mixture of 80 $erent 2 an! 20 $erent C2 gases on a mass basis@ enters the noAAle of a turboet engine at 600 &a an! 1000 "ith a lo" 'eloit%. an! it ex$an!s to a $ressure of 85 &a# ,f the isentro$i effiien% of the noAAle is 92 $erent. !etermine a: the exit tem$erature an! : the exit 'eloit% of the mixture# ssume onstant s$eifi heats at room tem$erature# 13-56 eonsi!er rob# 13-55# sing ;;/ or other@ soft"are. first sol'e the state! $roblem an! then. for all other on!itions being the same. resol'e the $roblem to !etermine the om$osition of the nitrogen an! arbon !ioxi!e that is re)uire! to ha'e an exit 'eloit% of 800 rns at the noAAle exit# 13-57 $iston-%lin!er !e'ie ontains a mixture of 0#5 &g of *2 an! 1#6 &g of 2 at 100 &a an! 300 # *eat is no" transferre! to the mixture at onstant $ressure until the 'olume is !ouble!# ssuming onstant s$eifi heats at the a'erage tem$erature. !etermine a: the heat transfer an! : the entro$% hange of the mixture#
Gas Mixtures
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13-58 n insulate! tan& that ontains 1 &g of 2 at 15=C an! 300 &a is onnete! to a 2-m3 uninsulate! tan& that ontains 2 at 50=C an! 500 &a# +he 'al'e onneting the t"o tan&s is o$ene!. an! the t"o gases form a homogeneous mixture at 25=C# (etermine a: the final $ressure in the tan&. : the heat transfer. an! : the entro$% generate! !uring this $roess# ssume +o B 25=C# Ansers< a: 444#6 &a. : 187#2 &. : 0#962 & 13-59 eonsi!er rob# 13-58# sing ;;/ or other@ soft"are. om$are the results obtaine! assuming i!eal-gas beha'ior "ith onstant s$eifi heats at the a'erage tem$erature. an! using real-gas !ata obtaine! from ;;/ b% assuming 'ariable s$eifi heats o'er the tem$erature range# 13-60 $iston-%lin!er !e'ie ontains 6 &g of *2 an! 21 &g of 2 at 160 an! 5 >a# *eat is no" transferre! to the !e'ie. an! the mixture ex$an!s at onstant $ressure until the tem$erature rises to 200 # (etermine the heat transfer !uring this $roess b% treating the mixture a: as an i!eal gas an! : as a noni!eal gas an! using magata in a stea!%-flo" !e'ie# +he om$ression $roess is internall% re'ersible. an! the mass flo" rate of air is 2#9 &gse (etermine the $o"er in$ut to the om$ressor an! the rate of heat reetion b% treating the mixture a: as an i!eal gas an! : as a noni!eal gas using magat
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=r* Cengel, Y.A., and Bles, M.A.,!"#$M%&Y'AM(C) *An #ngineering A++ra-, 5t #ditin in )( unit,MGra/"ill, 2006. re+ared * Ass.r.)ai ri+re,-&.
