上游充通大学 SHANGHAI JIAO TONG UNIVERSITY Engineering Thermodynamics I Lecture 31 Chapter 7 Entropy (Section 7.3) Spring,4/20/2018 强 Prof.,Dr.Yonghua HUANG MMAMMA http://cc.sjtu.edu.cn/G2S/site/thermo.html 1日G
Engineering Thermodynamics I Lecture 31 Spring, 4/20/2018 Prof., Dr. Yonghua HUANG Chapter 7 Entropy (Section 7.3) http://cc.sjtu.edu.cn/G2S/site/thermo.html
Retrieve property data Tables,graphs,equations,software TABLE A-17 Ideal-gas properties of air h U K kJ/kg P kJ/kg V. :kJ/ke.K 200199.97 0.3363 142.56 1707.01.29559 p,v,T 210 209.97 0.3987 149.69 1512.0:1.34444 220 219.97 0.4690 156.82 1346.0:1.39105 230 230.02 0.5477 164.00 1205.01.43557 240 240.02 0.6355 171.13 1084.0:1.47824 u and h 250 250.05 0.7329 178.28 979.0:1.51917 Reference value 260 260.09 0.8405 185.45 887.81.55848 270 270.11 0.9590 192.60 808.01.59634 280 280.13 1.0889 199.75 738.01.63279 Entropy s 285 285.14 1.1584 203.33 706.1:1.65055 290 290.16 1.2311 206.91 676.1:1.66802 295 295.17 1.3068 210.49 647.9:1.68515 : 298 298.18 1,3543 212.64 631.91.69528 TABLE A-4 300 300.19 1.3860 214.07 621.2:1.70203 Saturated water-Temperature table ……305.305.22 1.4686 217.67 596.0 1.71865 Specific volume Internal energy Enthaipy. Entropy. 而En■ggg m-/kg kJ/kg kJ/kg kJ/kg-K Sat. Sat. Sat. Sat. Sat. Sat. Sat. : Sat. Sat. Temp. press. liquid, vapor, liquid, Evap.. vapor, liquid. Evap. vapor. liquid. Evap.. vapor TC Pat kPa U h hi 0.01 0.6117 0.001000 206.00 0.000 2374.9 2374.9 0.001 2500.9 2500.9 0.0000 9.15569.1556 0.8725 0.001000 147.03 21.019 2360.8 229R 21.020 2489.1 2510.1 0.0763 8.94879.0249 1.2281 0.001000 106.32 42.020 2346.6 2388.7 42.022 2477.2 259.2 0.1511 8.74888.8999 5 1.7057 0.001001 77.885 62.980 2332.5 2395.5 62.982 2465.4 2528.3 0.2245 8.55598.7803 20 2.3392 0.001002 57.762 83913 2318.4 2402.3 83.915 2453.5 2537,4 0.2965 8.36968.6661 25 3.1698 0.001003 43.340 104.83 2304.3 2409.1 104.83 2441.7 2546.5 0.3672 8.18958.5567 30 4.2469 0.001004 32.879 125.73 2290.2 2415.9 125.74 2429.8 2555.6 0.4368 8.01528.4520 5.6291 0.001006 25.205 146.63 2276.0 2422.7 146.64 2417.9 2564.6 0.5051 7.84668.3517 0 7.3851 0.001008 19.515 167.53 2261.9 2429.4 167.53 2406.0 2573.5 0.5724 7.68328.2556 9.5953 0.001010 15.251 188.43 2247.7 2435.1 188.44 2394.0 2582.4 0.6386 7.52478.1633 0 12.352 0.001012 12.026 209.33 2233.4 2442.7 209.34 2382.0 2591 0.7038 7.37108.0748 15.763 0.001015 9.5639 230,24 2219.1 2449.3 230.26 2369.8 2600.1: 0.7680 7.22187.9898 19.947 0.001017 7.6670 251.16 2204.7 2455.9 251.18 2357.7 26088 0.8313 7.07697.9082 的 25.043 0.001020 6,1935 272.09 2190.3 2462.4 272.12 2345.4 2617.5 0.8937 6.93607.8296 1.202 0.001023 5.0396 293.04 2175.8 2468.9 293.07 2333.0 2626.1 0.9551 6.79897.7540 上游究通大学 April 20,2018 2 SHANGHAI JIAO TONG UNIVERSITY
April 20, 2018 2 Retrieve property data p, v, T u and h Entropy s Tables, graphs, equations, software Reference value
Reference state for entropy definition of entropy change 4s=5-s-(川) int Arbitrarily choosing reference state x,then at any state y, replace state 1 replace state 2 Because of cancel" s=s+(9 int rev ____Only for constant composition applications, for chemical reactions,use absolute values (3d law) (Chap.15) 上游气通大粤 April 20,2018 3 SHANGHAI JIAO TONG UNIVERSITY
April 20, 2018 3 Reference state for entropy definition of entropy change Arbitrarily choosing reference state x, then at any state y, replace state 1 replace state 2 Only for constant composition applications, for chemical reactions, use absolute values (3rd law) (Chap. 15) Because of “cancel
Retrieve from table Tables C_A-6,C_A7 for water and C_A-13,C_A14 for refrigerant R134a 个 S0.01℃，sat liq.=0 S.40r，℃sat li.=0 (superheated)Vapor data:s~fT,p) ·Example:water,,state1(3MPa,500°C)→state2(0.3MPa,T2), S2=S1.T2=? IC_Tab.A-6 C_Tab.A-6 S1=7.2338k/kgK=S2 interpolating T2=183℃ (sub-cooled)Liquid data:s~fT,p) s(T,p)~s(T) ·Example:water,state1(25bar,200°C C Tab.A-4 C Tab.A-7 SE200c=2.3309k/kgK S1=2.3294k/kgK 上游气通大粤 April 20,2018 4 SHANGHAI JLAO TONG UNIVERSITY
April 20, 2018 4 Retrieve from table Tables C_A-6,C_A7 for water and C_A-13,C_A14 for refrigerant R134a (superheated) Vapor data: s~f(T, p) • Example: water, state 1 (3MPa, 500˚C) state 2 (0.3MPa, T2 ), s2=s1 . T2=? (sub-cooled) Liquid data: s~f(T, p) s(T,p)~sf (T) • Example: water, state 1 (25bar, 200˚C) C_Tab.A-6 s1=7.2338 kJ/kg·K=s2 C_Tab.A-6 interpolating T2= 183 ˚C C_Tab.A-7 s1=2.3294 kJ/kg·K C_Tab.A-4 sf, 200˚C=2.3309 kJ/kg·K s0.01 ˚C, sat. liq.=0 s-40˚C, sat. liq.=0
Retrieve from table-cont. Saturation data:Sp Sg Two-phase data: s=(1-x)st+xsg=st+x(sg-St) Example:R134a,state 1(0C,u1=138.43kJ/kg) C_Tab.A-11 u=49.79,ug=227.06---two-phase C_Tab.A-11 s-(1-x)st xsg W一Uf =0.5 ug -uf =0.5580kJ/kg·K 上游充通大学 April 20,2018 5 SHANGHAI JIAO TONG UNIVERSIT
April 20, 2018 5 Retrieve from table - cont. Saturation data: sf , sg Two-phase data: • Example: R134a, state 1 (0˚C, u1=138.43kJ/kg) uf=49.79, ug=227.06 C_Tab.A-11 two-phase =0.5 C_Tab.A-11
Retrieve from software IT /EES /Refprop... Interactive Thermodynamics VERSION 西回x Interactive Thermodynamics 3.0 ©回凸匙国回画￥圆■☒国■四回圆回团三网圆日回围网马？刻 ansliane Tinlae To Accompany: Fundamentals of Engineering gES (pranounced 'ease')is an acronon for Engineering Bquation Solver.The basic function provided by EES is the solution of a set of algebraic equations.EES can efficiently solve thousands of coupled non-linear Thermodynamics,6th edition algebraic equations.EES can also be used to solve initial value differential equations,do linear and non- linear regression,unit conversion,uit consistency checking,optinization,and uncertainty analysis,and Michael J.Moran produce publication-quality pl Howard N.Shapiro A major difference between EBS Engineering Equation Solver nathenatical and thernophysical property functi plexented such that 21992-20105A.Keln Academic Professional V8.718 (12/03/10] wo other properties. Simdlar capability is provided be,all common refricerants,.s.惠，fl34a,fl2 and NASA thernodynaric propert 91:Educational version distributed bry McGraw-Hill ons are also Student technical support Contact your instructor. onal property data may be added by the user and E Faculty only technical support into@fchart.com.FAX (608]836-8536 EES provides the capebility to Continue n a spreadsheet-like teble.The user determines whi Ute Adrinididet table cells.EES will solve the table to detern Higher n is provided to display the relationship betwe Education Ides property ǖagrans《9uch8 s pressure entharpy publication quality. DEVELOPED BY intellipro EES offers the advantages of a simple set of intuitive ccmmands with uhich a novice can quickly leam touse 2008 John Wiley Sons,inc.I Portions 2008 Intepro,Inc 第H种：2Cg5ir4p:阳Tasert C1ok0过C对k灯Taorni:a地tCa:0mCN9m0） PROCEDURE pump(P in,P_out,Eff h_in,h_out,p) p=1∥bar h in:=ENTHALPY (STEAM,P=P in,x=0): v:=volume (STEAM,P=P in,x=0) v=0.8475∥m3kg p=1.5∥bar wp:=v*(P_in-P_out)/Eff*Convert ((ft3/1b_m)*(psia),Btu/lb_m) hout:=hin-网p v vsat_Px("Water/Steam",p,x) T=8∥℃ END s ssat_Px("Water/Steam",p,x) s =s_PT("Ammonia",p,T) PROCEDURE turbine (h in P in p out Eff h out,Wt) s_in:=entropy (STEAM,h=h_in,P=P_in) h out_id:=enthalpy (STEAM,s=s in,P=P out) w_t:=(h_in-h_out_id)*Eff 上泽通大学 h out:=h in-w t April 20,2018 END SHANGHAI JIAO TONG UNIVERSITY
April 20, 2018 6 Retrieve from software IT /EES /Refprop… Interactive Thermodynamics
Retrieve from graph T steeper uesuo3=n ueisuoo d h p constant T=constant Critical point T=constant Ip constanty Low p Low p Saturated liquid constant constant 人-=096 -x=0.2 Saturated vapor Saturated vapor h(T,p)≈h(T p constant r=0.90 x=0.9 ritical point T-s diagram (h,p,v,x) h-s diagram (p,T,x) ~Ideal gas Mollier diagram 上泽通大学 April 20,2018 7 SHANGHAI JIAO TONG UNIVERSITY
April 20, 2018 7 Retrieve from graph T-s diagram (h, p, v, x) h-s diagram (p, T, x) steeper Low p h(T,p)≈h(T) ~Ideal gas Mollier diagram Low p
Using the Tds equations A pure,simple compressible system undergoing an internally reversible process Neglecting△PE,△KE 7=pdv Energy balance: (Q)t= rev: dU+(δw rev s=(9 int Tds D 1st Tds equation: Tds dU pdv 上游究通大学 April 20,2018 8 SHANGHAI JLAO TONG UNIVERSITY
April 20, 2018 8 Using the Tds equations A pure, simple compressible system undergoing an internally reversible process Neglecting ∆PE, ∆KE Energy balance: 1 st Tds equation:
Using the Tds equations -cont. H=U+pV.----dH=du+d(pv)=du+pdv+vdp i du pdv dH-Vdp 1st Tds equation:Tds=dU pdv 2nd Tds equation: Tds dH-V dp 上游充通大学 April 20,2018 9 SHANGHAI JLAO TONG UNIVERSITY
April 20, 2018 9 Using the Tds equations – cont. 1 st Tds equation: 2 nd Tds equation:
Tds equations on unit mass/mole Unit mass Unit mole ①Tds=du+pdu Td=du+pd而 2) Tds dh -vdp Tds dh Udp Entropy -a property, the equations Applies to any process,reversible or irreversible Between two equilibrium states 上游充通大学 April 20,2018 10 SHANGHAI JIAO TONG UNIVERSITY
April 20, 2018 10 Tds equations on unit mass/mole Unit mass Unit mole 1 2 • Applies to any process, reversible or irreversible • Between two equilibrium states Entropy – a property, the equations