1 LI NI U ''Nhit ng lc hc '' l mt mn hc thuc khi kin thc k thut c s; mn hc trang b chosinhvinngnhnnglngnhit,ngnhkthutckh,ngnhnglc...nhngkin thc su hn v nhit ng lc hc trn c s nm c kin thc v vt l ph thng, vt l i cng, k thut nhit... Nhit ng lc hc l mn hc nghin cu nhng qui lut bin i nng lng c lin quan n nhit nng trong cc qu trnh nhit ng, nhm tm ra nhng phng php bin i c li nht gia nhit nng v cc dng nng lng khc. C s nhit ng c xy dng t th k XIX, khi xut hin cc ng c nhit. Mn nhit ng c xy dng trn c s hai nh lut c bn: nh lut nhit ng th nht v nh lut nhit ng th hai. Nhngktqutctronglnhvcnhitngkthutchophptaxydngcsl thuyt cho cc ng c nhit v tm ra phng php t c cng c ch ln nht trong cc thit b nng lng nhit. CunbigingcbinsonvisnggpkincaccthygioVin nhit-lnhTrngihcBchkhoaHnivthamkhomtstiliuncngoi khc.VlbinsonlnulmtiliugingdychosinhvinhihcTrng i hc K thut cng nghip Thi Nguyn nn khng trnh khi nhng thiu st, nhm ln ti rt mongc bn c tham kho v ng gp kin. Mi kin ng gp xin gi v a ch: Trng i hc KTCN Thi nguyn, ng 3-2, Thnh ph Thi Nguyn. Cc tc gi PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com2 Chng 1 NHNG KHI NIM C BN V TRNG THI VT CHT TH KH 1.1. MT S KHI NIM C BN 1.1.1. Nguyn l lm vic ca thit b nhit Thitbnhitlnhngthitbdngtinhnhqutrnhtruynti,traoiv chuyn ha nhit nng. Thitbnhitbaogmchyu:ngcnhitlmvictheochutrnhthunchiu, my lnh hoc bm nhit lm vic theo chu trnh ngc chiu, ngoi ra cn c mt s thit b khc ch lm vic theo mt s qu trnh nh thit b kh nn, thit b sy, iu ha khng kh.v.v a. ng c nhitng c nhit l thit b nhit c chc nng l bin nhit nng thnh c nng sau c th chuyn ha n thnh cc dng nng lng khc nh in nng hoc th nng. Nguyn l ca ng c nhit l: mi cht nhn nhit lng q1 t ngun nng c nhit cao T1 chuyn ha mt phn thnh c nng lo hoc in nng, ri nh phn nhit lng cn li q2 cho ngun lnh c nhit T2 thp hn thc hin chu trnh thun. q1 = q2 + lo(1-1) Ngunnngcthnhnnhittphnngchyca nhinliutrongccbungt,tphnnghtnhn nguyn t trong l phn ng, t nng lng bc x nhit ca mt tri hoc ngun a nhit trong lng t. Ngun lnhthnglmitrngxungquanh:khngkhv nctrongkhquyn.ngcnhitcrtnhiuloi: my hi nc, ng c t trong, tuabin hi, tuabin kh, ngcphnlc,tnlav.v,ngynayngita ch to thnh cng mt s ng c nhit c bit c th chuyn i trc tip nhit nng thnh in nng nh : pin nhit - in, pin nhit - in t. Phm vi ng dng: ng c nhit c s dng rngritrongcctrungtmnnglngnhnhmy nhit in, nh myin nguyn t, nh my a nhit in hoc nh my in mt tri; trong cc thit b giao thngvntinht, tuho,tuthy,mybay,tn la, tu du hnh v trv.v T2 < T1 T1 q1 q2 lo Hnh 1.1. S ng c nhit PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com3 b. My lnh v bm nhit Mylnhvbmnhittuycchcnngkhcnhaunhngnguynllmvichon tongingnhau.Nhshtrcannglngbnngoi(cnng,innng,nhitnng v.v)michtnhnnhitlngq2tnguncnhitthpT2,riemnhitlng cng vi phn nng lng do bn ngoi h tr lo, tt cnhitlngctruynchonguncnhit cao T1 thc hin mt chu trnh ngc chiu. q2 + lo=q1(1-2)v My lnh c chc nng l ly nhit t ngun c nhit thp T2 nn nhit lng c ch l q2 v Bm nhit c chc nng l nh nhit cho ngun c nhit cao T1 nn nhit lng c ch l q1 Phmvingdng:mylnhvbmnhit csdngrngritrongvicboqunccloi nng, lm, thy sn; cc thit b ngnh y, vin thngv.v 1.1.2. Mt s khi nim v nh ngha 1.1.2.1.H thng nhit a. nh ngha Hthngnhitltphpnhngitngctchranghincucctnhcht nhit ng ca chng, phn cn li gi l mi trng. Ranh gii gia h thng nhit v mi trng c th l b mt tht cng c th l b mt tng tng. b. Phn loi h thng nhit H thng kn: l h thng m mi cht khng i qua b mt ranh gii, khi lng mi cht trong h thng kn khng thay i. Hthngh:lhthngmmichtcthquabmtranhgiiivohocra khi h thng. H thng c lp: l h thng khng c bt k s trao i nng lng no vi mi trng xunh quanh. H thng on nhit: l h thng khng trao i nhit vi mi trng nhng c th c s trao i cng. H thng ng nht: l h thng m mi cht ch gm c mt pha ng u v tnh cht vt l v ha hc.H thng khng ng nht: l h thng m mi cht tn ti nhiu pha, gia cc pha c ranh gii r rt, c s thay i t bin tnh cht l ha gia cc pha. T2 T1>T2 q1 q2 lo Hnh 1.2. S my lnh v bm nhit PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com4 1.1.2.2. Ngun nhit Ngun nhit l cc i tng trao i nhit trc tip vi mi cht; ngun c nhit cao l ngun nng, ngun c nhit thp hn gi l ngun lnh. Gi thit nhit dung ca ngun ln n mc gia c nhit khng thay i trong qu trnh truyn nhit. 1.1.2.3. nh ngha v mi cht (cht mi gii)Mi cht l nhng cht m thit b dng truyn ti v chuyn ha nhit nng vi cc dng nng lng khc. V nguyn tc, mi cht c th bt c pha no, nhng trong thc t thng dng th kh hoc hi v chng c kh nng gin n ln, thun tin cho vic trao i cng. Yu cu v mi cht: v C kh nng sinh cng ln: th tch thay i ng k khi nhit thay i. v C kh nng truyn ti nhit nng ln: c nhit dung ring ln. v Khng gy n mn thit b, an ton v khng chy n. v R tin, d kim, khng gy ng hi cho con ngi v thn thin vi mi trng. 1.2. S thay i trng thi v chuyn pha ca n cht 1.2.1. S thay i trng thi v chuyn pha ca n cht Xt trng hp lm th nghim i vi mi cht l nc: ly 1kg nc vo trong bnh kn, trn c pittng di chuyn c, p sut trnpittng lungi 1bar, nhit ban ugi thit l 20C . Cp nhit cho mi cht, ta quan st thy nhit tng t 20Cn 99,64 C th mt b phn nc bt u ha hi, nhit 99,64 C gi khng i cho n khi git nc cui cng hathnhhi;nutiptccpnhitthnhittnglnmi.Thtchringcancban ubng0,0010018m3/kg20C,tngkhngbaonhiu n0,0010432m3/kgkhibtu ha hi 99,64C; tng rt nhanh khi ha hi, bng 1,691 m3/kg khi va ha hi xong (tng khong 600 ln) ; nu tng nhit n 600C th th tch ring bng 4,028 m3/kg. Nu cho nc 600C thi nhit p sut 1bar khng i th nhit gim xung, n 99,64Cthmtbphnhingnglithnhnc,nhitkhngichonkhihiva ngng ht; nu tip tc thi nhit, nhit gim xungcho n khi bng 0C, mt b phn nc ng c, nhit khng thayi, khi nc ng ht nhit li gim. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com5

Lm th nghim trn cc p sut khc nhau v biu th trn th p - t v T - s ta thy:vKhi p < p3 : th khi cp nhit, pha rn chuyn trc tip thnh pha hi khng qua pha lng v ngc li khi thi nhit th pha hi chuyn thnh pha rn. vKhi p = p3: th tn ti ng thi c pha rn, lng, hi bo ha, trng thi gi l trng thi ba th hoc ba pha. i vi nc im 3 th ( p3 = 0,00611 bar v t3 = 0,01C ) vKhi p3 < p < pk: khi p sut tng nhit ng c thng gim xung (ng ON), nhit ha hi tng ln (on OK), th tch ring ca nc bo ha tng, ca hi bo ha gim. vKhi p= pk: qu trnhcng tn tigia nc v hi rt ngn li, s khc nhaugia nc bo ha v hi bo hacng nh nhit lng ha hi dn n 0, tt c khi cht lng cng hahimtlc,trngthibtuchintnggiltrngthitihn.ivinc im ti hn K ( pk = 221,3 bar ; tk = 374,15C )vKhi p > pk: th qu trnh chuyn t pha rn sang pha lng khng khc nhau l my nhng qu trnhchuyntphalngthnhphahikhngcranhgiirrng,khngcngiaionpha lng cng pha hi cng tn ti, khng phn bit c pha lng v pha hi. r +h r + l+ h l + h h l r K TK sk l + h l r + l rh O K N pT P PP P P P Hnh 1.3. S thay i trng thi v chuyn pha ca n chts t Hnh 1.4. th v s thay i trng thi v chuyn pha ca n cht PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com6 Lm th nghim trn vi cc mi cht khc nhau, v nh tnh chng u ging nhau, v nh lng c khc nhau v ta c kt qu sau.Bng 2-3. Thng s trng thi ti hn v trng thi ba pha (th) ca mt s n cht im 3 thim ti hnMi cht t3; oCp3; kPatk; oCpk; bar Thu ngn (Hg)+14901510 Nc (H2O)+0,010, 6113+374,15221,29 Cacbonic(CO2)-56,5518+3173,8 Sulfuric(SO2)-75,4167+157,278 Amoniac(NH3)-77,66,06+132,3112,8 Nito(N2)-209,912,5-11733,91 Oxy(O2)-2190,15-118,850,8 Hydro(H2)-2597,194-9,8513 1.2.2 Mt s khi nim a. Nng chy v ng c Nngchylqutrnhchuyntpharnsangphalng;qutrnhngcli,tcl chuyntphalngsangpharngilngc.Khinngchymichtnhnnhit,khi ng c mi cht nh nhit, hai nhit lng c tr s bng nhau, gi l nhit n nng chy hoc nhit n ng c; i vi nc p sut kh quyn bng 333,37 kJ/kg. b. Ha hi v ngng t Ha hi l qu trnh chuyn t pha lng sang pha hi; qu trnh ngc li, tc l chuyn tchuyntphahisangphalnggilngngt.Khihahimichtnhnnhit,khi ngngtmichtnhnhit,hainhitlngctrsbngnhaugilnhitnhahi hoc nhit n ngng t, n ph thuc vo bn cht v thng s ca mi cht. Nc p sut kh quyn c nhit n ha hi bng 2258 kJ/kg. Tytheoiukintinhnhkhcnhau,qutrnhhahicchiathnhqutrnh bay hi v qu trnh si. Qu trnh bay hi ch tin hnh trn b mt thong, qu trnh si tin hnh trong c khi mi cht. Nhit m mi cht tin hnh qu trnh ha hi hoc ngng t gi l nhit bo ha hoc nhit si, nhit bo ha ph thuc vo p sut; nc kh quyn c nhit bo ha xp x 100C. c. Thng hoa v ngng kt Thnghoalqutrnhchuyntpharnsangphahivqutrnhngcli,tcl chuyn t pha hi sang pha rn gi l qu trnh ngng kt. Khi thng hoa mi cht nhn nhit, khi ngng kt mi cht nh nhit, hai nhit lng c tr s bng nhau gi l nhit n thng hoa hoc nhit n ngng kt. im 3 pha, nhit n thng hoa ca nc bng 2828,18 kJ/kg. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com7 d. Mt s nh ngha v trng thi ca mi cht 1. Mi cht si (mi cht bo ha): l mi cht trong qu trnh ha hi hoc ngng t, cng l nc cng tn ti vi hi. 2. Hi bo ha kh: l hi trng thi bt u ngng t hoc khi mi cht lng va ha hi xong v cng l hi khi hai pha hi v nc (hoc l hi v rn ) cng tn ti. 3.Hiboham:lhnhpgiahibohakhvimichtboha.Tsgiakhi lng hi bo ha kh v hi bo ha m gi l kh, k hiu l x%; t s gia khi lng mi cht bo ha vi hi bo ha m gi l m ca hi bo ha m, k hiu y = (100 - x)%. 4. Hi qu nhit: l hi c nhit ln hn nhit bo ha cng p sut hoc hi c p sut nh hn p sut bo ha cng nhit . 5. Hi v kh: Hi thng dng i vi nhng cht c nhit ti hn tng i cao, d dng ha lng trong iu kin nhit v p sut thng thng; cn kh l dng i vi nhng cht c nhit ti hn tng i thp, kh ha lng trong iu kin p sut v nhit thng thng. 6. Kh l tng v kh thc:Trong thc t ch c kh thc, khng c kh l tng.Vi bt k mi cht no, p sut gim v nhit tng n mt lc m nh hng ca th tch bn thn phn t v lc tng tc gia cc phn t nh n mc c th cho php b qua, lc mi cht c th coi l kh l tng; khi khng th b qua th tch bn thn cng nh lc tng tc ca cc phn t, ta gi l kh thc. iu kin p sut v nhit thng thng, cc mi cht 2 nguyn t nh: oxy, nit, khng kh d t n iu kin c thcoi l kh l tng; cn i vi nhngcht nh l hinc,amniaccthcoilkhthc;nhnghinctrongkhngkhhoctrongsn phm chy cng c xem l kh l tng v phn p sut ca hi nc rt thp, khi lng ring ca n trong rt nh. 1.3. Thng s trng thi ca mi cht mttrngthixcnhcamicht,cnhngilngcgitrhontonxc nh, cc i lng ny gi c gi l thng s trng thi, chng l hm s n tr ca trng thi m khng ph thuc vo qu trnh thay i trng thi, nn bin thin ca thng s ch ph thuc vo trng thi u v trng thi cui ca qu trnh m khng ph thuc vo ng i; cn trong mt chu trnh bin thin ca chng bng khng.Hay ni cch khc thng s trng thi c vi phn ton phn.Khimichttrngthicnbng(vcvnhit),nghalnguvpsutv nhit th thng s trng thi mi c gi tr ng nht v xc nh, trong k thut chng ta ch nghin cu cc trng thi cn bng. 1.3.1 Nhit v nh lut nhit th khng Nhitbiuthmcnnglnhcamicht;nhitbiuthgitrtrungbnh ng nng ca cc phn t chuyn ng. Nhit c th trc tip o c trn c s nh lut nhit th khng: Nu hai vt (h) c nhit t1 v t2 cng bng nhit t3 ca vt (h) th ba th nhit ca hai vt bng nhau, tc l t1 = t2. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com8 - Thang o nhit bch phnK hiu nhit bch phn l t, n v o l 0C(Cellcious - Tn nh bc hc sng lp thang o). Chn cht xy dng thang o: Nh bc hc Cellcious chn nc nguyn cht p sut tiu chun (p = 760 mm Hg). - trng thi bng tan ca nc nguyn cht, ngi ta n nh l00C - trng thi nc si, n nh l 1000C. Trong khong (0100) ta chia lm 100 phn bng nhau mi phn l 10C Sau khi c thang o ngi ta mi ch to cc loi nhit k o nhit .Nhn xt: Tr s t0C khng phn nh mc chuyn ng ca cc phn t m n ph thuc vo cht dng xy dng thang o.- Thang o nhit tuyt i (thang o nhit Kelvin) Theothang onyngitakhiunhitlT,nvo 0K(Kelvin-tnnhbc hc sng lp thang o).C s xy dng thang o: da vo mi quan h gia nhit v tc chuyn ng trung bnh ca nguyn t, phn t vt cht.

3k2mT (1-3) Trong : - tc chuyn ng ca phn t trong vt cht; = NiNi (1-4) i - vn tc trung bnh ca Ni phn t trong tngN phn t; m - khi lng ca mt phn t;k - hng s Boltzman; k = 1,3805.10-23 (J/). Nh vy, ta thy tr s T0K hon ton phn nh chuyn ng ca nguyn t, phn t nn trong cc cng thc tnh ton ng hc ca cht kh ngi ta dng tr s T0K ch khng dng tr s t0C. TcngthctrntathyT=00Kkhi=0;iunykhngthxyra.Vvy,00K c gi l khng l tng (khng tuyt i). PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com9 - Quan h gia thang o bch phn v Kelvin: xy dng mi quan h gia hai thang o ngi ta chn mt trng thi lm mc l trng thi bng tan. trng thi ny t = 00C v T = 2730K. V 10C v 10K c ln nh nhau cho nn ta c th biu din hai trc nhit nh sau: Nh vy, ta c quan h: ToK = toC + 273 - Thang o nhit Rankine ( 0R ) v thang o nhit Faranhiet ( 0F ) Thango 0RdonhbchcRankinetmracnthango 0Fdonhbchc Faranhiet. Tt c cc thang o u ly hai trng thi lm mc; trng thi nc ang tan v trng thi nc si p sut tiu chun. ln ca 10C bng ln ca 10K bng 1001 khong cch gia hai im mc. ln ca 10R bng ln ca 10F bng 1801khong cch gia hai im mc. ln 10F bng ln 10R bng95 ln ca 10C v bng 95 ln 10KNh vy, trng thi nc ang tan: t = 00C, T = 2730K, T = 320F = 4620R Cng thc quan h gia cc thang o. tC = TK - 273 = 95(tF - 32) = 95TR - 273(1-5) Bng 1-1. Nhng im mc nhit p sut tiu chun im mc Nhit (oC) im mc Nhit (oC) im si ca oxy-182,97im si ca lu hunh444,6 im ba pha ca nc0,01im ng c ca bc960,8 im si ca nc100,00im ng c ca vng1063 0oCtoC ToK -273oC 0oK273oK toC ToK PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com10 1.3.2 p sut tuyt i Lc ca mi cht tc dng vung gc ln mt n v din tch b mt tip xc c gi l p suttuyt i ca mi cht. Biu thc xc nh: SFp (1-6) Trong : F - Lc tc dng ca mi cht, n v o l N ( Newton ) S - Din tch b mt tip xc, n v o l (m2). n v c bn ca p sut l 2Nm, cn gi l Pa - H thng n v o p sut: vH thng Pascal: k hiu l 1Pa = 12mN, bi s ca chng nh Kilpascan (1KPa = 103Pa), Mgapascal (1MPa = 103 KPa = 106 Pa); vH thng Bar : k hiu lbar; 1Bar = 105Pa; vH thng Atmosphere (at): Theo n v ny ngi ta ly p sut trung bnh ca kh quyn lm n v o; 1atmosphere k hiu l 1at;1at = 1kG/cm2 = 0,981 bar; vCc h thng n v khc: - Minimt ct thu ngn, k hiu l mmHg. - Minimt ct nc, k hiu l mmH2O. Cng thc lin h gia cc n v o: 11]1

2mN = 1Pa = 10-5Bar = 981 , 01.10-5at = 32 , 1331mmHg = 81 , 91mm H2O(1-7) - o p sut o p sut ngi ta dng mt dng c gi l p k, nguyn l v cu to ca p k rt a dng nhng y ta phn loi theo cng dng. chuyn mn ho dng c o nhm tng chnh xc ngi ta ch to cc loi p k sau: Baromet: l loi p k chuyn dng o p sut kh tri, s ch ca Baromet k hiu l pkt . Manomet: l loi p k chuyn dng o phn p sut ca cht kh ln hn p sut kh tri. S ch ca n ngi ta gi l p sut tha hoc p sut d, k hiu l pt (pd).PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com11 Chn khng k: l loi p k o phn nh hn p sut kh tri ca p sut cht kh gi l chn khng, k hiu pck.Xc nh p sut cht kh (p sut tuyt i) p = pkt - pck(1-9) -TrnghppsutchtkhlnhnpsutkhtritadnghailoipklBarometv Manomet, khi p sut cht kh:p = pkt + pt (1-8) - Trng hp p sut cht kh nh hn p sut kh tri ta dng hai loi p k l Baromet v Chn khng k, khi p sut cht kh: p = pkt pck (1-9) Lu : khi o theo chiu cao ct thy ngn, phi qui v chiu cao 00C theo cng thc: h0 = ht.(1 - 0,000172.t)(1-10) h0 - chiu cao ct thu ngn 00C ht - chiu cao ct thu ngn t0C. 1.3.3. Th tch ring v khi lng ring Thtchringlthtchcamtnvkhilngvkhilngring(mt)l khi lng ca mt n v th tch, chnh l s nghch o ca th tch ring. Nu tch mt lng mi cht c khi lng l G (kg) v th tch l V(m3) th th tch ring: GVlim v,V V , m3/kg (1-11) p pd pkt Pck P < Pkt P > Pkt P Hnh 1-5.Quan h cc loi p sut PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com12 Khi lng ring:1v , kg/m3 (1-12) y:V - th tch nh nht c th coi mi cht l mi trng lin tc. 1.3.4 Ni nng Ni nng ca mi cht l tng ni ng nng v ni th nng ca cc phn t. Ni th nng do lc tc dng tng h gia cc phn t to ra nn n ph thuc vo khong cch gia cc phn t hay th tch ring, ni ng nng do chuyn ng ca cc nguyn t, phn t gy ra nn n ph thuc vo nhit . Vy ni nng l hm ca nhit v th tch: u=f (t,v) (1-13) ivikhltng,cthbqualctngtcgiaccphnt,nnnithnng bng khng, v ni nng ch bao gm ni ng nng v ch ph thucvo nhit ; do ni nng l hm n tr ca nhit , u = f (t) ivikhltngtrongmiqutrnhbini,ninnglunc xc nhbng biu thc:du=CvdT v u=u2 - u1=Cv(T2- T1)(1-14) Trong : Cv - nhit dung ring khi lng ng tch. i vi 1 kg mi cht, ni nng k hiu l u, vi G kg c U = Gu. n v ca ni nng cnggingnhccdngnnglngkhc,thngdnglkJ,kW.hhoccc nvkhc: kcal , Btu v Chu v.v Quan h gia cc n v l: 1kJ = 0,239 kcal = 277,78.10-6 kW.h = 0,948 Btu = 0,527 ChuTrong k thut thng ch cn tnh lng bin thin ni nng u, nn c th chn mt trng thi thun tin no lm mc; thng chn ni nng ca nc bo ha ti trng thi ba th bng khng. 1.3.5 Entanpi Trong khi tnh ton v phn tch v nhit, thng gp biu thc (u + pv), n gin v thuntintathaybngigilentanpi;trongulninng,pvlthnngpsuthoc nng lng y. - i vi 1 kg mi cht ta c: i = u + pv , J/kg(1-15) - i vi G kg mi cht ta c: I = G.i = U + pV , J(1-16) Entanpi l thng s trng thi, khi ta ly vi phn chnh l vi phnton phn:di= du + d(pv)(1-17) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com13 Entanpicakhthccnggingnhninnglhmphthucvohaitrongba thng s trng thi c bn: p, v , T. Ringivikhltngthnngpsutcthbquannentanpichphthuc vo nhit i = f(T) v bin ientanpi trongmi qu trnh u cxc nh bng biu thc:di = CpdT ; i=i2 - i1=Cp (T2 -T1 )(1-18) Trong : Cp - nhit dung ring khi lng ng p. Trong k thut cng ging nh ni nng ta ch cn tnh bin thin ca entanpi i nn c th chn im gc m ti entanpi c gi tr bng 0. i vi cc mi cht lnh nh: NH3, R12 chn entanpi ca cht lng bo ha - 40C bng khng. 1.3.6 EntropiEntropi l mt thng s trng thi, k hiu l s, c vi phn bng: Tdqds , kJ/kgK hoc dS = G.ds = TdQ (1-19) dqlnhitlngvcngnhtraoivimitrngkhinhittuyticamicht bng T(K).Entropi khng th trc tip o c, c trng cho qu trnh nhn nhit v thii nhit; khi nhn nhit th s tng, thi nhit th s gim. Trong tnh ton cng ch cn tnh s nn c th chn trng thi mc bt k thng ly cng mc tnh u v i. Lu : ds l vi phn ton phn cn dq khng phi l vi phn ton phn, biu th lng nhit v cng b tham gia vo qu trnh bao gm nhit lng trao i vi mi trng v nhit lng do cc qu trnh khng thun nghch c ma st sinh ra. 1.3.7.Execgi Execgi l mt thng s trng thi biu th nng lng c ch ti a c th nhn c khi cho mi cht tin n trng thi cn bng vi mi trng bn ngoi. Execgi ch phn nng lngtiacthsdngctrongiukinmitrngxungquanhcnphnnng lng khng th s dng c trong iu kin mi trng xung quanh gi l anecgi. Execgi khng th o c trc tip m c tnh theo: e = (i - i0) - T0(s - s0)(1-20) E = G.e = (I - I0) - T0(S - S0)(1-21) Trong : i0, T0, s0 - entanpi, nhit tuyt i, entrpi ca mi cht trng thi cn bng vi mi trng; i ,T ,s - entanpi, nhit tuyt i, entrpi ca mi cht trng thi cn xc nh. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com14 1.3.8. Ni nng t do v entanpi t do Ni nng t do v entanpi t do l cc thng s trng thi: ni nng t do l tiu chun cnbngcaqutrnh ngnhit-ngtch;entanpitdoltiuchuncnbngcaqu trnhngnhit-ngp.Khimicht(h)tinhnhccqutrnhtrnthccilng tng ng gim dn v t gi tr cc tiu trng thi cn bng. - Ni nng t do cn gi l nhit th ng nhit ng tch hoc hm Helmholtz- Entanpi t do cn gi l nhit th ng nhit ng p hoc hm Gibbs. vi vi 1kg mi cht: Ni nng t t do: z = u Ts(1-22) Entanpi t do: = i Ts(1-23) vi vi G kg mi cht: Z = G.z = U TS(1-24) = G. = I TS(1-25) n v ca chng cng ging nh cc n v nng lng khc. 1.4 Trng thi ca mi cht Khi mt trng thi cn bng c xc nh th gi tr ca tt c cc thng s trng thi u xc nh, nhng xc nh mt thng s trng thi ca mi cht th khng cn phi xc nh tt c cc thng s trng thi m trong tng iu kin c th ch cn mt s thng s do nh lut pha ca Gibbs xc nh. 1.4.1 nh lut pha ca Gibbs (nm 1875) Gibbs a ra nh lut pha cho mt h cn bng (h khng c phn ng ha hc): V = C+ 2 - P(1-26) Trong : P - s pha cng tn ti trong h ; C - s thnh phn trong h ; V - s thng s c lp ti thiu cn thit xc nh mt trng thi. i vi mi cht n cht (C = 1), mt pha (P = 1) th s thng s ti thiu cn thit l: V = 1 + 2 -1 = 2 . Nh vy, i vi mi cht n trng thi kh, xc nh mt thng s trng thi th cn bit hai thng s c lp. Th d: nh p v v cn thng s th ba, th d l T c xc nh theo phng tnh: T = f (p,v)hoc F(p,v,T) = 0 . PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com15 1.4.2. Phng trnh trng thi ca kh l tng Phng trnh trng thi l phng trnh lin h gia cc thng s trng thi vi nhau. Phng trnh trng thi c th xc nh c bng thc nghim hoc bng l thuyt. i vi mt n cht pha kh l phng trnh lin h gia ba thng s c lp thng l ba thng s c bn p, v, T. T thuyt ng hc phn t hoc bng thc nghim trn c s cc nh lut Boyle - Mariotte (Bi Marit), Gay - Lussac (Gay - Luyxc) v Avogadro (Avgar). - i vi 1 kg kh l tng: pv = RT (1-27) Trong : p - p sut ca cht kh,N/m2 ; v - th tch ring, m3/kg ; T - nhit tuyt i,0K ; R hng s cht kh, J/kg0K ; - i G kg kh l tng: pGv = GRThay pV = GRT(1-28) - i vi 1 kilomol cht kh: Kilmol k hiu (kg/kmol) l lng vt cht tnh bng kg c tr s bng phn t lng ca cht .pv = RT hayp.v = R.T (1-29) y: v = V - th tch ca 1kilomol (m3/kmol) R = R - hng s ph bin ca cht kh (J/kmol 0K)Vy phng trnh trng thi ca mt kilomol cht kh l: p.V = RT (1-30) T quan h (1-27) ta c th tnh c gi tr R nh sau: R = . pVT

Theo nh lut Avgadr: iu kin tiu chun vt l (p = 760 mmHg ; t = 0C) th tch ca kilmol kh l tng V = 22,4 m3 . Vy ta c: R = 5760.10 .22, 47500 273,15 + = 8314 (J/kmol.K) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com16 T hng s cht kh c xc nh: R = R= 8314 , J/kg K- i vi M kilmol cht kh l tng: p.M.V = M.RThay pV = MRT (1-31) 1.4.3 Phng trnh trng thi ca hn hp kh l tng i vi hn hp ng u cc kh l tng khng c phn ng ha hc vi nhau c th coi tng ng vi mt cht kh l tng ng nht, c th s dng c cc nh lut Boyle - Mariotte v Gay - lussac cng nh cc phng trnh trng thi. Nhng cn thay vo cc ilngtngngcahnhptrncsbitcccslngvtlhnhp ca cc kh thnh phn. a. Thnh phn ca hn hp vThnh phn khi lng ca mt cht kh thnh phn:gi = niG G GG+ + + ...2 1 = iiGG = GGi(1-32) y : Gi - khi lng ca thnh phn kh th i ; G - tng khi lng ca tt c cc kh thnh phn. vThnh phn th tch v thnh phn mol: ri = iiVV = VVi (1-33) y : Vi - th tch cht kh ca kh thnh phn ;V - tng th tch ca hn hp kh. ri = iiMM = MMi (1-34) y : Mi - s kilomol ca kh thnh phn ; M - tng s kilomol ca cc kh thnh phn. Ta c : Vi = MiVi v V = MV ; thay vo ri = Vi/V c : ri = VVi = MVV Mi i

Theo nh lut Avogadro cng p sut v nhit th Vi = V nn : P , T, V1,G1 P , T , V , G P, T, V2, G2 + 0 0+

+ 0 0 ++ + + Hnh 1-6. Tch hn hp theo phn th tch PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com17 ri = VVi = MMi (1-35) Ta cng chng minh c : ri = PPi y : Pi- phn p sut ca cht kh thnh phn ; P - p sut ca hn hp kh. Phng trnh trng thi ca mt cht kh thnh phn di hai dng : piV = GiRiT(a) pVi = GiRiT(b) Chia (a) cho (b) theo v ta c :pPi = VVi = ri (1-36) Theo nh lutDalton th p = niiP1, tc l p sutca hn hp bng tng phn p sut ca cc cht kh to thnh hn hp. vQuan h gia hai loi thnh phn: gi = 1i ini iirr hoc gi = /i iiir RrR (1-36a, b) ri = i ii ig Rg R hoc ri = /i iiigg (1-37a, b) b. Xc nh cc i lng tng ng ca hn hp 1.Khilngcahnhp:theonhlutbotonkhilng,khilngbngtngkhi lng ca cc cht kh thnh phn.G = 1niiG(1-38) 2.Thtchcahnhp:trongiukinkhngcphnnghahcththeonhlut Amagat - Leduc bng tng th tch ca cc thnh phn. V = 1niiV(1-39) Nu tch hn hp theo phn p sut th th tch hn hp bng th tch ca bt k cht kh thnh phn no. P1, T, V, G1 P , T , V , G P2, T, V, G2 + 00+ + 0 0 ++ + + Hnh 1-7. Tch hn hp theo phn p sut PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com18 3. S kilmol ca hn hp: trong iu kin khng c phn ng ha hc bng tng s kilmol ca cc cht kh thnh phn. M = 1niiM(1-40) 4. Nhit ca hn hp kh : bng nhit ca cc kh thnh phn. 5. p sut ca hn hp: theo nh lut Dalton bng tng phn p sut ca cc kh thnh phn: p = 1niip(1-41) 6. Phn t lng tng ng ca hn hp: = 1ni iir (1-42) hoc = 11nii ig(1-43) Ta chng minh nh sau: T G = 1niiG; Gi = Mii ; G = M. ta c: M. = 1ni iiM =1ni iiMM = 1niiiMM = 1ni iir 7. Hng s cht kh tng ng ca hn hp: R , R HngsphbincahnhpRvnbng8314J/kmolK,cnhngschtkh tng ng c th tnh theo tng ng ca hn hp. R = 8314 , J/kg K(1-44) R = 1ni iig R(1-45) R = 1iirR(1-46) Ta chng minh bng cch thay = 11nii ig vo R =8314 , ta c: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com19 R =8314 = 83141niiig = 18314niiig = 1ni iig R 8. Th tch ring ca hn hp: v = 1ni iig v= 1niiig(1-47) T v = VG, thay V = 1niiV , ri thay Vi = Givi v = iVG= i iGvG= iiGvG= 1ni iig v 9. Khi lng ring hoc mt ca hn hp c th tnh theo: 1v (1-48) 1 ni iir (1-49) 1iig(1-50) 1.4.4. Phng tnh trng thi ca kh thc th hin s khc nhau gia kh thc v kh l tng ngi ta a ra mt i lng khng th nguyn gi l nn Z : RTpvz (1-51) Vi kh l tng Z = 1, vi kh thc Z 1. nn Z ph thuc vo nhit , p sut v tnh cht vt l ca kh . Khi nghin cu ngi ta cho thy, nu p 0 v nhit ln (cng c ngha v ) , nn ca cht kh Z 1, lc ny kh thc c coi l kh l tng.Khi nhng trng thi m Z sai khc 1 qu nhiu, vt qua gii hn cho php, th ta khngthsdngcccnhlutBoyle-Mariotte,Gay-lussuccngnhphngtrnh trng thi Clapeyron m phi xy dng kt qu bng thc nghim, chnh l di dng phng trnh, bng s v th. a) Phng trnh Van der Waals (p + 2va)(v- b) = RT(1-52) a, b l cc h s thc nghim v trng thi ti hnPDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com20 KK2pT R6427a ;KKpRT81b Trong : TK , pK - nhit v p sut mi cht trng thi ti hn. b) Phng trnh Beattie-Bridgman pv2 = RT[v + B0(1 - vb)](1 - 3vTc) A0(1 - va)(1-53) Trong : a, b, c, A0 v B0 - nhng hng s xc nh bng thc nghim. c) Phng trnh Viran D.Mayer-N.Bogolioubov Bng phng php ton hc v vt l l thuyt, nh vt l ngi M D.Mayer v nh ton hc X Vit N.Bogolioubov a ra phng trnh c coi l chnh xc nht cho n hin nay. pv = RT(1 - kkn1 kv 1 kk +)(1-54) Trong : k-hsvirianchphthucvonhit,chaxcnhcbngphngphp thun ty l thuyt m phi xut pht t nhng kt qu thc nghim. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com21 Chng 2NHIT V CNG - CC PHNG PHP XC NH Nhit v cng l hai hnh thi ca nng lng, chng ch xut hin khi c s trao i nng lng gia cc vt. - Hnh thi cng c th hin km theo s dch chuyn dng v m (cc i lng vmlccilngcthcnongomc,cc ilngvimlccilng khng cn ong o m c: dx, dy) -Hnhthinhitcthhintrongtrnghpcschnhlchnhitgiacc vt; (nu khng c s chnh lch v nhit th s khng c s trao i nng lng nh vy khng xut hin nhit nng). Ch :Khcviccthngstrngthi,nhitvcnglccilngctrngchoqu trnh, n ph thuc vo tnh cht ca qa trnh. 2.1.Nhit dung ring v cch tnh nhit2.1.1.Khi nim v nhit dung ring Xt mt n v cht kh vi qu trnh thay i trng thi v cng nh; ta cung cp cho chtkhmtnhitlngdq(kJ/nvchtkh),nhitthayimtlngdt;ts dtdq c k hiu l C - gi l nhit dung ring. dqCdt ; [kJ/v cht kh.](2-1) nh ngha nhit dung ring:Nhit dung ring ca cht kh l nhit lng cn thit cung cp cho mt n v cht kh nhit ca n tng ln mt theo mt qu trnh no . Ni chung nhit dung ring ph thuc vo bn cht cht kh, nhit v p sut. Thng thngtacthbquasphthuccanhitdungringvopsutccpsutkhng qu ln. Nhit dung ring ph thuc vo nhit nn c khi nim nhit dung ring thc v nhit dung ring trung bnh. 2.1.2.Phn loi nhit dung ring Nhitdungringphthucvonhit,nvolngvtchtvqutrnhcp nhit ca khi kh nn c cc loi nhit dung ring sau: a. Phn loi theo nhit Nhit dung ring thc l nhit dung ring ti mt nhit no . Ta c biu thc: dqCdt v 21ttq Cdt (2-2) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com22 Nhit dung ring trung bnh l nhit dung ring trong mt khong nhit t = t2 - t1 no . Ta c biu thc: C21tt= 2 1qt t = qt (2-3) Kt hp (2-2) v (2-3) ta c: C21tt=qt =1t 21ttCdt(2-4) b. Phn loi theo n v o lng vt cht Nhit dung ring khi lng: khi n v o khi lng l kg, chng ta c nhit dung ring khi lng, k hiu C (kJ/kg.) Nhitdungringthtch:nunvchtkhl1m3tiuchun(m3tc)tacnhit dung ring th tch, k hiu l C [kJ/m3tc.]. Nhit dung ring kilmol: nu n v ocht kh l 1 kilomol tac nhit dung ring kilomol, k hiu l C [kJ/kmol.]. T nh ngha trn ta c quan h gia cc loi nhit dung ring: C = C'.vtc = C(2-5) Trong : vtc - th tch iu kin tiu chun vt l, mtc/kg; - kilmol ca cht kh (kilmol l lng vt cht tnh bng kg ctr s bng phn t lng) . c. Phn loi theo qu trnh trao i nhit Nhitdungringngp:khiqutrnhnhnnhitxyra psutkhngitac nhit dung ring ng p. Cp nhit dung ring khi lng ng p; C'p nhit dung ring th tch ng p; Cp nhit dung ring kilmol ng p.Nhit dung ring ng tch: khi qu tnh nhn nhit xy ra th tch khng i ta c nhit dung ring ng tch. Cv nhit dung ring khi lng ng tch; C'v nhit dung ring th tch ng tch; PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com23 Cv nhit dung ring kilmol ng tch.i vi kh l tng quan h gia nhit dung ring ng p v nhit dung ring ng tch biu th bng cng thc Mayer: Cp - Cv = R(2-6) Trongnhitng,tsgianhitdungringngpvnhitdungringngtch c biu th: pvCC = ''pvCC = pvCC= k(2-7) y: k - s m on nhit. i vi kh thc tr s k ph thuc vo bn cht kh v nhit ca cht kh. Vi kh l tng, tr s k ch ph thuc vo bn cht (cu to phn t) ca cht kh. Cv = 1Rk (2-8) Cp = k.1Rk (2-9) Cn = Cv.1n kn (2-10) 2.1.3. Nhit dung ring ph thuc vo nhit a. Nhit dung ring ca kh l tng ivikhltng,nhitdungringkhngphthucvonhitvcnh ngha theo (2-8), (2-9) v bng 2.1. Bng 2.1. Nhit dung ring ca kh l tng. kcal/kmol KkJ/kmol K Loi kh Tr s kCvCpCvCp Mt nguyn t Hai nguyn t Ba v nhiu nguyn t 1,6 1,4 1,3 3 5 7 5 7 9 12,6 20,9 29,3 20,9 29,3 37,7 b. Nhit dung ring ca kh thc ivikhthc,nhitdungringphthucvonhitnntacngckhinimnhit dung ring thc v nhit dung ring trung bnh: Tng qut, nhit dung ring thc ph thuc vo nhit thng c biu din bng hm s sau: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com24 C = a0 + a1t + a2t2 + ...+ antn (2-11) y: a0 , a1 , a2 ... an l cc hng s thc nghim; n - s m t chn, ngha l chn n cng cao th chnh xc cng cao. Nu ly n = 0 ngha l C = a0 = const , lc ny ta coi kh l kh l tng, nhit dung ring l hng s v khng ph thuc vo nhit . Nu ly n = 1 ta c nhit dung ring ph thuc vo nhit c quan h tuyn tnh: C = a0 + a1t vNhit dung ring trung bnh trong khong 0 C n tC (t = t2 - t1) 0tC= 1t0.tC dt (2-12) 0tC= 1t0.tC dt= 1t0 10( )ta a t dt += a0 +12at = a0 + a1't (2-13) Thc t cn tnh nhit dung ring trung bnh trong khong nhit bt k t t1 n t2 tc l khong nhit t = t2 - t1 21ttC= 1t 21.ttC dt = 1t 2 10 0. .t tC dt C dt 1 1 1 ] 21ttC= 1t 2 12 10 0. .t tC t C t 1 ](2-14) Gi tr nhit dung ring 0tC (k hiu Ctb) trong khong nhit 0C n tC c xc nh t cc bng s. 2.1.3. Nhit dung ring ca hn hp kh Mun nng nhit ca hn hp kh ln mt cn phi nng nhit ca tng cht kh thnh phn trong hn hp ln mt . NugiClnhitdungringkhilngcahnhpkhvCilnhitdungring khi lng ca kh thnh phn ta c: G.C = G1.C1 + G2.C2 + ...+ Gn.Cn (2-15) C = 1GG.C 1 + 2GG.C2 + ...+ nGG.Cn C = g1.C1 + g2.C2 + ...+ gn.Cn = 1ni iig C(2-16) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com25 Suy lun tng t ta cng c cc biu thc sau: C' = '1ni iirC(2-17) C = 1ni iirC(2-18) Trong : gi - thnh phn khi lng; ri - thnh phn th tch hoc thnh phn kilmol; C' , C - nhit dung ring th tch, kilmol ca hn hp; Ci' , Ci - nhit dung ring th tch, kilmol ca ca kh thnh phn. 2.1.5. Cch tnh nhit a. Tnh theo nhit dung ring Xut pht t biu thc: dq = C.dt 2112dt . C q (2-19) vTrng hp C = const q12 = C.( t2 - t1) = C.t(kJ/kg)(2-20) Vi G (kg) mi cht:Q = G.q(KJ)(2-21) Q = Vtc.C'.t , (KJ)(2-22) Q = M.C.t , (KJ)(2-23) vTrng hp C const hay C = a0 + a1t ; (NDR ca kh thc) ( ) ( ) ( )22111 212 0 1 0 1 2 1 2 1aa t. .2ttttt tq dt a a t t t tC+1 + + 1 ](2-24) Trong : 21ttC - NDR trung bnh trong khong nhit t t1 n t2 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com26 Nh vy, khi NDR ca mi cht ph thuc nhit ta phi xc nh NDR trung bnh trong khong nhit t t1 n t2 bng cch thaych s t trong biu thc C = a0 + a1t bng trung bnh cng nhit trng thi u v trng thi cuica qutrnh. TrongmtstiliukthutnhitngitathngchoNDRtrungbnhtrong khong nhit t 0 n t. V vy ta phi s dng tnh cht ca tch phn tch biu thc xc nh nhit lng thnh tng cc tch phn: qt1t2 = q0t2 - q0t1 = 2 1t t2 10 0C .t C .t (2-25) Bng 2.2. NDR trung bnh ca oxy v khng kh (0oC1500oC vi c =ao+a't; a'=a1/2) KhNDR khi lng KJ/kgoKNDR th tch KJ/m3tcoK O2 t0pC0, 9203+0,0001065t t0vC0, 6603+0,0001065t t0'pC1,3168+0,0001577t t0'pC1,3168+0,0001577t Khng kh t0pC0,9956+0,00009299t t0vC0,7088+0,00009299t t0'pC1,2866+0,0001201t t0'pC0,9757+0,0001201t b. Tnh theo entropi Trongqutnhngnhitkhngtnhtheonhitdungringvnhitdungringca qu trnh CT = (CT = dqdt= 0dq=) T biu thc nh ngha entrpi ta d dng suy ra cch tnh nhit theo entropi. Ta c: ds = dqT (2-26) dq = T.ds hay q12 = 21.ssT ds(2-27) Xt th T - s: - Trc tung: T0K - Trc honh: s(kJ/kg.)Theo tnh cht ton hc:21s1 2sdt(s 12s ) T.ds Nhvy,dintchnmdiqutrnh1-2trnthT-sbiudingitrnhit lng ca qu trnh . V vy, th T - s gi l th nhit. ds T2 T s s1 s2 T1 Hnh 2-1. th T -s 1 2 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com27 Ch : - Nhn vo th T - s ta thy q12 khng phi l mt thng s trng thi m l hm s ca qu trnh.Nghalcngtrngthi1,2nutinhnhtheoccqutrnhkhcnhauthq12khc nhau. - Ta thy dq lun cng du vi ds v T > 0 nn ta quy c: + Nu q > 0 mi cht nhn nhit. + Nu q < 0 mi cht nh nhit. -Trongqutrnhtnhnhitlngpdngcngthc: 21.12ssds T q tacnbithmnhit ph thuc entropi. Nu l qu trnh ng nhit ta c q = T(s2 - s1) 2.2.Nng lng ton phn ca h thng nhit ng 2.2.1.Cc dng nng lng trong h thng nhit ng a.Ngoingnng:lnnglngcachuynngvm(chuynngvtth)cxc nh bng biu thc: Wd = G.22 , J(2-28) Trong : G - khi lng ca vt, kg ; - tc ca vt, m/s . Bin i ngoi ng nng ca vt s l: Wd = Wd2 - Wd1 = G.2 22 12 = G.22 (2-29) b. Ngoi th nng: l nng lng ca lc trng trng, n ph thuc vo chiu cao so vi mt t ca vt, c xc nh bng biu thc: Wt = G.g.h , J(2-30) Trong : h - cao ca vt so vi mt t, m ; g - gia tc trng trng, m2/s . Bin i ngoi th nng ca ca vt l: Wt = Wt2 - Wt1 = G.g.(h2 - h1) = G.g.h (2-31) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com28 c. Ni nng (ni nhit nng): l ton b nng lng bn trong ca vt, ni nng bao gm ni ng nng v ni th nng. Ni ng nng do chuyn ng ca cc phn t, nguyn t gy ra nn n ph thuc vo nhit . Ni th nng do lc tc dng tng h gia cc phn t gy ra nn n ph thuc vo khong cch cc phn t hay th tch ring. Ni nng k hiu l u (J/kg) hay U (J). Ni nng l hm ca nhit v th tch u = f(T,v). Ring i vi kh l tng, ni nng ch ph thuc vo nhit u = f(T).Bin i ni nng ca vt l: U = U2 - U1 (2-32) d. Nng lng y (hay l th nng p sut)Nng lng y c k hiu l D (J) hoc d (J/kg) v c xc nh theo biu thc: D = pV = G.pv ;(J)(2-33) D = p2V2 - p1V1 = G(p2v2 - p1v1)(2-34) Nnglngychctronghh,khidngkhchuynngnnglngythay i v to cng lu ng y dng kh chuyn ng. l bn dng nng lng c trong h nhit ng, c bn dng nng lng trn u l cc hm trng thi. Khi h nhit ng thay i, chng ch ph thuc vo trng thi u v cui m khng ph thuc vo qu trnh bin i. 2.2.2.Nng lng ton phn ca h nhit ngKh hiu nng lng ton phn ca h nhit ng l W (J) hoc w (J/kg) , ta c biu thc sau: W = U + D + Wd + Wt (2-35) w = u + d + 22 + gh2-36) i vi h kn khng c nng lng y (D = 0), khng c ngoi ng nng (Wd = 0). Do biu thc nng lng ton phn ca h kn l: W = U + Wt (2-37) w = u + ghu(2-38) Tronghkn,ngoithnngthngcgitrrtnhsovininngnnthng c b qua. Mt khc v vt th trong h kn khng chuyn ng nn trng tm ca h khng i v chiu cao ca h so vi mt t cng khng i, do bin i th nng ca h kn s bng khng (Wt = 0). Vy bin i nng lng ton phn ca h kn s l: Wk = U = U2 - U1 (2-39) wk = u = u2 - u1 (2-40) i vi h h, v U + D = I do nng lng ton phn ca h h l: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com29 Wh = I + Wd + Wt(2-41) wh = i + 22 + gh (2-42) Bin i nng lng ton phn ca h h: Wh = I + Wd + Wt(2-43) wh = i + 22 + g.h(2-44) Thng thng trong h h, ngoi th nng v bin i ngoi th nng c gi tr rt nh so vi cc thnh phn khc nn thng b qua (Wt = 0 ; Wt = 0) v khi ta c biu thc: wh = i + 22 (2-45) wh = i + 22 (2-46) Trongmtstrnghpcahhnhqutrnhtrongmynn,qutnhhnhp gia cc dng cht kh..., ngay c gi tr ng nng ca h cng nh so vi entanpi. Do ta c th b qua ngoi ng nng (2/2 0) w = i(2-47) wh = i(2-48) 2.3.Cc loi cng 2.3.1. Cng thay i th tch Cngthayithtchlcngdomichttronghsinhra(khiginn)hocnhn c (khi b nn) khi th tch ca mi cht c thay i. Cng thay i th tch k hiu l L (J) hoc l(J/kg) . Gisc1kgchtkhpsutp,thtchv(hnh2.1);khichtkhginnmt lng dv, cht kh thc hin cng dl . V dv c gi tr v cng b nn s tng th tch ny xem nh l cc im trn b mt S ca cht kh dch chuyn c mt qung ng dx (vung gc vi b mt haycng chiu vi lc p sut p). Vycng m cht kh thc hin c l: dl = p.S.dx , v S.dx = dv nn cng thay i th tch c dng: dl = pdv(2-49) 2112 vvl pdv, (kJ/kg)(2-50) Vi G (kg) mi cht L = G.l12 (kJ) p dv v p v2 v1 Hnh 2-3. th trng thi p-v 1 2 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com30 Nhn xt: Cngthayithtchctrsdng(l12>0) khichtkhginn;ngclicng thay i th tch c tr s m (l12 < 0) khi b nn. Trn th p-v ( th cng) cng thay i ca 1kg cht kh trong qa trnh bin i 1-2 c biu din bng din tch hnh 12v2v1. T th ta thy cng thay i th tch l mt hm ca qu trnh. Cng thay i th tch c trong c h kn v h h. 2.3.2. Cng k thut Cng kthut khiu lLkt(J) hoc lkt (J/kg).Cng kthut l cng ca dngcht khichuynng(hh)thchinckhipsut ca cht kh thay i. Cng k thut c nh ngha bng biu thc: dlkt = -vdp(2-51) lkt12 = 21ppvdp (2-52) Cng k thut c tr s dng (lkt > 0) khip sut gim trong qu trnh bin i, ngc li c tr s m nu p sut tng trong qu trnh bin i. Trn th p-v cng k thut ca 1kg dng kh trong qu trnh bin i 1-2 c c biu th bng din tch 12p2p1. T y ta thy cng k thut l hm ca qu trnh. 2.3.4. Cng ngoi Cng ngoi c k hiu l Lkt (J) hoc l(J/kg). Cng ngoi l cng m h trao i vi mitrng.ychnhlcnghuchmtanhncthhoccngtiuhaotmi trng tc dng ti h. tm biu thc tng qut ca cng ngoi, chng ta nhn thy mi cht trong h nhit ngckhnngsinhcngtcdngtimitrngkhithtchntng,ngoingnng gim, ngoi th nng gim, nng lng y gim. Biu thc cng ngoi c dng: ln12 = l12 + (d1 d2) + 22221 + g(h1 h2) (2-53) dx 1kg p, v dv S Hnh 2-2. Xc nh cng thay i th tch v p p1 p2 dp 1 2 Hnh 2-4. th xc nh cng k thut PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com31 ln12 = l12 - (d2 d1) - 22122 - g(h2 h1) (2-54) dln = dl d(d) - d

,_

22 - gd(h)(2-55) V trong h kn, khng c nng lng y, khng c ngoi ng nng v bin i ngoi th nng bng khng. T (2-55) c dng: dln = dl = pdvv ln12 = l12(2-56) i vi h h, ta bin i nh sau: dl d(d) = pdv d(pv) = pdv pdv vdp = -vdp = dlkt Vy t (2-55) ta c: dln = dlkt- d

,_

22 - gd(h)(2-55) ln12 = lkt12 - 22122 - g(h2 h1)(2-56) lkt12 = ln12 + 22221 + g(h1 h2)(2-57) i vi dng kh hoc hi chuyn ng trong ng (V d: ng tng p, ng tng tc) khng sinh cng ngoi (ln12 = 0). Cng k thut m dng kh thc hin (do gim p sut) s gy nn s thay i ng nng v th nng ca dng kh. Ngoi ra thy c s lin quan gia cng kthut, cng thay i th tch v bin i nng lng y trong h h ta c: d(pv) = pdv + vdp (d) = l12 lkt12 lkt12 = l12 -(d)(2-58) Biu thc (2-58) cho thy cng k thut trong qu trnh nhit ng no ca h h l tngisgiacngthayithtchvsbininnglngy.Nutrongqutrnh khng c s bin i nng lng y p1v1 = p2v2 (qu trnh ng nhit) th cng k thut c gi tr bng cng thay i th tch. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com32 Chng 3 NH LUT NHIT NG I V CC QU TRNH C BN CA CHT KH 3.1. nh lut nhit ng I 3.1.1. Ni dung v ngha nhlutnhitngmtlnhlutbotonvchuynhonnglngngdng trong phm vi nhit. Nhit nng c th c chuyn ho thnh cc dng nng lng khc. Mt lng nhit nng b tiu hao th s c mt lng xc nh nng lng khc c hnh thnhv tng nng lng ca h thng khng thay i. nhlutnhitngthnhtcptivicbinhagianhitvcngvc c pht biu: Nhit c th c th bin thnh cng v ngc li cng cng c th bin thnh nhit. 3.1.2. Phng trnh nh lut nhit ng I a. Dng tng qut ca phng trnh nh lut nhit ng I Gi s mi cht trong h nhn nhit lng Q t mi trng, lc ny nng lng ton phn ca h s bin i mt lng W = W2 - W1 v h c th sinh cng ngoi Ln12 tc dng ti mi trng. T nhn xt ny v theo nh lut bo ton v bin ha nng lng ta c phng trnh cn bng nng lng nh sau: Q = W + Ln12 (3-1) q = w + ln12 (3-2) b. Phng tnh nh lut nhit ng I i vi h kn v h v i vi h kn: Theo cc biu thc (2-38) v (2-56) ta c: wk = uv ln12 = l12 Thay vo (3-2) ta c:q = u + l12 dq = du + vdp(3-3) Ta bit h kn: i = u + pv nn u = i - pv v du = di - pdv - vdpThay vo (3-3) ta c: dq = di vdp = di + dlkt (3-4) vi vi h h: Theo (2-40) ta c: wh = i + 22 + g.h(3-5) Thay vo (3-2) ta c: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com33 q = i + 22 + g.h + ln12 Mt khc kt hp (2-57): lkt12 = ln12 + 22 + g.hDo : q = i + lkt12 (3-6) dq = di + dlkt (3-7) Nu by gi ta thay i = u + pv hay di = du + pdv + vdp vo (3-7) ta li c biu thc: dq = du + pdv + vdp - vdp = du + pdv dq = du + dlkt (3-8) Khi thay cc quan h du = CvdT; di = CpdT vo (3-3) v (3-4) ta c dng phng trnh nh lut nhit ng I dng cho c h kn v h h ca kh l tng. dq = CvdT + pdv(3-9) dq = CpdT - vdp(3-10) c. Phng trnh nh lut nhit ng I cho dng kh hoc hi chuyn ng Dng kh chuyn ng trong cc ng dn l mt h h khi khng thc hin cng ngoi vi mi trng (ln12 = 0). T phng trnh nh lut nhit ng I theo (3-2) ta c: q = w = i + 22 + g.h y: h = h2 - h1 l hiu s gia chiu cao so vi mt t ca on ng khi ra v khi vo ca dng kh. V h thng l nh cho nn bin i th nng gh cng c gi tr rt nh so vi bin i ng nng v entanpi v thng c b qua gh 0. Vy phng trnh nh lut nhit ng I cho dng kh s l: q = w = i +22 (3-11) dq = di + 22d _ ,(3-12) d. Phng trnh nh lut nhit ng I i vi cc qu trnh hn hp Khi hn hp cc cht kh khng thc hin cng i vi mi trng (ln = 0) v gi thit rngkhngtraoinhitvimitrng(dq=0).Vytdngtngqutcaphngtrnh nh lut nhit ng I ta c: W = 0 ; Wh1 = Wh2 = const (3-13) y:PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com34 Wh1 - nng lng ton phn ca h trc khi xy ra qu trnh hn hp; Wh2 - nng lng ton phn ca h sau khi xy ra qu trnh hn hp. 3.2. Qu trnh hn hp ca kh 3.2.1.Hn hp trong th tch cho Gi s cho mt bnh kn vi th tch V bn trong c mt vch ngn N (hnh 3.1). Pha tri vch ngn c cha cht kh 1 c (p1, V1, T1); bn phi vch ngn cha kh 2 c ( p2, V2, T2). Khi b vch ngn, hai cht kh s hn hp vo nhau. y cn xc nh nhit T, p sut p ca hn hp khi bit th tch V ca hn hp. Theo tnh cht ca hn hp kh ta c: V = V1 + V2 G = G1 + G2

y:G - khi lng ca hn hp kh; G1, G 2 -khi lng ca kh thnh phn. H nhit ng trc khi xy ra qu trnh hn hp gm cht kh 1 v cht kh 2 trong bnh l h kn, nng lng ton phn ca h c biu th bng ni nng: Wh1 = U1 + U2

H nhit ng sau khi xy ra qu trnh hn hp l hn hp kh cng trong bnh, nng lng ton phn ca h l ni nng ca n: W2 = U Theo nh lut nhit ng I cho cc qu trnh hn hp ta c: Wh1 = Wh2 U = U1 + U2 (3-14) i vi kh l tng, nu quy c ni nng ca kh 0C bng khng th ni nng nhit Ti no s l ui = Cvi Ti . Vy t (3-14) ta c: GCvT = G1Cv1T1 + G2Cv2T2

1 1 1 2 2 2+v vvGC T G C TTGC= 1 1 1 2 2 2 v vvg C T g C TC+ Theo cng thc (2-14) Cv = giCvi , vy ta c: T = 1 1 1 2 2 2 v vvg C T g C TC+=1 1 1 2 2 21 1 2 2++v vv vg C T g C Tg C g C Tng qut i vi hn hp ca n cht kh l tng, ta c: Hnh 3-1. Hn hp trong th tch cho N p1 V1 T1 p2 V2 T2 p V T PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com35 11ni vi iini viig C TTg C(3-15) Khi bit th tch hn hp V v nhit T tnh theo (3-15) ta c th xc nh c p sut p ca hn hp kh l tng t phng trnh trng thi: GRTpV; i iR g R = iGGRi , vy GR = i iG R Ta c: p = TV(G1R1 + G2R2) v p = TV(1 11pVT + 2 22p VT)Tng qut i vi hn hp n kh l tng ta c: p = TV1ni iiipVT(3-16) 3.2.2. Hn hp theo dng Hnhptheodngctothnhkhitaningdnccdngkhthnhphnvo mt ng chung. H nhit ng trc khi xy ra qu trnh hn hp gm cc dng kh 1 v dng kh 2 l h h, nng lng ton phn ca h c biu th bng entanpi (b qua ng nng v th nng ca dng kh). Lc ny ta c:Wh1 = I1 + I2 Hnhitngsaukhixyraqutrnhhnhpldngkhhnhp(hh),nng lng ton phn cng c biu th bng entanpi Wh2 = I TphngtrnhnhlutnhitngIchoqutrnhhn hp ta c: Wh1 = Wh2 v I = I1 + I2

G.i = G1.i1 + G2.i2 v i = g1.i1 + g2i2 Tng qut, khi c n dng kh hn hp ta c: n1 ii ii g i(3-17) i vi kh l tng, khi quy c entanpi 0K bng khng (3-17) ta c: CpT = nii pi iT C g1(3-18) Hnh 3-2. Hn hp theo dng PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com36 pi in1 ii pi iC gT C gT (3-19) Khi bit p sut v nhit tnh theo (3-19) ta c th tnh c th tchkhi s dng phng trnh trng thi ca kh l tng i vi hn hp: pV = GRT V =pT GR = i iR GpT= ii iTV ppT(3-20) vVi kh thc (v d hi nc) ta c th gii bi ton bng th i-s: Thc t l qu trnh hn hp l qu trnh khng thun nghch, nhng khi gi thit qu trnh hn hp on nhit l thun nghch th biu thc bin i entropi s bng khng: S = 0 hay Sh1 = Sh2

S = S1 + S2 G.s = G1.s1 + G2.s2 v s = g1.s1 + g2 .s2

Tng qut ta c: n1 ii is g s (3-21) Vylnugithitqutrnhhnhponnhitlthunnghchthtrngthihn hp trn th i-s (hnh 3-3) tha mn cc ng thc (3-19) v (3-21) . Ta thy trng thi hn hp 3 phi nm trn ng hn hp 1-2 v c chia theo t l nghch vi g1 v g2 . Ngha l on 1-3 v 3-2 phi tha mn: 2 33 1 = 12gg Khi bit im 3 l trng thi ca hn hp, t th i-s ta d dng xc nh c nhit , th tch ring v p sut ca hn hp. Chng minh im hn hp 3 tha mn (3-17) v (3-21): Tht vy, hai tam gic vung 1b3 v 3a2 ng dng vi nhau nn ta c: 32ba = 1 33 2 hay 1 33 2s ss s= 21gg T : g1(s3 s1) = g2(s2 s3) (g1 + g2)s3 = g1s1 + g2s2 3 g2 b a g1 2 1 i2 i3 i1 i s s2 s3s1 Hnh 3-3. th i-s qu trnh hn hp theo dng theo dng PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com37 s3 = g1s1 + g2s2 ; tha mn (3-21) Cng t hai tam gic ng dng trn ta c: 1 33 2 = 13ba hay 21gg = 1 33 2i ii i T ta cng tm c: i3 = g1i1 + g2i2 ; tha mn (3-17) 3.2.3.Hn hp khi np vo th tch c nh Gi s ta c mt bnh th tch V trong c cha sn mt cht kh c khi lng G1 p sut p1 v nhit T1 (hnh 3-4). By gi qua ng ng dn ta np thm vo bnh dng kh c khi lng Gi , p sut pi (pi > p1) v nhit Ti . Lc ny trong bnh xy ra qu trnh hn hp, ta cn xc nh nhit T v p sut p ca hn hp. H nhit ng trc khi xy ra qu trnh hn hp gm khi kh c trong bnh (h kn) v dng kh np thm vo (h h). Vy nng lng ton phn ca h trc khi xy ra qu qu trnh hn hp l: Wh1 = U1 + Ii Sau khi hn hp, hn hp kh trong bnh l h kn vi nng lng ton phn l ni nng U. Vy ta c:Wh2 = U TphngtrnhnhlutnhitngIcho qu trnh hn hp ta c: Wh1 = Wh2 v U = U1 + Ii Gu = G1u1 + Giii v u = g1u1 + giii Tng qut, khi np vo bnh t 2 n n+1 dng kh ta c: u =g1u1 + +12nii pi iT C g(3-22) Mt khc Cv = vi iC gVy ta c: ++Vi i1 n2 ii pi i 1 1 v 1C gT C g T C gT (3-23) KhibitnhitTvthtchV,tacthtmcpsutpcahnhpkhl tng t phng trnh trng thi: pV = GRT P1 G1 T1 pi Gi Ti p T V Hnh 3-4. Hn hp khi np vo th tch c nh PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com38 p =VT GR = i iR GVT= ii iTV pVT(3-24) 3.3. Cc qu trnh nhit ng c bn ca kh l tng 3.3.1. Khi nim qu trnh nhit ng Qu trnh nhit ng l qu trnh bin i lin tc ca cc thng s trng thi t trng thi cn bng ny sang mt trng thi cn bng khc theo mt qu trnh no . 3.3.2. Cc gi thit khi nghin cu qu trnh nhit ng - Mi cht l 1 kg kh l tng - Qu trnh l qu trnh thun nghch: l nhng qu trnh ch gm nhng trng thi cnbng,khitinhnhtheochiuthunvtinhnhngctrlithhvmi trng l khng i. + Qu trnh thun nghch l qu trnh trong mi cht bin i qua cc trng thi u l cc trng thi cn bng. + Trng thi cn bng l trng thi trong cc thng s trng thi ca h thng phn b ng u trong ton b h thng v cn bng vi mi trng. 3.3.3. Xt qu trnh tng qut a bin Qu trnh a bin l mt qu trnh tng qut ca kh l tng, trng thi thay i theo mt quy lut bt k.Phng trnh biu din qu trnh a bin: Da vo biu thc ca nh lut nhit ng I q = Cv.dT + p.dv q = Cp.dT - v.dpGi s nhit dung ring ca qu trnh a bin l Cn ta c: q = CndT(3-25) Ta c: CndT = Cv.dT + p.dvCndT. = Cp.dT - v.dp (Cn - Cp).dT = - v.dp (Cn - Cv).dT = p.dv Chia phng trnh trn cho phng trnh di ta c: pdvvdpC CC Cv np n (3-26) t:v np nC CC Cn (3-27) Tac:npdv+vdp=0;ylphngtrnhviphnbiudinmiquanhgiaccthngs trong qu trnh a bin. Gii phng trnh vi phn ny ta c phng trnh biu din qu trnh a bin. gii phng trnh trn ta tin hnh phn ly bin s ta c:0pdpvdvn +Tch phn hai v, rt gn: pvn = const ;n c gi l s m a bin(3-28) T biu thc s m a bin n ta c th xc nh c nhit dung ring ca qu trnh a bin:1 nk nC Cv nng vi mi gi tr ca n ta c mt qu trnh nhit ng c th v tm c biu thc nhit dung ring ca qu trnh . PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com39 Quan h gia cc thng s ca qu trnh suy ra t phng trnh ca qu trnh nh sau: 12pp = n21vv

,_

; 12vv = n121pp

,_

(3-29) tm quan h gia nhit v p sut hoc th tch, ta s dng phng trnh trng thi: p1v1 = RT1 v p2v2 = RT2 , suy ra 12TT = 12pp.12vv = 12pp.n121pp

,_

Vy 12TT =n1 n12pp

,_

= 1 n21vv

,_

(3-30) Cng thay i th tch ca qu trnh a bin c th tm t quan h dl = pdv khi rt pvn = p1v1 th vo ly tch phn t v1 n v2, qua bin i cui cng ta c: l12 = 21vvnn1 1dvvv p= p1v1n dv v21vvn = 1 nv pn1 1(v11-n v21-n) = 1 nv p1 1( 1- n 112vv

,_

)l12 = 1 npv1(1 1 n21vv

,_

)= 1 npv1(1 n1 n12pp

,_

) Cng k thut ca qu trnh a bin: dlkt = ndl lkt12 = 1 nv pn1 1(1 n1 n12pp

,_

) Nhit dung ring ca qu trnh a bin Cn c th tm c: Cn = Cv.1 nk n (3-31) Lng nhit trao i vi mi trng trong qu trnh a bin: dq = CndT hay q = Cn(T2 T1) (3-32) hocq = u + l12 v q = i + lkt12 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com40 bin thin entrpi ca qu trnh a bin s l: ds = Tdq =TdT Cn, suy ra s = s2 s1 = Cnln12TT(3-33) 3.3.4. Mt s qu trnh nhit ng c bn a.Qu trnh ng p Khi nim : Qutrnhngplqutrnhnhitngctinhnhtrongiukinpsut khng i. p = const T phng trnh p.vn = const, vin = 0 ta c p = const. Vy vi n = 0 ta c qu trnh ng p. Quan h gia cc thng s : p dng phng trnh trng thi: pv = RT Trng thi 1:p1.v1 = R.T1 Trng thi 2:p2.v2 = R.T2 Vi p1 = p2 = const chia hai phng trnh cho nhau ta c:1212vvTT(3-34) (Trong qu trnh ng p th tch t l thun vi nhit T) Biu din qu trnh trn th p-v v T-s: cngngptrnthT-stacngphivtngimmttheocchm T =f(s)p=const. ng ng p l tp hp nhng ng cong lgarit c b li quay v pha trc honh, ng biu din cng xa trc tung c tr s cng nh: pa > pb > pc. Xc nh bin thin ni nng, cng, nhit lng ca qu trnh: + bin thin ni nng: Vi mi qu trnh ta c: du = CvdT Vi qu trnh 1-2: u = CvT = Cv(T2 - T1) = Cv(t2 - t1); [kJ/kg](3-35) + Cng ca qu trnh:- Cng thay i th tch ca qu trnh: 2 1 p p1 = p2 v1v2v T T2 T1 s1s2s lgn 1 2 Hnh 3-5 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com41 21gndv . p l ; [J/kg] = 10-3.p(v2 - v1);[kJ/kg] (3-36) - Cng k thut ca qu trnh: 0 dp . v l21kt (3-37) + Nhit lng ca qu trnh; qu trnh ng p c nhit dung ring l Cp cho nn ta c:q = CpdT v q = Cpt = CpT = Cp(T2 - T1) = Cp(t2 - t1);[kJ/kg]. p dng nh lut nhit ng 1:q = u + lgn = CvT + p(v2 - v1)suy ra CpT = CvT + R.T(3-38) Ta suy ra: Cp = Cv + R ;Cp - Cv = R ; y chnh l cng thc Mayer . Nh vy, p dng nh lut nhit ng 1 vo qu trnh ng p ta chng minh c cng thc Mayer.b. Qu trnh ng tch Khi nim : Qutrnhngtchlqutrnhnhitngctinhnhtrongiukinthtch khng i : v = const. Vi n = ta c qu trnh ng tch. p dng phng trnh trng thi: pv = RT Vi trng thi 1: p1.v1 = R.T1 Vi trng thi 2: p2.v2 = R.T2 Vi v1 = v2 = const chia hai phng trnh cho nhau ta c: 1212ppTT (3-39) (Trong qu trnh ng tch p sut t l thun vi nhit T) Biu din qu trnh trn th p-v v T-s : Ta xt qu trnh 1-2 Trn th p-v ng v = const l tp hp cc ng thng song song vi trc tung. T th ta thy ngay cng thay i th tch lgn = 0. biu din ng v = const trn thT-s ngi ta phi v tng im theo cc hm T = f(s)v=const. c im v = const trn th T-s l ng cong logarit c dc cao, quay b li v pha trc honh, ng biu din cng xa trc tung c gi tr cng ln; va < vb < vc. Xc nh bin thin ni nng, cng, nhit lng ca qu trnh : + bin thin ni nng; vi mi qu trnh ta c: du = CvdT Hnh 3-6 v1= v2v 2 1 s2 s1s 1 2 lkt q p p1 p2 T T1 T2 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com42 Vi qu trnh 1-2: u = CvT = Cv(T2 - T1) = Cv(t2 - t1); [kJ/kg](3-40) + Cng ca qu trnh:- Cng thay i th tch ca qu trnh: 21gn0 dv . p l(v qu trnh v = const c dv = 0) (3-41) - Cng k thut ca qu trnh:) p p ( v dp . v l1 221kt ;[J/kg](3-42) + Nhit lng ca qu trnh; qu trnh ng tch c nhit dung ring l Cv cho nn ta c:q = CvdT v q = Cv(T2 - T1) = Cv(t2 - t1); [kJ/kg](3-43) Mt khc theo nh lut nhit ng 1: q = u + lgn = u = Cv(T2 - T1)(3-44) + Nhn xt: Trong qu trnh ng tch nhit lng ca qu trnh hon ton dng thay i ni nng. c. Qu trnh ng nhit Khi nim:Qutrnh ngnhitlqutrnhnhitngctinhnhtrongiukinnhit khng i: T=const. p dng phng trnh trng thi: pv = RT Trng thi1:p1.v1 = R.T1 Trng thi2:p2.v2 = R.T2 Trng thin:pn.vn = R.Tn V T1 = T2 = ... =Tn cho nn p1.v1 = p2.v2 = = pn.vn = const. Vy phng trnh biu din qu trnh ng nhit l: pv = const. (T phng trnh pvn = const vi n = 1 ta c qu trnh ng nhit) Quan h gia cc thng s : T phng trnh pv = const ta c: p1.v1 = p2.v2suy ra 21p2vvpp ;(3-45) (Vy trong qu trnh ng nhit p sut v th tch t l nghch vi nhau). Biu din qu trnh trn th p -v v T s : Trn th p-v ng T=const c biu din bng ng cong hypecbol i xng. Trn th T-s ng T=const l ng thng song song vi trc honh. Xc nh bin thin ni nng, cng, nhit lng ca qu trnh : + bin thin ni nng; vi mi qu trnh ta c: du = CvdT p p1 p2 T1 = T2 T s1 s2 s v1 v2 v 21 1 2 Hnh 3-7 lgn q PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com43 Vi qu trnh ng nhit 1-2 ca kh l tng: u = 0+ Cng ca qu trnh:- Cng thay i th tch ca qu trnh: 21gndv . p l ;[J/kg].Trong qu trnh ng nhit p lun thay i.T cng thc pv = const ta c pv = p1v1 suy ra vv pp1 1 .Thay tr s p vo biu thc xc nh cng ta c: 211221211 1 gnppln RTvvln RTvdv. v p dv . p l ; [J/kg](3-46) (Trong qu trnh ng nhit ta c th thay 21p2vvpp) - Cng k thut ca qu trnh: Trong qu trnh ng nhit p1v1 = p2v2 ngha l cng lu ng bng khng cho nn cng k thut bng cng thay i th tch.+ Nhit lng ca qu trnh: Theo nh lut nhit ng 1 ta c: q = u + lgn

Vi kh l tng khi T = const th u = 0.V vy: 211221211 1 gn kt 12ppln RTvvln RTvdv. v p dv . p l l q ;[J/kg].(3-47) Mt khc ta c Tqds cho nn q = Tds. Vy:q = T.s = T.(s2 - s1); [kJ/kg](3-48) d. Qu trnh on nhit Khi nim: Qu trnh on nhit l qu trnh thay i trng thi mt cch lin tc trong iu kin khng trao i nhit vi mi trng.q = 0 th q = 0; q=CndT = 0 dn n Cn=0. Ta cng c: q=Tds =0 nn ds =0 v s = const. Qu trnh on nhit c entropi khng i. xydngphngtrnhbiudinqutrnhonnhittadavonhlutnhit ng 1:q = Cv.dT + p.dv q = Cp.dT - v.dpV qu trnh on nhit c q = 0 cho nn ta c: Cv.dT + p.dv = 0 Cp.dT - v.dp = 0 Cv.dT = - p.dv (a) Cp.dT = v.dp(b)Chia (b) cho (a) ta c dvdp.pvCCvp cho nn ta c:0dvdp.pvk + PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com44 Gii phng trnh vi phn trn ta c: lnvk + lnp = const lnpvk = const;pvk = const;k - s m ca v trong qu trnh on nhit cho nn n c gi l s m on nhit. Vy ta c phng trnh biu din qu trnh on nhit: pvk = const Quan h gia cc thng s: + p = f(v); T pvk = const ta suy ra k2 2k1 1v p v p ; k2112vvpp

,_

; (3-49) + T = f(v); p dng phng trnh trng thi ta c: Vi trng thi 1: p1.v1 = R.T1 Vi trng thi 2: p2.v2 = R.T2 Chia phng trnh di cho phng trnh trn ta c: 121212vv.ppTT(*) Thay tr s ca 12pp t (2-39) vo (*) ta c: 1 k2112k2112vvvv.vvTT

,_

,_

; (3-50) + T = f(p);Thay tr s ca 12vvt (3-49) vo (*) ta c: k1 k12k1211212pppp.ppTT

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,_

; (3-51)Biu din qu trnh trn th p-v v T-s: Nhn xt V k > 1 cho nn ng on nhit trn th p - v l ng hybecbol dc hn ng ng nhit. T cng thc Tqds , vi qu trnh on nhit q = 0 suy ra ds = 0 v s = const nn ng on nhit trn th T - s l ng thng song song vi trc tung. Xc nh bin thin ni nng, cng, nhit lng ca qu trnh: + bin thin ni nng; vi mi qu trnh ta c: du = CvdT s1 =

s2s 1 2 T1 T2 T 2s 2T 1

v1v2v p p1 p2 T=const T=const Hnh 3-8 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com45 Vi qu trnh 1-2: u = CvT = Cv(T2 - T1) = Cv(t2 - t1) ;[kJ/kg](3-52) + Cng ca qu trnh:V qu trnh on nhit c q = 0, theo nh lut nhit ng 1 ta c: u + lgn = 0 ;lgn = - u = Cv(T1 - T2);[kJ/kg].(3-53) Mt khc ta c th xc nh cng ca qu trnh theo cng thc: 2121kk1 1 gnvdv. v . p dv . p l; [J/kg] (V pvk = const ;p1v1k = pvk)(3-54) Tch phn v rt gn ta c: ) T T (1 kR) v p v p (1 k1l2 1 2 2 1 1 gn ; [J/kg](3-55) + Nhit lng tham gia vo qu trnh: q = u + lgn = 0 lgn= - u= - Cv(T2 - T1)Xc nh bin thin entrpi ca cc qu trnh nhit ng c bn :Cng thc chung: Tqds (3-56) Theo phng php tng qutTa da vo nh lut nhit ng 1 cho kh l tng: q = CvdT + pdvq = CpdT - vdp Ta c:TpdvTdTC dsv+ Theo phng trnh trng thipv = RT cho nn:vRTpVy: vRdvTdTC dsv+ (3-57) 1212vvvln RTTln C s + (3-58) Hoc:TvdpTdTC dsp (3-59) Theo phng trnh trng thipv = RT cho nn: pRTvVy: pRdpTdTC dsp (3-60) 1212pppln RTTln C s (3-61) Theo tng qu trnh c th - Vi qu trnh v = const: q = CvdT ; TdTC dsv ; 12vTTln C s (3-62) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com46 - Vi qu trnh p = const: q = CpdT ; TdTC dsp ; 12pTTln C s (3-63) - Vi qu trnh T = const: Tdqds ; Tqs (3-64) - Vi qu trnh on nhit: q = 0 ; ds = 0 ; s = const.(3-65) Nhn xt chung cho cc qu trnh:T phng trnh tng qut ca qu trnh a bin v biu thc NDR (nhit dung ring) 1 nk nC Cv n tathyrngnhngqutrnhngtch,ngp,ngnhit,onnhitl nhng trng hp ring ca qu trnh a bin. + Nu n =0, phng trnh pvn= const c dng p = const, NDR Cn= kCv= Cp; y l qu trnh ng p.+ Nu n = t ta c th bin i nh sau: ly cn bc n hai v phng trnh pvn= const ta c p1/nv=constnn khi n = t th v = const, biu thc NDR khi c Cn= Cv; qu trnh a bin s l qu trnh ng tch. + Nu n = 1 th phng trnh pvn = const thnh pv = const NDR Cn= =CT; l qu trnh ng nhit. + Nu n = k th pvk = const, NDR s l Cn= Ck= 0; l qu trnh on nhit. Tabiudinmtqutrnhabinbtktrnthp-vvT-s ;cbiudinbngcc ng i t im A ra mi pha (Hnh 3-9). y, ta biu din cc trng hp ring ca qu trnh a bin l cc qu trnh ng p, ng tch, ng nhit, on nhit. Chng ta xem du ca cng thay i th tch, nhit lng v bin i ni nng ca qu trnh a bin bt k nh sau: -Lyngngtchn=t;lgn=0lmranhgii,miqutrnhabinitimA hng v pha phi ng ng tch c cng thay i th tch lgn > 0 v v > 0. Ngc li mi qu trnh a bin xut pht t im A hng v pha tri ng ng tch c lgn < 0 v v < 0. - Ly ng on nhit n =k, q=0 lm ranh gii, mi qu trnh a bin t im A i v bn phi ng on nhit c q > 0 (mi cht nhn nhit) do s >0. Ngc li mi qu trnh xut pht t im A i v pha tri ng on nhit c q < 0 (mi cht thi nhit) do s 0 v T> 0; vi qu trnh a bin c chiu ngc li s c u< 0 v T< 0. n=1 p v n=0 A n=+ n=- n=k n=k n=0 n=-n=+ n=1A n=0 n=k n=1 n=1 n=k

n=+ T s Hnh 3-9PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com47 3.4. Cc qu trnh nhit ng ca kh thc Cc qu trnh nhit ng c bn (gi thit l thun nghch) xy ra i vi kh thc bao gm cc qu trnh: ng tch, ng nhit, ng p v on nhit. Tnhtonccqutrnhnhitngcnghalphixcnhccthngstrngthi uvcuicaqutrnh,xcnhcng,lngnhit,sthayininng,sthayi entanpi v entrpi. Vic tnh ton ch yu l s dng bng, hoc th ca tng mi cht ( thi-s,lgp-i...)vphngtrnhnhlutnhitngIchokhthc.Trngthiucaqu trnhcxcnhbnghaithngscho,trngthicuicaqutrnhcxcnh bng mt thng s cho ca trng thi cui vtnh cht ca qu trnh: nh qu trnh ng tch, ng p... 3.4.1. Xc nh bin i entanpi, entrpi v ni nng Trongccqutrnhnhitngcbnktrn,binientanpi,ninngventrpi c xc nh nh sau: i = i2 i1 (3-66) u = u2 u1 = (i2 p2v2) (i1 p1v1) (3-67) s = s2 s1(3-68) Cnlurngiviqutrnhngnhitcakhthcu0,i0chkhng phi bng khng nh i vi kh l tng. i vi kh thc cc qu trnh xy ra bao gi cng l cc qu trnh khng thun nghch. Nhng vy, y ta gi thit cc qu trnh ny l thun nghch nn qu trnh on nhit l thun nghch ca kh thc s c Tdqds = 0 hay s = 0; s = const. y qu trnh on nhit thun nghch cn gi l qu trnh ng entrpi. Diychngtasnghincuccqutrnhxyraivihinc,vihica cc cht lng khc s hon ton tng t 3.4.2. Qutrnh ng tch Hnh 3.10 biu din qu trnh ng tch ca hi nc trn th i-s . y trng thi u c xc nh (im 1) khi bit p1 v nhit t1. Trng thi cui c xc nh (im 2) khi bit p sut p2 v ng c tnh ca qu trnh ng tch v2 = v1 . T im 1 v im 2 ta c th xc nh c cc thng s cn li. Cng thay i th tch ca qu trnh ng tch l12 = 21vvpdv= 0(3-69) Cng k thut ca qu trnh ng tch: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com48 lkt12 = 21ppvdp = v(p1 p2)(3-70) Nhit ca qu trnh ng tch: q = u + l12 = u = u2 u1(3-71) xc nh cc thng s trng thi u v cui ca qu trnh bng cch dng bng s ta lm nh sau: Khi bit trng thi u l hi qu nhit (t1 > t(ps)) t bng nc v hi qu nhit theo p1, t1 tra c v1, i1 v s1. Nu trng thi cui l hi bo ha m th trc tin ta phi xc nh kh x2 t phng trnh: v1 = v2 = v2 + x2(v2 v2) x2 = '2"2'2 1v vv v(3-72) Khi bit x2 ta c th xc nh c cc thng s cn li ca trng thi cui. i2x = i2 + x2(i2 i2 )(3-73) s2x = s2 + x2(s2 s2 )(3-74) y v2, v2, i2 , i2 tra bng nc v hi nc bo ha theo p sut p2

3.4.3.Qu trnh ng p Hnh 3.11 biu din qu trnh ng p ca hi nc trn th i-s trng thi u c xc nh khi bit p sut p1 v nhit t1 . Trng thi cui c xc nh khi bit v2 v ng c tnh ca qu trnh p2 = p1. T cc im 1 v 2 xc nh, ta c th tm c tt c cc thng s tng ng cn li. Cng thay i th tch ca qu trnh: l12 = 21vvpdv= p(v2 v1)(3-75) Cng k thut ca qu trnh ng p: P1 t1 x = 1 P2 i s x2 1 2 v = const i s x = 1 P1 t1 1 2 x2 P = const v2 Hnh 3-10. th i-s qu trnh ng tchHnh 3-11. th i-s qu trnh ng p PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com49 lkt12 = 21ppvdp = 0(3-76) Nhit ca qu trnh ng p: q = i + lkt12 = i = i2 i1(3-77) xc nh cc thng s trng thi u v cui ca qu trnh bng cch dng bng s ta lm nh sau: Khi bit trng thi u l hi qu nhit (t1 > t(ps)) t bng nc v hi qu nhit theo p1, t1 tra c v1, i1 v s1 . Nu trng thi cui l hi bo ha m th trc tin ta phi xc nh kh x2 t phng trnh: v2 = v2x = v2 + x2(v2 v2) x2 = '2"2'2 2v vv v(3-78) Khi bit x2 ta c th xc nh c cc thng s cn li ca trng thi cui. i2x = i2 + x2(i2 i2 )(3-79) s2x = s2 + x2(s2 s2 )(3-80) y v2, v2, i2 , i2 tra bng nc v hinc bo ha theo p sutp2 = p1

3.4.3.Qu trnh ng nhit Hnh 3.13 biu din qu trnh ng nhit ca hi nc trn thi i-s. y trng thi u c xc nh khi bit kh x1 v nhit t1. Trng thi cui c xc nh khi bit p2 v c im ca qu trnh t2 = t1 . T cc im 1 v 2 ta xc nh c cc thng s cn li. Nhit ca qu trnh: q = 21ssTds= T(s2 s1) (3-81) Cng ca qu trnh suy ra t phng trnh nh lut nhit ng I l12 = q u lkt12 = q i(3-82) xc nh cc thng s trng thi u v cui ca qu trnh bng cch dng bng s ta da vo kh x1

v1 = v1x = v1 + x1(v1 v1) i1 = i1x = i1 + x1(i1 i1)(3-83) s1 = s1x = s1 + x1(s1 s1) y cc thng s v1 , v1 , i1 , i1 ...c xc nh t bng nc v hi nc bo hatheo nhit t1, khi bit trng thi 2 l hi qu nhit (t2 > ts(ps)) t bng nc v hi qu nhit theo t2 v p2 ta tra c v2 , i2 v s2 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com50 3.4.5. Qu trnh on nhit Hnh3.13biudinqutrnhonnhitthunnghch(ngentropi)cahinc. Trngthiucxckhibitp1vt1.Trngthicuicxcnhkhibitp2vtnh chtcaqutrnhs1=s2.Tccim1v2xcnhtacthddngtmccc thng s cn li. Nhit ca qu trnh: q = T.s = 0(3-84) Cng ca qu trnh suy ra t phng trnh nh lut nhit ng I q = u + l12 = 0 l12 = - u = u1 u2(3-85) q = i + lkt12 = 0 lkt12 = i = i2 i2 (3-86) Tacthxc nhccthngscatrngthiuvcuibngcchdngbngs. Khi bit trng thi u l hi qu nhit, t p1 v t1 tra bng nc cha si v hi qu nhit ta c v1, i1 v s1. Khi bit trng thi cui l hi bo ha m, ta xc nh kh x2 t phng trnh: s1 = s2 = s2 + x2(s2 s1)x2 = '2"2"2 1s ss s(3-87) y s2, s2 tra bng nc v hi nc bo ha theo p sut p2, cc thng s cn li v2 , i2 v s2 tnh tng t.x = 1 i s t2 1 x1 t1 P2 2 P1 t1 1 2 P2 x2 ss1 = s2 i x = 1 Hnh 3-12. th i-s qu trnh ng nhitHnh 3-13. th i-s qu trnh on nhit PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com51 Chng 4 QU TRNH LU NG V TIT LU Trong cc chng trc, ta nghin cu cc qu trnh c bn ca kh v hi ch hn chtrongccqutrnhthunnghchmkhngxtnvntccadngmicht.Trong chngnytasnghincuhaiqutrnhkhctronghthngh,cchnschuyn ng v m ca dng mi cht; l qu trnh lu ng v tit lu, trong qu trnh tit lu cn c xem l qu trnh khng thun nghch. A. QU TRNH LU NG 4.1. Nhng khi nim c bn Trongkthut,qutrnhlungcngdngrtrngri,nhkhinghincu dngmichttrongqut,mynn,tuabinkh,tuabinhi,ngcphnlc,tnla,v.v Trong qu trnh lu ng, vn tc v p sut mi cht thay i; qua ng tng tc, vn tc ca dngmichttng,psutgim;quangtngp,psutcamichttng,vntcca dng mi cht gim. 4.1.1. Nhng gi thit khi nghin cu qu trnh lu ng 1. Gi thit u tin l lu lng khi lng ca dng mi cht qua mi tit din ca ng dn u bng nhau v khng thay i theo thi gian; gi thit c biu th bng phng lu ng v n nh: G = 11 1vf = 22 2vf = = vf= const (4-1) hoc G = 1 1 1f = 2 2 2f = = f= const(4-1) Trong : G lu lng khi lng ca dng mi cht kg/s hoc kg/h; 1f ; 2f ;,f -dintchtitdincadngca vo, ca ra hoc mt tit din bt k (m2); 1 , 2 ,,-vntctrungbnhcadngmi cht cc tit din tng ng (m/s); 1v ,2v ,, vv 1 , 2 ,,- th tch ring v khi lng ring ca mi cht cc tit din tng ng; m3/kg v kg/m3. I I II II +d Hnh 4-1. Lu ng lin tc v n nh PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com52 Phng trnh trn c xy dng nh sau: lu lng mi cht vo tit din I l f , ra khi tit din II l) f (xf + dx. Trong mt n v thi gian, khi lng mi cht gia hai tit din tng ln. ) f (t = f- [ f+ x ( f ) dx] hoc: x ( f ) +) f (t = 0 (a) Phng trnh (a) l phng trnh lin tc ca dng lu ng mt chiu. Trong iu kin lu ng n nh th t = 0, nn ta c: dxd( f ) = 0(b) V f= const (c) Nn (c) hoc 4.1 (a); 4.1 (b) l phng trnh lu ng lin tc v n nh. 2. Gi thit th hai l vn tc trn mi im ca cng mt tit din u bng nhau v bng vn tc trung bnh trong tit din . Thc ra, trn cng mt tit din, vn tc rt khc nhau, st vch bng khng, tm ng vn tc thng l ln nht. 3. Gi thit th ba l mi cht lu ng trong iu kin on nhit thun nghch, ngha l trong qu trnh lu ng khng c hin tng ma st, hin tng xoy, v.v v khng trao i nhit vi mi trng xung quanh; nh vy trong qu trnh lu ng ds = 0; s = const v trn cc th T s; i s c biu th bng mt on thng song song vi trc tung. 4.1.2 Tc truyn m v tr s Mach Khi kho st qu trnh lu ng, ngi ta thng dng n tc truyn m a, cng tcltclantruynccchnngnhtrongmitrng.Trnghpchung,theokh ng hc ta c: pa (4-2) Vi qu trnh lu ng on nhit thun nghch ta c: kpa (4-2a) hoc: kpv a (4-2b) Vi kh l tng cn c th vit:kRT a (4-2c) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com53 y: p p sut tuyt i v v - khi lng ring v th tch ring R - hng s cht kh T - nhit tuyt i k - s m on nhit Nunguntochtngnmtrongdngmichtchuynngvivntc,thtc truyn m thanh theo dng mi cht l v ngc chiu dng mi cht l (a - ). Hnh4.2biuthcctrnghptruyndmtrongmitrngtnhvmitrngchuyn ng ngc chiu truyn m sau khi m thanh pht ra 2 giy. Hnh 4.2a biu th truyn chn ng trong mi trng tnh; 4.2b -truyn chn ng trong mi trngchuynngvivntcdim;4.2c-truynchnngtrongmitrngchuyn ng vi vn tc truyn m; 4.2d -truyn chn ng trong mi trng chuyn ng vi vn tc siu m. T4.2cvdtathy:trongdngtruyntntivngynlngxc nhbihnhcn Mach,nghalkhidngchuynngvivntclnhnhocbngtctruynmth trong dng mi cht tn ti mt vng m s chn ng nh hoc m thanh khng th truyn ti c. T cc cng thc (4-2a, b v c) ta thy tc truyn m a ph thuc vo bn cht (k v R) v thng s (p, V hoc T ) ca mi cht; i vi kh l tng ta thy khi nhit ca mi cht gim th tc truyn m trong mi cht cng gim. Khikhostschuynngcadngmicht,ngitacndngmtilngkhcdo nh vt l Mach ngi o xut, l tr s Mach: M = a(4-3) Tr s Mach M l t s gia vn tc ca dng vi tc truyn m a trong mi trng . Vi dng di m M < 1; vi dng siu m M > 1 v khi M = 1 th vn tc ca dng bng tc truyn m thanh trong mi trng . 21 1.2 21 2.1 2 1 2 2 1 Vng ng Vng tnh 2 1 Vng tnh Vng ng a bc d Hnh 4-2. Truyn chn ng trong mi trng tnh v ng PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com54 4.2.MT S CNG THC C BN Di y gii thiu mt s cng thc c bn dng cho kh l tng cng nh kh thc khi lu ng qua ng tng tc cng nh ng tng p. 4.2.1. Quan h gia s thay i vn tc vi s thay i p sut So snh hai dng ca phng trnh nh lut nhit ng I: dq = di vdp = di + 2d2 Ta c: 2d2 = - vdp hoc d= - vdp(4-4) T cc cng thc (4-4) ta thy dv dp lun ngc du nhau, v v v lun lun dng c ngha l trong dng mi cht lu ng, khi vn tc tng (trong ng tng tc) th p sut gim v khi p sut tng (trong ng tng p) th vn tc ca dng gim. Cng lu l, khi qua ng tng tc, khng nhng p sut m nhit ca mi cht cng gim, v lu ng c coi l on nhit thun nghch, nn: T2/T1=(p2/p1)(k-1)/k;mkhinhitgimththeo4.2c,tctruynmtrongcng gim. 4.2.2. Quan h gia s thay i vn tc vi s thay i mt T cng thc (4-4), nu thay v= 1 ta c: d= - dp v c th vit: d= ddp. d(a) Thay a t cng thc (4-2) vo ta c: d=-a2 d (b) Thay tr s M vo th c; d = - M2 d (4-5) T cng thc (4-5) c th rt ra kt lun: 1.d v dlun ngc du nhau; v M2, v lun lun dng, nh vy khi vn tc ca dng tng (trong ng tng tc) th mt gim v ngc li. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com55 2.Trng hp tr s M rt nh, ngha l khi vn tc ca dng nh hn rt nhiu so vi tc truyn m, th c th coi d = 0, ngha l coi mi cht l khng nn c. 4.2.3. Quan h gia s thay i vn tc vi s thay i tit din Ta ly lgarit phng trnh lu ng lin tc v n nh ri vi phn, ta c: d + fdf + d = 0 (4-6a) T ta c cc nhn xt: 1.Vi cht lng khng nn c, tc d = 0, ta c: fdf = - d (4-6b) Nh vy l i vi cht lng khng nn c khi qua ng tit din gim dn th vn tc ca dng tng ln v ngc li. 2.i vi cht lng nn c ta thay cng thc (4-5) vo (4-6a) c: -M2 d + fdf + d = 0 hoc fdf = (M2 - 1) d (4-6c) 2< a1< a ng tng tc 2< a1< a ng tng p 2> a 1> a ng tng tc 2> a1> a ng tng p Hnh 4-3. Hnh dng ng c dng di m Hnh 4-4. Hnh dng ng c dng trn m PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com56 Ta thy du ca df v d tu thuc vo du ca (M2 - 1) v f v lun dng, do c th rt ra mt s kt lun: a.Trong phm vi M2 1 < 0 tc M < 1 th df v d lun ngc du nhau, ging nh i vichtlngkhngnnc.nhvy,ividngdimcngnhdngcht lng khng nn c, ng tng tc c tit din nh dn v ng tng p c tit din ln dn (Hnh 4.3a, b). b.i vi dng siu m, M > 1 th c kt lun ngc li: df v d lun lun cng du, nghalngtngtcctitdinlndnvngtngpctitdinnhdn(Hnh 4.3a, b). c.Khi M = 1 th d l hu hn ch vi iu kin fdf = 0, cho nn vi ng tng tc a t vn tc di m thanh thnh siu m th phi c c ng m mt bn c tit din nh dn v bn kia c tit din ln dn. Khi ng tng tc lm vic bnh thng th vn tc ca dng c ng bng tc d truyn m trong mi trng . d.Ch nhn hnh dng ca ng khng kt lun l tng tc hay tng p m phi kt hp xem vn tc ca dng khi vo ng l di m hay siu m. 4.2.4. Vn tc v lu lng ca dng Vn tc v lu lng ca dng l hai i lng rt cn xc nh khi nghin cu qu trnh lu ng trong ng tng tc hay tng p. a. Vn tc ca dng T cng thc (4-4) ta c: d2/2 = - vdp; Ta cng c: lkt = - vdp Do vy: 2d2 = lkt (4-7a) Ly tch phn (4-7a) c: 22- 21= 2lkt12 (4-7b) T c :2 = 21 12 ktl 2 +(4-7c) y: 1 - vn tc ca dng ca vo ca ng; m/s; 2 - vn tc ca dng ca ra m cng c th mt v tr bt k no ca ng; m/s; lkt12 - cng k thut ca mi cht trong qu trnh lu ng on nhit; J/kg. Cc cng thc trn ng cho c ng tng tc v ng tng p. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com57 b. Lu lng ca dng Theo iu kin lu ng lin tc v n nh th lu lng qua mi tit din u bng nhau v bng mt s khng i, nn ch cn tnh lu lng qua mt tit din no m thy thun li nht. Cng thc chung tnh lu lng khi lng l cc cng thc (4-1a, b), ch cn lu l khi chn mt tit din fi no , th phi ly cc thng s vi, icng nh vn tc iti tit din . 4.3. NG TNG TC ngtngtclngmkhimichtlungquanthvntctng.xcnhng khngphinhnhnhdngngmphibitchcchnrngdngmichtcvntc lun lun tng ln. Theo hnh dng c th chia lm ba loi ng tng tc (Hnh 4.5) 1.ng tng tc nh dn: loi ny c tit din gim dn, tc l df < 0. T cng thc (4-6c) ta thy, ng tng tc nh dn ch c th lm vic viM < 1, ngha l ch c th dng cho dng di m. Nu dng siu m vo ng c tit din nh dn th vn tc s gim, p sut tng, nh vy ng tr thnh ng tng p. 2.ng tng tc ln dn: loi ny c tit din tng dn, tc l df > 0, n ch lm vic vi dng c M > 1, nu dng vo c M < 1, s bin thnh ng tng p. ng tng tc ln dn t gp trong thc t. 3.ngtngtchnhp:cngilngtngtcLaval,domtonngtngtcnh dn ghp vi mt on ng tng tc ln dn. Ch ghp c tit din nh nht gi l c ng. ng tng tc hn hp c dng kh rng ri v c th dng cho vn tc dng t di m, thm ch mi trng tnh n vn tc siu m. Ba loi ng tng tc trn tuy c hnh dng khc nhau, lm vic trong phm vi vn tc khc nhau, nhng c c im ging nhau: qua ng, vn tc dng lun lun tng ln, mi cht thay i theo quy lut qu trnh on nhit thun nghch, c thdng cc cng thc cng nh th khi tnh qu trnh gin n on nhit thun nghch ca kh l tng hoc kh thc. Hnh 4.6 biu th qu trnh lu ng trn th i s, giao im ca cc ng p1 v t1 xc nh trng thi mi cht vo ng, cn p2 l p sut ca mi cht ca ra ca ng. Ta thy quangtngtc,ntopikhngi,vntctng,psut,nhit,entanpivvntc truyn m trong u gim. i s i1 i2 x=1 2 1 p1 t1 p2 s1=s2 a b c Hnh 4-5. Cc dng ng tng tc Hnh 4-6. Qu trnh lu ng ca ngtng tc trn th i-s PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com58 4.3.1. ng tng tc nh dn L ng tng tc c tit din gim dn, df < 0, n ch lm vic vi mi cht khng nn c hoc mi cht nn c trong phm vi M < 1. a. Vn tc ca dng i vi ng tng tc, vn tc ca vo nh hn nhiu so vi vn tc ca ra, nhiu khi bng khng, nn cng thc (4-7c) c th vit thnh: 2= ktl 2 ; m/s (4-9a) lkt cng k thut trong qu trnh lu ng, tc qu trnh gin nh on nhit.Thay gi tr ca lkt = i1 i2 vo (4-9a) c: 2=) i i ( 22 1 ; m/s (4-9b) Cng thc (4-9b) dng c cho c kh thc v kh l tng nhng hay dng cho kh thc vi vic s dng th i s hoc bng s. Ch ltrongcng thc ly i theon v J/kg, nu dng n v kJ/kg nh trong cc bng th: 2= 44,82 1i i ; m/s (4-9c) Nu thay lkt ca kh tng vota c: 2= ( )11]1

,_

k / 1 k121 1pp1 v p1 kk2 ; (m/s) (4-9d) C th thay: p1v1 = RT1 v c 2= ( )11]1

,_

k / 1 k121pp1 RT1 kk2 ; (m/s) (4-9) Cc cng thc (4-9a, b, c v d) dng tnh vn tc ca dng ca ra ca ng tng tc, trong p2, i2 l thng s ca mi cht ca ra ca ng, khng phi l ca mi trng sau ng. Nu thay thng s mt tit din bt k, s tnh c vn tc ca dng tit din . Quanhgia 2 vip2/p1theo(4-9d)cthbiudintrnhnh4-7.Tathyvntcca dng ph thuc vo bn cht (k, R), vo thng s ban u (p1, v1, T1) c bit ph thuc rt nhiu vo mc gin n = p2/p1. Khi =1th 2 =0, gimngitrtihn 1ccpp th 2 bngvntctruynm, thng gi l vn tc ti hn, k hiu bng cv c gi l t s p sut ti hn. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com59 max c c 1 =p2/p1 Hnh 4-7. Quan h gia2 v p /pNu cthtiptcgimth 2 tiptctng,nu 0 th: 2 1 1 maxv p1 kk2 ; m/s (4-10) Trong thc t, i vi ng tng tc nh dn,khng th gim n 0, m ch gim n c , nn vn tc dng cng ch c th tng t 0 n vn tc ti hn cm khng th t c max . T s p sut ti hn: c= 1 kk1 k2

,_

+(4-11) c chng minh nh sau: Ta c: c=

,_

k1 kc 1 11 v p1 kk2(a) hay 1 1c ck1 kcv pv p11 k2

,_

(b) Theo qu trnh on nhit:p1v1k = pcvck ta c: k1 kck1 k1c1 kc11 1c cppvvv pv p

,_

,_

(c) Thay (c) vo (b) c: ( )( )1]1

k1 kck / 1 kc11 k2 (d) V cui cng c t s ti hn: ( ) 1 k / kc1 k2

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+ Tcngthc(4-11)tathy:tspsuttihn c chphthucvobnchtca mi cht (ph thuc k). i vi kh l tng: 1 nguyn t vi k = 1,67, ta c c= 0,484 2 nguyn t: k = 1,4 v c= 0,528 3 nguyn t tr ln: k = 1,3 v c= 0,546 PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com60 Vi hi nc bo ha kh, c th ly gn ng k = 1,135 v c= 0,577. Vi hi nc bo ha m c k = 1,035 + 0,1.x khi x 0,7; nu x = 0,7 th k = 1,105 v c = 0,583. Vi hi nc qu nhit k = 1,3; c = 0,55. Khi khng cn tnh chnh xc, c th ly cxp x 0,5 ngha l qua ng tng tc nh dn, p sut khng th gim xung qu 1/2.Khi t n c , ta tnh c vn tc ti hn: ( )c 1 c2 i i ; m/s(4-12a) Hoc thay tr s c vo (4-9d) c: c 1 1k2 p vk 1+; m/s(4-12b) hoc:c 1k2 RTk 1+; m/s(4-12c) Trong : ic entanpi ca mi cht trng thi ti hn, xc nh theo 1c cp p v sc = s1. b. Lu lng dng T phng trnh lu ng lin tc v n nh: 1 1 2 21 2f f fG ... constv v v ; kg/s Thay gi tr ca vn tc v thng s trng thi vo tit din tng ng bt k, s tnh c lu lng qua tit din , m cng l lu lng ca dng, thng tnh theo ca ra ca ng. Thay (4-9b) vo (4-1a) c: ( )2 1 22f 2 i iGv ; kg/s (4-13a) y: i1, i2 v v2 l thng s mi cht ca vo v ra ca ng tng tc, xc nh theo qu trnh gin n on nhit trn c s bit thng s ca trng thi u (vd p1 v t1) v mt thng s trng thi cui th d p2 v s2 = s1. Nu thay (4-9d) vo (4-1a) ta c: ( ) k 1/ k 1/ k2 1 111 kG f 2 p v 1v k 1 1 ] PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com61 Sau khi bin i ta c: ( ) k 1 / k 2/ k 121p kG f 2k 1 v+ 1 ]; kg/s (4-13b) y: f1, 1 , p1, v1 - cc i lng ca vo ca ng tng tc; f2, 2 , p2, v2 - cc i lng tng ng ca ra ca ng tng tc; c th thay bng cc i lng mt tit din tng ng bt k. T cc cng thc (4-13a, b) ta thy: lu lng khi lng G ph thuc vo din tch tit din ng, bn cht mi cht, thng s ban u v mc gin n camicht.Quamtngtngtcxcnhv michtcthngsbanuxcnh,thGch phthucvo vquanhcthbiudin trn hnh 4.8. Ta thy khi = 1 th G = 0, gim th G tng t 0 n mt gi tr Gmax ri li gim n 0 khi = 0. Ta c th xc nh c Gmax nu ly o hm bc 1 ca G theo cho bng 0 v o hm bc hai m; gii ra ta c Gmax tng ng vi: kk 1c2k 1 _ + , Nh vy lu lng t n gi tr cc i vi t s p sut ti hn. Thay gi tr ca cvo(4-13a v b) c: ( )2 1 cmaxcf 2 i iGv ; kg/s (4-14a) v( ) 2/ k 11max 21p k 2G f 2k 1 v k 1 _ + + ,; kg/s (4-14b) c. Kho st ng tng tc nh dn theo p sut ca mi trng sau ng p2 Trong khi tnh ton cn bit thng s mi cht ca ra ca ng, nhng thng li d bit p sut ca mi trng sau ng p2, do vy phi bit xc nh p2 theo p2. Cho mi cht c thngsbanup1,v1,quangtngtcnhdnphunvomitrngcpsutp2iu chnhc bng bm chn khng (hnh 4-9). Tathy khi ' gim t 1n c th tng t0 G c Gmax 1 0 Hnh 4-8. Quan h G theo PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com62 n cv G tng t 0 n Gmax ging nh cc cng thc trn, nhng khi 'gim t cn 0 th vn tc v lu lng gia gi tr c v Gmax khng i, khc vi cc quan h trong cc cng thc. iu ny thc ra khng phi l mu thun gia l thuyt v thc t, v trong cc cng thc trn p2 l p sut ca mi cht ca ra ca ng tng tc, cn p2 l p sut ca mi trng sau ng. Ta bit rng s gim p sut mi trng pha sau lan truyn vo ng tng tc vi vn tc tuyt i bng( )2a , khi p2/p1 t n tr s ti hn, 2 = a th a - 2= 0, ngha l s gim p sut trong mi trng sau ng khng th lan truyn vo trong ng c, nn mc cho p2 gimxung,thmchchon0thp2vngibngpc,vvntcvngigitr c ,lu lng vn gi gi tr Gmax khng i. Nh vy khi bit p sut p2 ca mi trng saung, th phi xc nh p2 tit din cui ca ng tng tc nh sau: Khi: p2/p1 > cly p2 = p2 (4-15a) p2/p1 = cly p2 = p2 = pc(4-15b) p2/p1 < cly p2 = c 1p i2 nn 2t 2 < v t s: 2y2 (4-21) - h s vn tc, c th xc nh qua thc nghim, h s1 . Do vn tc ca dng gim nn ng nng ca dng cng gim. Ta c hiu sut ca ng tng tc bng t s gia ng nng thc t vi ng nng l thuyt: Hnh 4-12. Cc trng hp lm vic ca ng tng tc hn hp Hnh 4-13. Qu trnh lu ng dng thc t PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com68 222 2t 2ttt 22 2/ 2/ 2 _ ,(4-22) B. QU TRNH TIT LU 4.4.C IM CA QU TRNH TIT LU Tit lu l hin tng ca dng mi cht lu ng qua mt tit din thay i t ngt (hnh 4-14a), th d nh khi qua cc van ng m trn ng ng, cc xupap trong my nn hoc ng c, cc ca nghn trong lu lng k, van tit lu trong my lnh hoc bm nhit v.v Qua qu trnh tit lu p sut ca mi chtgim, nhng khng sinh ngoi cng mgy nn tn tht nng lng. Sdpsutgimxungvkhititlu tothnhxoymastrtmnh;vvy titlulmtqutrnhkhngthun nghchinhnh.gimpsutph thucvovntcvmccogim din tch tit din ca dng mi cht. Qutrnhtitlutinhnhrtnhanh, nhitlngtraoigiamichtv mitrngnhkhngngksovi nnglngcadng,nnqutrnhtit lu c th xem l qu trnh on nhit, nhng dng khng thun nghch nn khng phi l qu trnh ng entropi. xt thm c im ca qu trnh tit lu, ta dng phng trnh nh lut nhit ng I: ktq i l + ; V khng sinh cng nn lkt = 0 v v qu trnh coi l on nhit nn q = 0, v do qu trnh tit lu: i 0 (4-23a) hoc: i2 = i1 (4-23b) Nh vy, c im ca qu trnh tit lu on nhit l entanpi ca mi cht trc v sau tit lu bng nhau (hnh 4-14b). Cnlu:vqutrnhtitlulkhngthunnghchnnchbiudinbngnhngng chm gi thit ni lin trng thi trc v sau tit lu v cng khng th xem tit lu l qu trnh ng entanpi c. Trng thi trc khi tit lu c th c xc nh bng phng trnh, bng bng hoc ththeoiukincho,ivinchtmtphacnbithaithngstrngthiu, cn trng thi sau tit lu xc nh theo c im i2 =i1 v mt thng s cn phi cho, th d nh p2 hoc t2. Kho st qu trnh tit lu ca hi nc ta thy: Hnh 4-10. Hin tng tit lu PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com69 1.Qua tit lu, p sut gim xung, nng lng b tn tht khng sinh cng. 2.Nhit thng thng gim xung, cng c lc khng i, thm ch tng ln, nhng entanpi trc v sau lun lun bng nhau. 3. kh ca hi bo ha m thng tng, nhng cng c lc khng i, thm ch gim xung. 4.Thng c th a hi bo ha kh thnh hi qu nhit v qu nhit thng tng mc d nhit ca hi thng gim. Vi nhng c im trn nn tit lu thng l hin tng c hi (tn tht nng lng) nhng khtrnhkhinhkhicncvanngmv.vnhngcngnhiukhicli,cch ng p dng nh van tit lu gim nhit trong my lnh, trong thit b o m ca hi bo ha hoc o lu lng ca dng v.v HIU NG JOULE THOMSON Nm 1852 Joule Thomson nu ln quan h gia s thay i p sut vi nhit ca mi cht qua qu trnh tit lu nh sau: dT dp (4-24a) y l h s ca hiu ng Joule Thomson, c th xc nh theo phng trnh vi phn ca entanpi: ppvdi C dT v T dpT 1 _ + 1 ,1 ]

Qua qu trnh tit lu di = 0 nn ta c: ppvv T .dpTdT dpC 1 _ 1 , ] (4-24b) So snh (4-24a) v (4-24b) c: ppvT vTC _ , (4-25) Ta thy, qua tit lu p sut lun lun gim, dp < 0, nn theo (4-24a) du ca dT ngc vi du ca; m cng du vi: pvT vT _ , V Cp lun dng, do vy, qua tit lu nhit s gim, tc dT < 0, khi > 0, tc l: PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com70 pvT v 0T _ > , hoc ( )pvTvT>(4-26a) Nhit s tng khi: pvT v 0T _ < , hoc ( )pvTvT 0 tc l Mnm bn tri gc ta , th > 0, dt < 0, lc qua tit lu, nhitmichtgimxung.QuathlctathyT,dovykhngnnnhm ( )pvvTl nhit chuyn bin. Khi MO > 0 tc l Mnm bn tri gc ta 3.Khi MO < 0 tc l Mnm bn phi gc ta hoc MN < ON; T > Tcb th qua tit lu nhit mi cht tng ln, nhng lc ( )pvTvT , ngha l qua tit lu nhit mi cht gim,ngoi vng hai nhit , i0 < , ngha l qua tit lu, nhit tng. p sut cng thp, khong cch gia Tcb1 v Tcb2 cngln,khip0,vichtkhtuntheophngtrnhVanderWaals,ngitatmc Tcb1 = 6,75 Tk v Tcb2 = 0,75 Tk. - Trn p sutchuyn bin ti hn, ilun lunm, ngha l qua tit lu,nhit mi cht lun lun tng. CnchlnhngktqutnhtontrncsVanderWaalskhngvnhtnh, nhng cha tht khp v nh lng. Cng cn lu thm l hiu qu gim nhit ca hiu ngnhitcaqutrnhtitluonnhitkhngthunnghchkmhnhiungnhitca qu trnh gin n on nhit thun nghch. T cc phng trnh vi phn ta chng minh c: Hnh 4-16. Phn vng nhit chuyn bin PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com73 ( )pipvT vTCv ( )pspvTTC nn: s ipv0C >(v V v Cp lun dng); Ngha l bng gin n on nhit thun nghch lm lnh c hiu qu hn, nhng thit b cng knh nn trong thc t t c dng. 4.6. QU TRNH NN KH 4.6.1. Cc loi my nn My nn kh l my nn kh hoc hi n p sut cao theoyu cu. My nn tiu tncngnngpsutcamichtln.Theonguynllmvic,cthchiamynn thnh hai nhm: Nhm th nht gm my nn piston, my nn bnh rng, my nn cnh gt. my nn piston, kh c ht vo xylanh v c nn n p sut cn thit ri c y vo bnh cha (my nn roto thuc loi ny), qu trnh nn xy ra theo tng chu k. My nn loi ny cn c gi l my nn tnh v tc ca dng kh khng ln. My nn piston t c p sut ln nhng nng sut nh. Nhm th hai gm mynn ly tm, my nn hng trc v my nn eject. i vi cc my nn nhm ny, tng p sut ca mi cht, u tin phi tng tc ca dng kh nh lc ly tm, sau thc hin qu trnh hmdng bin ng nngca dng thnh th nng. Loi ny c th t c nng sut ln nhng p sut thp. Tuy khc nhau v cu to v c tnh k thut, nhng v quan im nhit ng th cc qu trnh tin hnh trong my nn hon ton nh nhau. Sau y ta nghin cu my nn piston. 4.6.2. My nn piston mt cp 4.6.2.1. Nhng qu trnh trong my nn piston mt cp l tng n gin, khi phn tch qu trnh nhit ng trong my nn, ta gi thit: - Ton b th tch xylanh l th tch c ch, ngha l nh piston c th p st np xilanh. - Dng kh chuyn ng khng c ma st, ngha l p sut ht kh vo xylanh lun bng p sut mi trng p1 v p sut y kh vo bnh cha lun bng p sut kh trong bnh cha p2. Nguyn l cu to ca my nn piston mt cp c biu din trn hnh 4-17, gm cc bphn chnh: Xylanh 1, piston 2, van ht 3, van x 4, bnh cha 5. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com74 Qu trnh lm ca mt my nn mt cp nh sau: Khi piston chuyn ng t tri sang phi, van 3 m ra ht kh vo bnh p sut p1, nhit t1, th tch ring v1. Cc thng s ny khng thay i trong qu trnh ht, do y khng phi l qu trnh nhit ng v c biu dinbngona-1trnthp-vhnh4-17.Khipistonimcnphi,pistonbtu chuyn ng t phi sang tri, van ht 3 ng li, kh trong xi lanh b nn li v p sut bt u tng t p1 n p2. Qu trnh nn l qu trnh nhit ng, c th thc hin ng nhit, on nhit hoc a bin c biu din trn th bng cc qu trnh tng ng l 1-2T,1-2s,1-2n. Khi kh trong xilanh t c p sut p2 th van x 4 s m ra, khi c y ra khi xylanh vo bnh cha 5. Tng t nh qu trnh ht, qu trnh y cng khng phi l qu trnh nhit ng, trng thi ca kh khng thay i v c p sut p2 nhit t2, th tch ring v2. Qu trnh y c biu din trn th bng qu trnh 2-b. 4.6.2.2. Cng tiu th ca my nn mt cp l tng Nh phn tch trn qu trnh ht a -1 v qu trnh np 2-b khng phi l qu trnh nhit ng, cc thng s khng thay i, do khng sinh cng. Nh vy cng ca my nn chnh l cng tiu th cho qu trnh nn kh 1-2. Nu ta coi l qu trnh nn l l tng, thun nghch th cng ca qu trnh nn c tnh theo cng thc: 21ppktdp . v l (4-28) + Nu qu trnh nn l ng nhit 1-2T, ngha l n = 1 v RTvpcng ca my nn s l: 211221211 1 gn kt 12ppln RTvvln RTvdv. v p dv . p l l q (4-29) Nu qu trnh nn l on nhit 1-2s, ngha l n = k v k1 1kv p pv cng ca my nn s l: ) T T (1 kR) v p v p (1 kkl2 1 2 2 1 1 kt (4-30) C th tnh cch khc, t dq = di + dlkt = 0, ta c dlkt = -di nn dq = di + dlkt= 0 hay: kt 1 2l i i (4-31) + Nu qu trnh nn l a bin, vi s m a bin n th n1 1nv p pv , khi cng ca my nn s l: Hnh 4-17. My nn pittong PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com75 ) T T (1 nR) v p v p (1 nnl2 1 2 2 1 1 kt (4-32) Cng ca my nn c biu din bng din tch a12b trn th p-v, ph thuc vo qu trnh nn. T th ta thy: nu qu trnh nn l ng nhit th cng my nn tiu tn l nh nht. Trong thc t, my nn tiu tn cng t nht th ngi ta lm mt cho my nn cho qu trnh nn gn vi qu trnh ng nhit. 4.6.2.3. Nhc im ca my nn mt cp Trong thc t trnh va p gia nh piston v np xylanh, gia nh piston v np xylanh phi c mt khe h nht nh. Khng gian khong h nay c gi l th tch tha Vt (Hnh 4.14). Do c th tch tha nn sau khi y kh vo bnh cha, vn cn li mt lng kh c p sut l p2 cha trong th tch tha. Khi piston chuyn ng t tri sang phi, trc ht lng kh ny dn n n p sut p1 theo qu trnh 3-4, khi van ht bt u m ra ht kh vo, do lng kh thc t ht vo xylanh l V = V1 V4. Nh vy, nng sut ca my nn thc t nh hn nng sut ca my nn l tng doc th tch tha.Ni cch khc, th tchthalmgimnngsutcamynn.nhginhhngcathtchthan lng kh ht vo my nn ngi ta dng i lng hiu sut th tch my nn, k hiu l : 1 41 3v v1v v (4-33) C th vit li (4-33): 4 3 1 41 3 1 3v v v v1v v v v (4-34) T (4-34) ta thy: khi th tch tha V3 cng tng th hiu sut th tch cng gim. - Khi p sut nn p2 cng cao th lng kh ht vo v = (v1- v4) cng gim, tc l cng gim v khi p2 = pgh th (v1 v4) = 0, p sut pgh gi l p sut ti hn. i vi my nn mt cp t s nn = p2/p1 khng vt qu 12. - Khi nn n p sut cao th nhit kh cao s lm gim nht ca du bi trn. Cc my nn thc t c : = 0,7 0,9. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com76 4.6.3. My nn nhiu cp Do nhng hn ch ca my nn mt cp nh nu trn, trong thc t ch ch to my nn mt cp nn kh vi t s nn = p2/p1 = 68. Mun nn kh n p sut cao hn ta dng my nn nhiu cp, gia cc cp c lm mt trung gian kh trc khi vo cp nn tip theo. 4.6.3.1. Qu trnh nn trong my nn nhiu cp Mynnnhiucpthcchtlgmnhiumynnmtcpnivinhauquabnh lm mt kh. S cu to v th p-v ca my nn hai cp c biu din trn hnh 4-18; I, II l xylanh cp 1 v cp 2, B l bnh lm mt trung gian.Khi c ht vo cp I p sut p1, c nn trong xylanh I n p sut p2, nhit ca kh tng t T1 n T2. Khi ra khi cpI c lm mt trong bnh lm mt trung gian B, nhit kh gim t T2 xung n T1 (bng nhit khi vo xylanh cp I). sau khi c lm mt bnh lm mt B, kh c ht vo xylanh II v c nn t p sut p3 = p2 n p sut p4. Cc qu trnh ca my nn hai cp c th hin trn hnh 4-18, bao gm: a-1 l qu trnh ht kh vo xylanh I (cp 1) p sut p1, 1-2- qu trnh nn kh trong xilanh I t p sut p1 n p2, 2-3 qu trnh y kh vo bnh lm mt trung gian B, nhit kh gim t T2 xung n T1, 3-3- qu trnh ht kh t bnh lm mt vo xilanh II (cp 2), 3-4 l qu trnh nn kh trong xi lanh II t p sut p2 n p1, 4-b l qu trnh y kh vo bnh cha. V clmmttrunggiannnthtchkhvocp2gimimtlngv=v2v3,do cng tiu hao gim i mt lng bng din tch 2344 so vi khi nn trong my nn mt cp c cng p sut u p1 v p sut cui p4. Nu my nn rt nhiu cp v c lm mt trung gian sau mi cp th qu trnh nn s tin dn ti qu trnh nn ng nhit. 4.6.3.2. Chn p sut trung gian Tsnntrongmicpcchnsaochocngtiuhaocamynnlnhnht, ngha l qu trnh nn tin ti qu trnh ng nhit. Nhit kh vo cc cp u bng nhau v bng T1, nhit kh ra khi cc cp u bng nhau v bng T2, ngha l: T1 = T2 v T2 = T4 p sut kh ra khi cp nn trc bng p sut kh vo cp nn sau, ngha l: p2 = p3 v p4 = p5. Trong trng hp tng qut, tacoi qu trnh nnl a bin v s m a bin cc cp u nh nhau, ta c: Cp nn I: 1 nn1212TTpp

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(4-35) Hnh 4-18. S my nn pittong hai cp PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com77 Cp nn II:1 nn3434TTpp

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(4-36) m ta c T1 = T2 v T2 = T4, do ta suy ra t s nn ca mi cp l: 3412pppp (4-37) hay:143412 2pppp.pp (4-38) Tngqut vi my nn m cp th: cmdpp (4-39) 4.6.3.3. Cng tiu hao ca my nn Cng ca my nn nhiu cp bng tng cng ca cc cp. Vi hai cp ta c:lmn = l1 + l2 trong : 111]1

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1ppRT1 nnln1 n121 1(4-40) 111]1

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1ppRT1 nnln1 n343 2(4-41) m T1=T3 v 3412pppp , nn l1=l2 v lmn=2l1=2l2. Tng t, nu my nn c m cp th cng tiu tn ca n s l: ( )1]1

1 RT1 nn . mml l n1 n1 1 mn(4-42) PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com78 Chng 5 NH LUT NHIT NG TH HAI 5.1. Chu trnh nhit ng Ta bit rng mun bin nhit thnh cng trong cc my nhit phi dng mi cht v cho mi cht gin n. Mun nhn c cng lin tc, mi cht phi gin n lin tc, nhng mi cht khng thgin n mi v tnh cht ca mi cht v kch thc ca myc hn. V vy mun nhn c cng lin tc, sau khi gin n ngi ta nn mi cht n tr v trng thi ban u v tip tc cho gin n, nn ln th hai...Mi cht thayi trng thi mt cch lin tc ri li tr v trng thi ban u nh vy, ta ni rng mi cht thc hin mt chu trnh hay mt qu trnh khp kn. Trong k thut ch yu nghin cu nhng chu trnh thun nghch, n ch tin hnh qua cc trng thi cn bng v c c im "thun nghch" ngha l c th tin hnh ngc tr li qua tt c cc trng thi i qua m mi cht v mi trng khng c g thay i. Ta thng nghin cu hai loi chu trnh : chu trnh thun chiu v chu trnh ngc chiu. 5.1.1. Chu trnh thun chiuChutrnhthunchiu:lchutrnhtinhnhtheochiuthunkimngh,chutrnh ny bin nhit thnh cng.- c im: ng cong gin n nm trn ng cong nn; Cng sinh ra (mang du dng) lnhncngnhnvo(mangdum).Vvy,tngcngcachutrnhmangdudng; ngha l chu trnh sinh cng.Xt chu trnh thun chiu trn th p - v (Hnh 5-1). - Qu trnh 1a2: mi cht gin n sinh cng (mang du dng), c biu din bng din tch v11a2v2, nhn nhit lng q1 ca ngun nng.- Qu trnh 2b1: qu trnh nn mi cht v trng thi ban u, mi cht nhn cng (mang du m), c biu th bng din tch v22b1v1, nh nhit lng q2 cho ngun c nhit thp.Saukhichtmigiihonthnhchutrnhtanhnthy:N nhn ca ngun nng nhit lng q1, sinh ra cng lo bng di