CANKAYA UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE MECHANICAL ENGINEERING DEPARTMENT ME 212 THERMODYNAMICS II CHAPTER 11 EXAMPLES SOLUTION
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1 CANKAYA UNIVESIY FACULY OF ENGINEEING AND ACHIECUE MECHANICAL ENGINEEING DEPAMEN ME HEMODYNAMICS II CHAPE EXAMPLES SOLUION ) he reure wthn a. m tank hould not exeed 0 ar. Chek the reure wthn the tank f flled wth 000 kg of water aor mantaned at 60 0 C ung the a) deal ga equaton ) an der Waal equaton ) edlh-kwong equaton d) Comrelty hart e) Steam tale Soluton: Analy: a) Ideal ga equaton: N.m (84 /8.0) (66K) kg.k ar. m 0 N / m 000 kg ) Van der Waal equaton wth a and from ale A-4: a N.m 84 (6K).K ar m 0 N / m ( ) 0.76ar (4% hgh ).9ar (%hgh ).ar(m /.K) m 0.4 ) edlh-kwong equaton wth a and from ale A-4:
2 a ( ) / N.m 84 (6K).K ar m 0 N / m ( ) m / 4.9 ar K m m (6K) / 0.4ar (% hgh ) d) Comrelty hart: 6 From ale A-, = 647. K, = 0.9 ar, thu; And; 0.4m / N / m N.m 84 (647.K).K.74 hen, Fg A- ge Z 0. 8 o; Z 0.8(.9) 0.48 (.% hgh ) e) Steam tale ge 00 ar.
3 ) Ung (a) the team tale at MPa,400 0 C () the refrgerant 4a at ar, 0 0 C hek the onteny of
4 ) Ealuate the artal derate for water aor at a fxed tate at temerature of 40 o C and ef olume of m /kg. a) Ue edlh-kwong equaton of tate and an arorate Maxwell relaton. ) Chek the alue otaned ung team tale data Soluton: and a ( ) a ( ) / At = 40 o C = K m 8.0 kg m kg Ue ale A-4: m a m / K Suttute nto equaton: kj.004 m.k ) = P (ar) (kj/kg.k) (
5
6 6 4) Deelo exreon for the olume exanty and the othermal omrelty for a) an deal ga ) a ga whoe equaton of tate (-) = ) a ga oeyng the an der Waal equaton Soluton: Analy: and a) Ideal ga: and, / hu; ) / and. hu: ) /( / Note: when = 0 thee exreon redue to thoe of art (a). ) From Van der Waal equaton:
7 a A the Van der Waal equaton not exlt n, the requred artal derate are not o ealy found a n art (a) and (). hu an exreon for / otaned a: /( ) o ( ) a / /( ) a( ) ( / ) /( ) a / /( ) ( / ) /( ) a / /( ) hu; κ = = /( ( a( ) ) [ ] [ ] a / ) = 7
8 ) Oxygen (O ) enter a ontrol olume oeratng at teady tate wth a ma flow rate of 9 kg/mn at 00 ar, 87 K and omreed adaatally to 0 ar, 400 K. Determne the ower requred, n kw, and the rate of entroy roduton, n kw/k. Ignore knet and otental energy effet. Soluton: Shemat and Gen Data: 8
9 O 00 ar 87 K 0 ar 400 K Analy: edung ma, energy and entroy alane ung the gen aumton, de dt Q W m h m e h e and W t m h h ds dt m Q j m j 0 m e e From tale t otanng for O that; 4K, 0.ar. hu: ,.97, hen, taulated enthaly and entroy dearture data ge: h h h h 0., 0.40, 0., 0.08 For O, tale ge: h 8 7 6kJ /. h 9
10 0 hen: kg 0.9kJ / m W M h h h h h h m W hu, 6.64 kw kj / kw 60 mn kg kj 0.9 mn kg 9 W Wth; o o ln ( ) ) ( and data from tale:.k 6.484kJ / ln Aordngly; K kw 0.06 kj / kw 60 mn kg.k kj 0.46 mn kg 9 Fnally, kg.k kj ) 8.4( M m
11 6) A loed, rgd, nulated eel hang a olume of 0.4 oxygen ( O ) ntally at 00 ar, reure eome 0 ar. Determne the m ontan 0 7 C. he oxygen trred y a addle wheel untl the (a) fnal temerature, n 0 C. () work, n kj. () amount of exergy detroyed n the roe, n kj. 0 Let 7 C 0
12 7) One of gaeou mxture oue a olume of 0. m at 00 0 C. he mxture ont of 69.% aron doxde and 0.% ethylene (C H 4 ) (molar-a). Etmate the mxture reure ung a) the deal ga equaton of tate ) Kay rule together wth the generalzed omrelty hart. ) he addte reure rule together wth the generalzed omrelty hart. d) he an der Waal equaton together wth mxture alue for the ontant a and Soluton: Analy: CO C H V = 0. m = 7 K CO : y = 0.69, C H 4 : y = 0.0 a) Ideal ga equaton of tate: n V ()(84 N.m /.K)(7K) ar 0.m 0 N / m ) Kay ule wth Z hart: Wth data from roerte tale; y hu; y y y (0.69)(04K) (0.0)(8K) 97.6K 79.4 ar (0.69)(7.9ar) (0.0)(.ar) 66.98ar 7K 97.6 K., (0.m / )( Pa) N.m 84 (97.6 K).K 0., Aordngly, Z 0. 6, o n Z Zdeal (0.6)(79.4 ar) 70.4 ar V ) Addte reure rule:
13 Z yz(,v) yz(,v) where; 0. (7.9 0 ) , Z 04 (84)(04) 0. (. 0 ) , 0.79 Z 8 (84)(8) Aordngly; Z yz(,v) yz (,V) (0.69)(0.68) (0.0)(0.8) 0.7 hen, n Z Zdeal (0.7)(79.4) 0. ar V d) Van der Waal equaton: Van der Waal ontant for CO an e otaned from tale a: m a.647 ar 0.048m / he reete alue for C H 4 an e otaned from rtal data: a (84) (8) 64 (. 0 ) 0 m 4.6ar 8 (84)(8) (8)(. 0 ) hen, m 0.074
14 4 / / / / j m.947 ar (0.0)(4.6) (0.69)(.647) a y a y a y a / 0.047m (0.0)(0.074) (0.69)(0.048) y y y j Wth thee alue; 68.7 ar (0.) ) (0. (84)(7) a
15 8) A rgd eel hang a olume of 0.0 m ntally ontan aron doxde ga at temerature 0 C and reure. Ethylene ga allowed to flow nto the tank untl a mxture ontng of 0% aron doxde and 80% ethylene (molar a) ext wthn the tank at a temerature of 0 C and a reure of 00 ar. Determne the reure, n ar, ung Kay rule together wth the generalzed omrelty hart. Shemat and Gen Data: V = 0.0 m CO o C, ntal C H enter mxture o C, 00 ar fnal y = 0. (CO ) y = 0.8 (C H 4 ) Analy: he ntal reure an e found ung where found from the omrelty hart ung /, where the rtal temerature of CO and, V where the rtal reure of CO and n the numer of of n CO reent ntally. o fnd n, onder the fnal ondton ontng of the mxture. y y y y (0.)(04K) (0.8)(8K) 87.K (0.)(7.9ar) (0.8)(. ar).74ar hen,. 08,.794 Z hen, the amount of mxture otaned ung Z V n mx or n mx fnal Z V fnal Sne the amount of CO reent n the fnal mxture (0. n mx ), the amount of CO fnalv reent ntally n = 0. n mx or n 0. Zfnal hu for the ntal ondton, 98/ and
16 Z Z V 0. V n V / f fnal fnal fnal hen from omrelty hart ge 6 0., gng 46.6 ar (0.6)(7.9)
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