P1 atm ar liqid Q
Gien and P Ser Heat Regin i, P < P sat > sat Cmressed Liqid Regin i, P > P sat < sat
SEAM PRESUE AND EMPERAURE ABLES
Satrated Liqid Line Satrated Var Line s s g g g g
ree ables emeratre able at saced s Pressre able at saced P s Sereat able at saced and P 6 Prerties emeratre Pressre Vlme Internal Energy Entaly Entry
Slid-Liqid-Gas Pase Diagram
Satratin liqid internal energy at 0 C 0. able Base Satrated liqid entaly at 5 C 104.89 kj/kg Satrated ar entry at 5 C 8.558 kj/kg K Entaly at 0 C, 00 kpa assme satrated liqid entaly at 0 C 8.96 kj/kg emeratre satrated ar wit an internal energy 96.1 kj/kg 15 C Entaly arizatin at 10 C 477.7 kj/kg
able A-7 Metric, able A-7E Englis, able A-4 Metric, able A-5 Metric, able A-4E Englis, able A-5E Englis, EMPERAURE ABLE PRESSURE ABLE able A-6, Metric,, able A-6E, Englis,, SUPERHEA ABLE
w Pase Real Gas Prerties ( ) g g g g g g g x x x x 1 Qality m m x m m m V V V + + + + g g g g x x x + + +
Qality, x 58.07 +.64 98. 686.7 BU/lb x + x ( + x + x 58.07 +.64 104.7 75.4 BU/lb g g g 00.0161.64 (64%) 467.7.0161 g ) 90 Find te rerties F emeratre able A-4E age 880 s 58.07 58.07b.169 ( ) water at 90 ( g ) s F, 00 t s g g g /lb. 110.7 1140..008 s s s s + x s g.196 +.64 1.856 1.15 BU/lb R.0161t / lb 00. t /lb g 467.7t / lb
10 MPa satrated steam as an entaly 010 kj/kg. Wat is its internal energy? + x 010 kj/kg 1407.56 + x 117.1 x.4574 + x g g 19.04 +.4574 1151.4 1919.69 kj/kg EES Prgram x qality(steam,p 10000., 010) x.4576 intenergy(steam, P 10000., 010) 1919.65 kj/kg
Steam at 0 C as an entaly 1800 kj/kg. Wat is te internal energy? + x 1800 kj/kg 8.96 + x 454.1 x.7 + x g g 8.95 +.7 19.0 1707.5 kj/kg
SEAM SUPERHEA ABLE
SUPERHEA ABLE Entaly at 700 C and.10 Ma 98. kj/kg emeratre at entry 8.864 and.05 Ma 400 C Entaly at.05 MPa and entry 10.666 kj/kg C 5147.7 kj/kg
Steam initially at a temeratre 1100 C and a ressre.10 MPa nderges a rcess dring wic its entry remains cnstant t a ressre.01 MPa. Wat is te entaly and temeratre te steam at te end te rcess? Entry at 1100 C,.1 MPa 10.1659kJ/kg K Entaly at.01 MPa, entry 10.1659 705.4 kj/kg emeratre at.01 MPa, entry 10.1659 600 C.01 MPa s
Engineering Eqatin Sler - EES Flid Prerty Inrmatin - 69 lids aailable ermysical Fnctins - 5 rerties calclated Eqatins Windw entaly(steam, 00.,P00) sereated ar entaly(steam,00.,x1) satrated ar intenergy(steam,00.,x0.) satrated liqid ressre(steam,00.,x0.) satratin ressre ermysical Fnctins entry intenergy ressre qality density entaly isidealgas temeratre lme Fnctin Argments H seciic entaly P ressre S seciic entry temeratre U seciic internal energy V seciic lme X qality
EES FLUIDS FUNCINS
able EES Prgram Satratin internal energy at 4 kpa l Pressre able g 11.45kJ/kg 415.kJ/kg l l g g intenergy(steam, P 4.,X 0) 11.kJ/kg intenergy(steam, P 414.9 4., X 1.) Entaly and lme water at 150 kpa and 0 C Internal energy water at 0 MPa and 00 C l l Sereat able satrated liqid @ 0 l l l l 15.75 kj/kg satrated liqid@0.001004m /kg emeratre able satrated liqid @ 00 1.0 kj/kg C C C l l l l l l entaly(steam, 15.67kJ/kg lme(steam,.001004m /kg intenergy(steam, 1.446 kj/kg 0., 0., 00., 500.) 500.) 0000.)
Linear Interlatin wit Variables @( 450 C, 7 MPa) Steam Sereat able 450 5 mpa 949.7 7 5 Fr te ressre table entry,.4 0 5 e desired ressre, 7 kpa, is 40 % te dierence between table ales. 7 MPa 898.4 mst be at te same dierence. 81.4 All te ter rerties at 7 kpa 0 MPa EES entaly(steam, 901.7 kj/kg.% 450., 7000) dierence, table and interlatin
Linear Interlatin wit Variables @( 450 C, 7 MPa) Steam Sereat able (5)949.7 450 C 450 5 mpa 949.7 7 MPa 898.4 0 MPa 81.4 @(7) B (0)81.4 A m x + b A C ( 81.4-949.7) ( 7 5) ( 0 5) 51. + 947.7 898.4 kj/kg B + @(5) + 947.7 C 5 7 0 EES entaly(steam, 901.7 kj/kg.% 450., 7000) dierence, table and interlatin
kg ar and 1 kg liqid R-14a is cntained in a rigid tank at 0 C. Wat is te lme te tank? I te tank is eated ntil te ressre? reaces.6 MPa? Wat is te qality, and entaly te mixtre liqid and ar? V V V V Ater eating, V cnstant, m cnstant cnstant x 1 1 1 1 1 V m 1kg.0008157 + kg.058.108 m V1 m + V @ 0 C + m.108 m 4 kg @.6 MPa + x.07.00008196.041.0008196 + x 1 g g.07 m /kg.787(78.7%) 79.84 +.787 179.71 11.7 kj/kg g g @ 0 C age 84, ablea 11 g @.6 MPa age 84, able 0 C A -1 Q.6 MPa 1.5716 MPa
kg ar and kg liqid R-14a is cntained in a istn cylinder deice. e lme te ar is.1074 cbic meters. Wat is te temeratre and ressre? I te cylinder and its cntents are eated ntil lme is.15 cbic meters wat is te qality? x g1 g at V V m g1 g1.058 m /kg @ 0 C,.15m.0 m /kg g.1074 m kg,.15 5.0 m /kg.058 m /kg.5716 MPa Dring te eating rcess te ressre V m @ 0 C + x g @ 0 C is cnstant..0.0008157.84 (8.4%).058.0008157 age 84, ablea 11 0 C 1 x rerty (rerty) (rerty) g rerty (rerty) + x (rerty) g Q
ermdynamic Prblem Sling ecniqe 1. Prblem Statement Carbn dixide is cntained in a cylinder wit a istn. e carbn dixide is cmressed wit eat remal rm 1,1 t,. e gas is ten eated rm, t, at cnstant lme and ten exanded witt eat transer t te riginal state int.. Scematic. Select ermdynamic System en - clsed - cntrl lme a clsed termdynamic system cmsed t te mass carbn dixide in te cylinder C 4. Prerty Diagram state ints - rcesses - cycle Q,, W Q W 1,1 5. Prerty Determinatin, s 1 6. Laws ermdynamics Q? W? E? material lws?
Linear Interlatin wit Variables @( 470 C, 7 MPa) Steam Sereat able 450 470 500 5 MPa 949.7 161.4 7 MPa 898.4 991.0 19.88 0 MPa 81.4 081.1 Interlate irst at 450 C and at 500 C between 5 and P 0 t get @ ( 450 and 500, 7). between 450 C and 500 C. 7 5 ressre.4 0 5 5 470 450 emeratre 500 450 entaly(steam, 470., 7000.) EES 00.95 kj/kg, 0 50 en interlate at 7 MPa.4.47% dierence, table and interlatin
Linear Interlatin wit Variables @( 450 470 500 Interlate at 450 C and 500 C between 5 and P 0 t get @ ( between 450 C and 500 C. m x + b ( 19.88 898.4) ( 470-450) ( 500 450) 991. 470 C, 5 MPa 949.7 161.4 450 and 500, kj/kg A C 7 MPa) 7 MPa 898.4 991.0 19.88 7). B + ( 450, 7) Steam Sereat able 0 MPa 81.4 en interlate at 7 MPa + 898.4 081.1 (470,7) (450) 898.4 P7 MPa (500) 19.88 C B A 450 470 500 EES entaly(steam, 470., 7000.) 00.95 kj/kg,.47% dierence, table and interlatin
Ideal Gas Law nr V R Weigt Mleclar n m Weigt Mleclar mles mass K kmle m kpa r K kmle kj 8.14 R lbmle R lb/lbm 1545.15 R weigt mleclar R R K R, re, temerat abslte - kpa sia, ressre, abslte - mr V R LAW GAS (PERFEC) IDEAL * * * * * 1 1 1 1 1 1 CHARLES LAW BLYES LAW ) (1atm and 0 SP gas at mlecles/mle 10 6.0.4 liters. any gas ne(1) mle LAW S AVGADR' C
water Ideal Gas R cnstant seciic eat
Wat is te mass 1. m and a gage ressre 500 kpa. Atmseric ressre xygen at 4 C is 97 kpa R m gage + atmsere 500 kpa + 97 kpa 597 kpa 8.14kJ/kmle V 597 kpa 1. m R.5981kPa m /kg K r kpa m /kmle ( 4 C + 7.16 K) K.5981 9.8 kg kpa m /kg alsablea 1 Wat is te lmemass 1. lbm and a gage ressre 500 sia. Atmseric ressreis14.7 sia. air at 14 F gage + V.5047t atmsere 1545.15lb / lbm R air 8.97 m R 1. lbm V 500 sia + 14.7 sia 514 sia R / lbmle t lb 5.6 lbm R 514 sia 144 t /in 5.6t lb/ lbm R ( 14 F + 459.69 R) als able A 1E in mlar nits
IDEAL GAS EQUAIN FRMS - Fr Air kpa kpa lb t lb t si lb t P m R m m t t t t kg mle kg kpa m 8.14 kg mle kpa m.87 kg mle K K lbmle t lb 1545.15 lbm R lbm t lb 5.5 lbm R lbmle si lb 10.7 lbmle R lbm BU.06855 lbm R R K R R K R kpa m R 8.14 / 8.96 kg mle K t lb R 1545.15 /8.96 lbm R t lb R 1545.15 /144 lbm R t lb R 1545.15 /8.96/778 lbm R
e seciic lme R 1.476 t e seciic lme kpa m R 8.14 kg mle air 1545.15 /8.96 5.5 t lb/lbm R R R /lb.8417 m /kg air at 75 5.5 t lb/lbm R 14.7 lb/in 144 in air at 4 / 8.96 K.87 kpa m /kg 101.5 kpa F and14.7 sia ( 459.69 R + 75 F) /t C and101.5 kpa ( 7.15 K + 4 F)
Air initially at a lme 1 m and a ressre 5 kpa exands at a cnstant temeratre t a lme m. Wat is te inal ressre? mass cnstant, R1 m 1V1 R 1 m V 1 1 R V 1 1 m 5 kpa m 117.9 kpa R 1 V1 R V ( 7.15 + ) 1 cnstant.86 4 kpa m V V 1 1 1 m mcnst cnst m
SPECIFIC HEAS FR GASSES
SPECIFIC HEA C cnst c ( ) d c ( ) c d c d d c sbsistting r d and d c wit same nits and k FR IDEAL GAS NLY d c d c d d c c c c c cnst Fr an ideal gas seciic eats are assmed cnstant By deinitin + sbstitting R + R dierentiating d d + Rd C d + R c d + Rd R k 1 R c
IDEAL GAS IMPRVEMENS Entaly,, internal energy,, and entry, s. are nt abslte bt Dierences rm a base. c c c able Base State c able Base State ( ) ( ) d d ( ),c c ( ) ables A -17, A -17 t A -, A - E
IDEAL GAS WIH VARIBLE SPECIFIC HEA
b) a) -104 600 able A - a, + 1 e)ees K t1000 seciic eat at te aerage temeratre able A - b, d) ( ) c d, c a + b + c + d 1 8.9( 1000 600) +.5(.0001571)( 1000 600 ) 5 1 9 4 4 (.8081 10 )( 1000 600 ) (.878081 10 )( 1000 600 ) b)aerage seciic eat er te temeratre range, c)rm temeratre seciic eat, d) ablea 18E @1000 Determine te entaly cange,, nitrgen in kj/kg as it is eated rm K (76 C,140 able A 18E, K @600 F) sing : e) 4 c EES. @800 a) c emirical seciic eat eqatin able A c, 544 kj/kmle/8.01 @800 1.11kJ/kg K K 1.09448.5 kj/kg 1.09448 kj/kg K 1.11 kj/kgk ( 1000 600) ( 1000 600) 448.5kJ/kg 415.6 kj/kg K 0,19 kj/kgmle 1756 kj/kgmle 1566 kj/kgmle 1566kJ/kgmle/8.01kg/kgmle 448.58 kj/kg entaly(nitrgen, 1000., 101.5) entaly(nitrgen, 600., 101.5) c c) seciic eat at rm temeratre 1544 kj/kmle 447.8 kj/kg 449.46kJ/kg
PRINCIPAL F CRRERSPNDING SAES CMPRESSIBILIY FACR Z Z is abt te same r all gasses at te same redced temeratre and te same redced ressre were: P Z Z R V mr P R R critical critical ( 0)
VAN DER WAALS EQUAIN F SAE - 187 a + ( b) R ( - ) a intermleclar rces b lme gas mlecles d a R critical critical critical 7 R 64 b 0 critical critical a critical d b critical R 8 critical critical 0 0 0 critical int
HERMDYNAMIC PRPERY MEASURMEN ermdynamic rerties are indeendent at r rcess and are exact dierentials. Heat and Wrk are nt exact dierentials bt are deendent n rcess r at. gas real ale r a gas,a 0 r an ideal Jle msn Ceicient c c 60 eqatins time, at a 6 termdynamic rerites d ds s d ) (s, s + s sed wit te First Law
J Ceicient cnstant
Crse Prerty Srces 1) Ideal Gas Law wit cnstant seciic eats ) ables Steam Rerigerant Air ) EES CD NIS r me wrk cnenience
EQUAIN F SAE ERRRS nitrgen
NIS Webbk Prerties tt://webbk.nist/g/cemistry/lid emeratre able r Water in.1 degree increments rm 40 t 40 degrees. Select Units Select able ye
Select lid
Set lw and ig temeratre and temeratre increment.