1、 l :1999-09-20 “:SE1 S “(19474032)Te: +(1963), 3, + 3 , =Sv V,C iTcI|:1001-3857(2000)01-0039-05A8 Z王 军, 尚志远( =Sv 2 , 710062)K 1:由自由体积理论研究了液体状态方程.提出了一个普适的液体状态方程,由此状方程出发,可导出大多数液体状态方程,这对实际应用有一定指导意义.1oM:液体;状态方程;自由体积ms |:O552.4+2 DS M :A1 18 $18 12 ,%8 s s H,|$ , A8 H, %8M . ,FA8 0 s 0EK. X,XA8 0 # 0F“ F
2、0”“”.L !s0WMTKK#s0,5 s0 8Cs0 ?.d9 (4, V| 8Cs0 AT) , 8 = . 7EA8 ?,5E =E0 +ii(r)-i(0), (1) E0 s0)1- 8 H ?,i(0) Bs0i1- 8H ?,i(r) is0 8 r H ?, p s0,5“d sf Z = 1N！(2 )3Nexp(-H/kT)drNdpN . H Hamitonf :H =Ni=1p2i2m +E(r1,r2 ,rN).m 0 ,p 0 . !“d8V,5 sZ = 1N！ mkT2 23N/2exp(-E/kT)drN .(1) T, TZ = 1N！ mkT2 23N/
3、2p exp(-E0/kT)i exp-(ri)-(0)dri .28 1 =Sv(1 S) Vol.28 No.12000 M3Journal of Shaanxi Normal University(Natural Science Edition) Mar.2000 DOI :10.15983/ki.jsnu.2000.01.009pN 0 p. 7f =exp-(r)-(0)/kTdr, 0 L8,fM 018, 0 7r) qv,y7 018v. 018M,# sf VZ = mkT2 3N/2exp(-E/kT)fN . (2) sf , V p 3 .2 18 / aA8 Z4 (
4、2) T sf ,y7 V p f . f “ - ? , ?Bts0 、L ! T. sf ?s1 |3, aeA8s0,A0s0,A v.1965 M,Flory4 A 2 , , ; =, r . Y Q s0W R; =-0 , ; =, r . 1 - .m =6 H, TB. L= ? T H s0W l 6 y,yN o Bz .3.4 Lennard-Jones ?f ?f f F.ds0,s0 ?f = + =Arn -Brm .m4, T,m |6,nB12, V=0 rer12-2 rer6, =40 r12- r6.Ns0“d, ? V ?s0 ?.N V“d ?E =
5、12 NZ SnArn -SmBrm .Z ,K #s0 .Sn,SmsYn ,1 +:A8 Z41 e Z,S6 =1.449 5, S9 =1.103 2, S12 =1.057 4. + ?f V A,f %, M.Floryw A Z H, V r31“, ? |Sutherland T,E = /Vn . n0.5 2W.eL9,Flory |n =1,i| TE =-NrS/2,m3 Sutherland ? wLFig.3 Sutherlands potential energy curvem4 Lennard-Jones ? wLFig.4 Lennard-Jones pote
6、ntial energy curveNr9 ,S s0W( .B ,VBM # ?, 1 , 7T = S2lk, p = S22, T = TT, p= pp, =.|E,f aA8 Z,ep T= 1/31/3 -1- 1 T. (5) Flory A 1 T Z.es0, |L =rl =1,f =b3 1/3 -1/33,ELennard-Jones ?f 9 ,=0 rr12-2 rr6,5 E =12 NZ0 Sn rr12-Sm r6=NA2 C r4-D 2,TA =Z0;r s0W ;C,DsYSn2Sm .N aA8 Z, Vp=A 22C 2-D +kT/ 1- 121/
7、6 1/3. (6) ? Z.es0, |L =rl =1.|s0 jB H, V IB“ o189 . !X,|Nds0F8V ZQ, * ,Bs0 VV1/3 -d 3,=s0$KV1/3 -d 3 -43d38 =, ,Ns0V1/3 -d 3 -N 43d381.y7BNs0F“ , V (8V1/3 -d 3 -N2 43d3, V Y,5V-N2 42 =Sv(1 S)28 43d3,V-b, b =4N 16d3 ,s0%84,y7Vf =V-b. | ?fE =-aV2, aA8 Z,5p = RTV-b -aV2 . (7)Flory A Z I n s0 f ,y7 a z
8、, ? |E =-aVn ,n =1,n |1,y7 L= f M v. I n f , |L VM ,f=b3 13 -13 3,E |Sutherland ?f ,E =-aVn , a ,n V , L=L E p.“, A8 Zp =LRT 1V(1-y)-i , (8)y = VV-1/3,i = E V =naVn+1. FloryA8 Z. V A,f,E , VB“ Z, O V(4) Tw,y7(4) T Ril. ID: 1 #,fQ. L Z M.: S,1986. 2. 8s0 M .:,1986. 3. d9 M.2.:,1989. 4 Rajagopalan S,
9、Suredra Tiwari A.Free volume and internal pressure studies in aqueous methanol mixtures at differenttemperatures J .Acustica, 1988,66:9294.5 Pandey H C, Jain R P, Pandey J D.Temperature and pressure dependence of free volume and intermolecular free-lengthJ .Acustca, 1975, 34:3640. 6 Chaturvedi C V,
10、Prakash S.Ultrasonic study of free volume in ternary mixtures of liquidsJ .Acustica, 1972,27:4648.7 Bondi A.Free volumes and free rotation in simple liquids and liquid saturated hydrocarbons J.The Journal ofPhysical Chemistry, 1954, 58(11):84 87. 8 Kannappan A N, Rajendran V.Effect of free volume and internal pressureon ion-solvent interaction of some aqueouselectrolytic solutions J .Indian Journal of Pure state equation;free volume1 +:A8 Z43
