CHAPTER 4. The First Law of Thermodynamics for Control Volumes

Transcription

1 CHAPTER 4 T Frst Law of Trodynacs for Control olus

2 CONSERATION OF MASS Consrvaton of ass: Mass, lk nrgy, s a consrvd proprty, and t cannot b cratd or dstroyd durng a procss. Closd systs: T ass of t syst ran constant durng a procss. Control volus: Mass can cross t boundars, and so w ust kp track of t aount of ass ntrng and lavng t control volu. 4- Mass s consrvd vn durng ccal ractons. Mass and nrgy E can b convrtd to ac otr accordng to wr c s t spd of lgt n a vacuu, wc s c /s. T ass cang du to nrgy cang s absolutly nglgbl.

3 Consrvaton of ass prncpl Control volu can b tougt of a rgon of spac troug wc ass flows. Mass ntrng Control olu C Mass lavng Total ass ntrng C _ Total ass lavng C Nt cang n ass wtn C C Not: -nlt, -xst, C-control volu T rat for C 4- wr s ass flow rat,. d dt

4 Flow troug a pp or duct locty profl scous ffcts T avrag vlocty avg s dfnd as t avrag spd troug a cross scton. T volu flow rat s t volu of flud flowng troug a cross scton pr unt t. 4-3

5 Copyrgt T McGraw-Hll Copans, Inc. Prsson rqurd for rproducton or dsplay T ass flow rat troug a dffrnt ara da can b xprssd as: d ρ n da locty noral to da ρ A n da kg/s ρ avg A kg/s 4-4 T volu flow rat: T ass and volu flow rats ar rlatd by : dnsty kg/ 3 avrag flud vlocty noral to A, /s A nda ρ v A av 3 s

6 Consrvaton of Enrgy Prncpl Total nrgy Total nrgy Total nrgy Nt cang crossng boundary of ass - of ass n nrgy as at and work ntrng C xtng C of C Mass n Q Q E n E out E C Mass out Ts quaton can also b xprssd n t rat for.. quantts pr unt t. n tr s no ass flow n and out of t syst, t nrgy quaton rducs to tat of a closd syst: Q E 4-5

7 Flow work or flow nrgy T nrgy rqurd to pus flud nto or out of a control volu. T forc appld on t flud lnt : F P A T work don n pusng t flud lnt nto t control volu:.. t flow work : flow F L PAL P kj On a unt ass bass w flow Pv kj/kg t flud pusng t flud nfront of t 4-6

8 Total Enrgy of a flowng flud For a nonflowng flud : u k p u gz kj/kg For a flowng flud t total nrgy θ Pv Pv u Hnc θ k p gz kj/kg gz kj/kg T total nrgy conssts of tr parts for a nonflowng flud and four parts for a flowng flud. 4-7

9 THE STEADY-FLO PROCESS Stady flow s dfnd suc tat all proprts at ac pont n a syst ran constant wt rspct to t..g. turbns, coprssors, and at xcangrs Undr stady-flow condtons, t ass and nrgy contnts of a control volu ran constant. Undr stady-flow condtons, t flud proprts at an nlt or xt ran constant do not cang wt t. 4-8

10 Consrvaton of ass Exapl: cv constant for stady-flow procss 4-9 If tr s only on nlt and on xt kg/s or A ρ A wr ρ ρ or A A dnsty kg/ 3 ν spcfc volu /kg 3 avrag vlocty /s A cross sctonal ara noral to ara v v

11 4-0 Consrvaton of nrgy for stady flow cv n out gz gz Q Q E E E Q θ θ For on-nlt, on-xt systs. sngl stra systs: } { z z g Q k p In any cass: k 0 p w q 0 or constant C E C E

12 So Stady-Flow Engnrng Dvcs.Nozzls and Dffusrs q w k p 4-

13 .Turbns and coprssors A odrn land-basd gas turbn usd for lctrc powr producton. Ts s a Gnral Elctrc LM5000 turbn. It as a lngt of 6., t wgs.5 tons, and producs 55. M at 3600 rp wt sta njcton. 4-

14 .Turbns and coprssors q w k p w 0 0 q w k p q w 4-

15 For stady flow Ex: Sta turbn Q { g z z } Q gz gz kg r 0.67 kg 3600 sc sc r 630 kg Q r 0.75k 3600 sc r 0.75kJ kj kj kg s 00 kg kg J s 9.8 J s 30 kg J s s s kj kj kj kj.05 30kJ 5kJ 0.09kJ kg kg kg kg kg 0.67 s 3.83k

16 3.Trolng alvs Trottlng valvs ar any knd of flow-rstrctng dvcs tat caus a sgnfcant prssur drop n t flud. at s t dffrnc btwn a turbn and a trottlng valv? T prssur drop n t flud s oftn accopand by a larg drop n tpratur, and for tat rason trottlng dvcs ar coonly usd n rfrgraton and ar-condtonng applcatons. Enrgy balanc q w k p u Pv u Pv Durng a trottlng procss, t ntalpy of a flud rans constant. But ntrnal and flow nrgs ay b convrtd to ac otr.

17 3.Trolng alvs Intrnal nrgy flow const. If Pv ncras tn u dcrass drop n tpratur If v dcras tn u ncrass ncras n tpratur For an dal gas, T and snc, t tpratur dos not cang T. P T 4-4

18 4. Hat xcangrs Mass flow rat of flud A: Mass flow rat of flud B: A B Enrgy quaton for blu C: Q B B A A B B A gz A gz Enrgy quaton for rd C: Q Q A A sngl stra k p 4-5

19 4-6 5.Mxng Cabrs Dvd by and lt y y y gz gz Q T T-lbow of an ordnary sowr srvs as t xng cabr for t ot- and t cold-watr stras.

20 6.Pp and Duct Flow Q Q k p Pp or duct flow ay nvolv or tan on for of work at t sa t Hat losss fro a ot flud flowng troug an unnsulatd pp or duct to t coolr nvronnt ay b vry sgnfcant. 4-7 n ar tratd as dal gas RT v P v Q s C p T T

21 4-8 A A ρ ρ ρ s s s kg Entalpy cang for ncoprssbl substanc: P P v T T C P P v u u Pv u P v u u

22 4-9 Enrgy quaton bcos: η η ϑ ϑ ϑ ϑ ϑ vlocty s wr } { } { P P P P z z g z z g P P v T T C Q l l s s s s Elctrc otor l s Elctrc Pup