{"text_format":"1","workbook":"xlsx","n_sheets":2,"sheets":["CO2 Functions","Example"],"not_rendered":{"charts":1,"images":0,"macros":1,"external_links":0,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"CO2 Functions","index":0,"n_rows":127,"n_cols":9,"rows_kept":127,"cut":false,"hidden":false,"merged":[]}
[null,"Physical Properties for Carbon Dioxide"]
[null,"Version 7.0 (WCO2v70IIR.bas)",null,null,null,"For Educational Use Only!"]
[null,"Report errors to R. L. Smith;  Email: smith@scf.che.tohoku.ac.jp"]
["Hint:  Select green box to see how to use function.  Be careful for units!  First letter of function is dependent variable;  other letters are independent variables; 1=CO2."]
["Example:  V_PT1(P,T) is Specific Volume as a function of Pressure (in Pa) and Temperature (in C)."]
["       Function units are in kg, m3, C, Pa, J"]
["Fundamental Constants","Function Name","Examples"]
["  Tc: critical temperature of CO2 (in C)","CO2_TC()",{"$f":"CO2_TC()","v":30.978200000000015},"oC"]
["  Pc: critical pressure of CO2    (in Pa)","CO2_PC()",{"$f":"CO2_PC()/1000000","v":7.3773},"MPa"]
["  Vc: critical volume of CO2      (m3/kg)","CO2_VC()",{"$f":"CO2_VC()","v":2.1385799828913601E-3},"m3/kg"]
["  rc: critical density of CO2     (kg/m3)","CO2_rhoc()",{"$f":"CO2_rhoc()","v":467.6},"kg/m3"]
["  Mw: molecular weight of CO2     (kg/mol)","CO2_MW()",{"$f":"co2_mw()","v":4.4009800000000002E-2},"kg/mol"]
[]
["Solid",null,null,"T [oC]","P [Pa]","Calculated Value"]
["  Pm:  melting pressure (S-L)","PMELT_T1(T)",null,-55.6,null,{"$f":"PMELT_T1(D15)/1000000","v":5.0187716140156295},"MPa"]
["  Tm:  melting temperature (S-L)","TMELT_T1(P)",null,null,5000000,{"$f":"TMELT_P1(E16)","v":-55.603977210211269},"oC"]
["  Psub:  sublimation pressure (S-V)","PSUB_T1(T)",null,-85,null,{"$f":"PSUB_T1(D17)/1000000","v":5.8193296171896378E-2},"MPa"]
[]
["Pressure-Volume (density)-Temperature"]
["Based on: R. Span and W. Wagner, A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa, J. Phys. Chem. Ref. Data 25(6), 1509-1596 (1996)."]
[null,null,"r [kg/m3]","T [oC]","P [Pa]","Calculated Value"]
["Saturation Curve: Vapor-liquid Equilibrium"]
["  Psat:  Vapor pressure (saturation pressure), Pa","PSAT_T1(T)",null,25,null,{"$f":"psat_T1(D23)/1000000","v":6.4343155956793536},"MPa"]
["  Tsat:  Vapor temperature (saturation temperature), oC","TSAT_P1(P)",null,null,100000,{"$f":"tsat_P1(E24)","v":-88.041842715134223},"oC"]
["  Hvap:  Heat (enthalpy) of vaporization, J/kg","HVAP_T1(T)",null,25,null,{"$f":"HVAP_T1(D25)*co2_mw()/1000","v":5.2657049382550625},"kJ/mol"]
["  Svap:  Entropy of vaporization, J/(kg K)","SVAP_T1(T)",null,25,null,{"$f":"SVAP_T1(D26)","v":401.30271587376501},"J/(kg K)"]
["     Liquid phase (saturated)"]
["r: Density, kg/m3","RHOL_T1(T)",null,25,null,{"$f":"rhol_t1(D28)","v":710.47149635543349},"kg/m3"]
["H: Enthalpy, H, J/kg","HL_T1(T)",null,25,null,{"$f":"hl_t1(D29)","v":274786.95904870937},"J/kg"]
["S: Entropy, S, J/(kg K)","SL_T1(T)",null,25,null,{"$f":"sl_t1(D30)","v":1248.4806330844126},"J/(kg K)"]
["Cp: constant pressure heat capacity, J/(kg K)","CPL_T1(T)",null,25,null,{"$f":"CPL_T1(D31)","v":6470.1097192223888},"J/(kg K)"]
["Cv: constant volume heat capacity, J/(kg K)","CVL_T1(T)",null,25,null,{"$f":"CVL_T1(D32)","v":1070.4871864240047},"J/(kg K)"]
["     Gas/vapor phase (saturated)"]
["r: Density, kg/m3","RHOG_T1(T)",null,25,null,{"$f":"rhog_t1(D34)","v":242.70968185722785},"kg/m3"]
["H: Enthalpy, H, J/kg","HG_T1(T)",null,25,null,{"$f":"hg_t1(D35)","v":394435.42230587167},"J/kg"]
["S: Entropy, S, J/kg K","SG_T1(T)",null,25,null,{"$f":"sg_t1(D36)","v":1649.7833489581776},"J/(kg K)"]
["Cp: constant pressure heat capacity, J/(kg K)","CPG_T1(T)",null,25,null,{"$f":"CPG_T1(D37)","v":8208.2023592444566},"J/(kg K)"]
["Cv: constant volume heat capacity, J/(kg K)","CVG_T1(T)",null,25,null,{"$f":"CVG_T1(D38)","v":1181.7445216540118},"J/(kg K)"]
["Single Phase Region"]
["Note: U, H, S, Cp, Cv can be used"]
["on the saturation boundary"]
["  T,P functions",null,"r [kg/m3]","T [oC]","P [Pa]","Calculated Value"]
["    V: specific volume, Wagner eqn., m3/kg","V_TP1(T,P)",null,40,11000000,{"$f":"V_TP1(D43,E43)","v":1.46301158110946E-3},"m3/kg"]
["    r: Density, kg/m3","RHO_TP1(T,P)",null,20,10000000,{"$f":"rho_tp1(D44,E44)","v":856.30982316237464},"kg/m3"]
["    f: fugacity, Pa","FUG_TP1(T,P)",null,40,10000000,{"$f":"fug_tp1(D45,E45)/1000000","v":5.8138575001680222},"MPa"]
["    U: internal energy","U_TP1(T,P)",null,40,10000000,{"$f":"U_TP1(D46,E46)","v":297128.40940233023},"J/kg"]
["    H: Enthalpy, H, J/kg","H_TP1(T,P)",null,40,10000000,{"$f":"h_tp1(D47,E47)","v":313039.32892389433},"J/kg"]
["    S: Entropy, S, J/kg K","S_TP1(T,P)",null,40,10000000,{"$f":"s_tp1(D48,E48)","v":1356.2366352728116},"J/(kg K)"]
["    Cv: constant volume heat capacity, J/(kg K)","CV_TP1(T,P)",null,40,10000000,{"$f":"CV_TP1(D49,E49)","v":1029.144918285908},"J/(kg K)"]
["    Cp: constant pressure heat capacity, J/(kg K)","CP_TP1(T,P)",null,40,10000000,{"$f":"cp_tp1(D50,E50)","v":5657.4615449880466},"J/(kg K)"]
["    w: speed of sound, m/s","W_TP1(T,P)",null,40,10000000,{"$f":"W_TP1(D51,E51)","v":269.8904143957871},"m/s"]
["  r,T functions"]
["     P: pressure, Wagner eqn., Pa","P_RT1(RHO,T)",628.61,40,null,{"$f":"P_RT1(C53,D53)/1000000","v":9.9999793034222133},"MPa"]
["     f: fugacity, Pa","FUG_RT1(T,RHO)",628.61,40,null,{"$f":"FUG_RT1(C54,D54)/1000000","v":5.8138542646695415},"MPa"]
["    U:  internal energy","U_RT1(RHO,T)",628.61,40,null,{"$f":"U_RT1(C55,D55)","v":297128.71421815571},"J/kg"]
["    H: Enthalpy, H, J/kg","H_RT1(RHO,T)",628.61,40,null,{"$f":"H_RT1(C56,D56)","v":313039.6403437258},"J/kg"]
["    S: Entropy, S, J/kg K","S_RT1(RHO,T)",628.61,40,null,{"$f":"S_RT1(C57,D57)","v":1356.2377348868754},"J/(kg K)"]
["    Cv: constant volume heat capacity, J/(kg K)","CV_RT1(RHO,T)",628.61,40,null,{"$f":"CV_RT1(C58,D58)","v":1029.1464681969273},"J/(kg K)"]
["    Cp: constant pressure heat capacity, J/(kg K)","CP_RT1(RHO,T)",628.61,40,null,{"$f":"CP_RT1(C59,D59)","v":5657.5184294408455},"J/(kg K)"]
["    w: speed of sound, m/s","W_RT1(RHOH,T)",628.61,40,null,{"$f":"W_RT1(C60,D60)","v":269.88924194517961},"m/s"]
["  Virial Coefficients"]
["     B: Second virial coefficient B, m3/kg","VIRIALB_T1(T)",null,25,null,{"$f":"VIRIALB_T1(D62)","v":-1.2301195752784189E-4},"m3/kg"]
["     C: Third virial coefficient C, m6/kg2","VIRIALC_T1(T)",null,25,null,{"$f":"VIRIALC_T1(D63)","v":4.7468334788673147E-9},"m6/kg2"]
["  P,V (or rho) functions",null,"P [Pa]","r [kg/m3]","V [m3/kg]","Calculated Value"]
["T:single phase temperature at P > Pc","T_PV1(P,V)",11000000,null,1.4630115811094652E-3,{"$f":"T_PV1(C65,E65)","v":39.999998111389097}]
[null,"T_PR1(P,RHO)",28370000,1000,null,{"$f":"T_PR1(C66,D66)","v":14.005453361488904}]
["T:single phase temperature at P < Pc, liquid phase","T_PVL1(P,V)",6600000,null,1E-3,{"$f":"T_PVL1(C67,E67)","v":-8.9540291972173929}]
[null,"T_PRL1(P,RHO)",38000000,1000,null,{"$f":"T_PRL1(C68,D68)","v":24.207032221037792}]
["T:single phase temperature at P < Pc, gas phase","T_PVG1(P,V)",6600000,null,0.02,{"$f":"T_PVG1(C69,E69)","v":425.61229421961758}]
[null,"T_PRG1(P,RHO)",380000000,900,null,{"$f":"T_PRG1(C70,D70)","v":618.58957005290335}]
[]
["Functions Useful for Compressors/Pumps/\nExpansions through Valves",null,"S J/kg K",null,"H J/kg"]
["  T:  single phase temperature at P, S","T_PS1(P,S)",1356.2,10000000,null,{"$f":"t_ps1(D73,C73)","v":39.997972003957685},"oC"]
["  T:  single phase temperature at P, H","T_PH1(P,H)",null,10000000,313039,{"$f":"t_ph1(D74,E74)","v":39.999941860015667},"oC"]
[]
[null,null,"r [kg/m3]","T [oC]","P [Pa]","Calculated Value"]
["  Joule-Thomson coefficient mu = (dT/dP)h","JT_RT1(RHO,T)",628.61,40,null,{"$f":"JT_RT1(C77,D77)*1000000","v":1.0992194082881561},"K/MPa"]
["  Isothermal throttling coefficient delt = (dh/dP)T","DELT_RT1(RHO,T)",628.61,40,null,{"$f":"DELT_RT1(C78,D78)","v":-1.5047064045027403E-2},"J/kg Pa"]
["  Isentropic temperature pressure coefficient bs = (dT/dP)s","BETAS_RT1(RHO,T)",628.61,40,null,{"$f":"BETAS_RT1(C79,D79)*1000000","v":2.9408433618843959},"K/MPa"]
[]
["Two Phase Region",null,"State","P [Pa]","H [J/kg]","X [-]"]
["     Quality X_PH1(P,H)","X_PH1(P,H)","I",5729194.4000000004,255864.6,{"$f":"x_ph1(D82,E82)","v":2.9201548340680432E-7},"T",20,"C"]
[null,null,"II",5729195.4000000004,350000,{"$f":"x_ph1(D83,E83)","v":0.61932561975915801},"HL",{"$f":"hl_t1(H82)","v":255864.55622977176},"J/kg"]
[null,null,"III",5729196.4000000004,407861.2,{"$f":"x_ph1(D84,E84)","v":0.99999990382436954},"HG",{"$f":"hg_t1(H82)","v":407861.24558538618},"J/kg"]
[null,null,null,null,null,null,"Psat",{"$f":"psat_T1(H82)","v":5729194.4242937686},"Pa"]
[null,null,null,"P [Pa]","S [J/kg K]"]
["     Quality X_PS1(P,H)","X_PS1(P,S)","I",5729196.4000000004,1187.7,{"$f":"X_PS1(D87,E87)","v":0},"T",20,"C"]
[null,null,"II",5729196.4000000004,1500,{"$f":"X_PS1(D88,E88)","v":0.6023103607834065},"SL",{"$f":"sl_t1(H87)","v":1187.7051990959792},"J/(kg K)"]
[null,null,"III",5729196.4000000004,1706.2,{"$f":"X_PS1(D89,E89)","v":1},"SG",{"$f":"sg_t1(H87)","v":1706.2000505210972},"J/(kg K)"]
[null,null,null,null,null,null,"Psat",{"$f":"psat_T1(H87)","v":5729194.4242937686},"Pa"]
["Derivative Properties"]
["  T,P functions",null,"r [kg/m3]","T [oC]","P [Pa]","Calculated Value"]
["     dP/dT derivative","DPDT_TP1(T, P)",null,40,10000000,{"$f":"DPDT_TP1(D93, E93)/1000000","v":0.27818429577735276},"MPa/K"]
["     dP/drho derivative = (dP/drho)T","DPDR_TP1(T,P)",null,40,10000000,{"$f":"DPDR_TP1(D94,E94)/1000000","v":1.3250426077735359E-2},"MPa/(kg/m3)"]
["     drho/dT derivative = (drho/dT)P","DRDT_TP1(T,P)",null,40,10000000,{"$f":"DRDT_TP1(D95,E95)","v":-20.994366078898004},"(kg/m3 K)"]
["     Isothermal compressibility = (1/rho)*(drho/dP)T","BETAT_TP1(T,P)",null,40,10000000,{"$f":"BETAT_TP1(D96,E96)*1000000","v":0.12005708426006263},"1/MPa"]
["     Volume coefficient of expansion =  (1/V)*(dV/dT)P","BETAP_TP1(T,P)",null,40,10000000,{"$f":"BETAP_TP1(D97,E97)","v":3.3397995437967828E-2},"1/K"]
["  r,T functions"]
["     dP/dT derivative","DPDT_RT1(RHO,T)",628.61,40,null,{"$f":"DPDT_RT1(C99,D99)/1000000","v":0.27818286993719987},"MPa/K"]
["     dP/drho derivative = (dP/drho)T","DPDR_RT1(RHO,T)",628.61,40,null,{"$f":"DPDR_RT1(C100,D100)/1000000","v":1.3250197681274252E-2},"MPa/(kg/m3)"]
["     drho/dT derivative = (drho/dT)P (derived)","DRDT_RT1(RHO,T)",628.61,40,null,{"$f":"DRDT_RT1(C101,D101)","v":-20.994620354256288},"(kg/m3 K)"]
["     Isothermal compressibility = -(1/V)*(dV/dP)T","BETAT_RT1(RHO,T)",628.61,40,null,{"$f":"BETAT_RT1(C102,D102)*1000000","v":0.1200594520322173},"1/MPa"]
["     Volume coefficient of expansion =  -(1/V)*(dV/dT)P","BETAP_RT1(RHO,T)",628.61,40,null,{"$f":"BETAP_RT1(C103,D103)","v":3.3398482929409785E-2},"1/K"]
["Transport Properties"]
["Based on correlations in Reid, Prausnitz and Poling (1987)"]
["     Liquid phase (saturated)",null,null,"T [oC]",null,"Calculated Value"]
["               Viscosity, Pa s","VMUL_T1(T)",null,25,null,{"$f":"vmul_t1(D107)","v":6.0602715238092372E-5},"Pa s"]
["               Kinematic viscosity (dense gas),  (=mu/rho),  m2/s  ","VNUL_T1(T)",null,25,null,{"$f":"vnul_t1(D108)","v":8.5299291455000396E-8},"m2/s"]
["               Surface tension, N/m","SIGMA_T1(T)",null,25,null,{"$f":"SIGMA_T1(D109)","v":5.3126362684029497E-4},"N/m"]
["               Thermal conductivity (saturated liquid), W/(m K)","kL_T1(T)",null,20,null,{"$f":"kL_T1(D110)","v":8.7335854642549934E-2},"W/(m K)"]
["     Gas/vapor phase (saturated)"]
["               Viscosity, Pa s","VMUG_T1(T)",null,25,null,{"$f":"vmug_t1(D112)","v":2.238400190287764E-5},"Pa s"]
["               Kinematic viscosity (dense gas),  (=mu/rho),  m2/s  ","VNUG_T1(T)",null,25,null,{"$f":"vnug_t1(D113)","v":9.2225418168710965E-8},"m2/s"]
["               Ideal gas thermal conductivity, W/(m K)","KID_T1(T)",null,25,null,{"$f":"KID_T1(D114)","v":1.6889509141672008E-2},"W/(m K)"]
["               Thermal conductivity (saturated vapor), W/(m K)","kG_T1(T)",null,20,null,{"$f":"kG_T1(D115)","v":2.6093839854912364E-2},"W/(m K)"]
["     Single Phase (Gas/vapor) Region"]
["          T,P functions",null,"r [kg/m3]","T [oC]","P [Pa]","Calculated Value"]
["               Viscosity (dense gas), Pa s","VMU_TP1(T,P)",null,40,10000000,{"$f":"VMU_TP1(D118,E118)","v":4.9264821409579048E-5},"Pa s"]
["               Kinematic viscosity (dense gas),  (=mu/rho),  m2/s  ","VNU_TP1(T,P)",null,40,10000000,{"$f":"vnu_tp1(D119,E119)","v":7.8370848374564731E-8},"m2/s"]
["               Thermal conductivity (dense gas), W/(m K)","k_TP1(T,P)",null,40,10000000,{"$f":"k_TP1(D120,E120)","v":6.8413538482249028E-2},"W/(m K)"]
["         r,T functions"]
["               Viscosity (dense gas), Pa s","VMU_RT1(RHO,T)",628.61,40,null,{"$f":"vmu_rt1(C122,D122)","v":4.9264663839284725E-5},"Pa s"]
["               Kinematic viscosity (dense gas),  (=mu/rho),  m2/s  ","VNU_RT1(RHO,T)",628.61,40,null,{"$f":"VNU_RT1(C123,D123)","v":7.8370792445689262E-8},"m2/s"]
["               Thermal conductivity (dense gas), W/(m K)","k_RT1(RHO,T)",628.61,40,null,{"$f":"k_RT1(C124,D124)","v":6.8413339209581148E-2},"W/(m K)"]
["Other"]
["Dielectric function of Moriyoshi et at. (1993).","EPS_RT1(RHO,T)",628.61,40,null,{"$f":"EPS_RT1(C126,D126)","v":1.36751163726669}]
[null,"EPS_TP1(T,P)",null,40,10000000,{"$f":"EPS_TP1(D127,E127)","v":1.36751266720357}]

{"sheet":"Example","index":1,"n_rows":117,"n_cols":9,"rows_kept":117,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Input Field"]
[null,"Calculation Field",null,"Example of using the rho_tp1(TinC,PinPa) function"]
[null,"Solver Field"]
[null,"Vector function",null,null,null,null,null,"Curve label:",{"$f":"CONCATENATE(E6,\" C\")","v":"40 C"}]
[null,"Note Field",null,"T [C]",40]
[null,"Optional/Disregard",null,"P [MPa]","rho [kg/m3]"]
[null,null,null,0.01,{"$f":"rho_tp1($E$6,D8*1000000)","v":0.16909995594188684}]
[null,null,null,0.02,{"$f":"rho_tp1($E$6,D9*1000000)","v":0.33834279869302897}]
[null,null,null,0.03,{"$f":"rho_tp1($E$6,D10*1000000)","v":0.50772882357461635}]
[null,null,null,0.04,{"$f":"rho_tp1($E$6,D11*1000000)","v":0.67725832688034371}]
[null,null,null,0.05,{"$f":"rho_tp1($E$6,D12*1000000)","v":0.84693160588069438}]
[null,null,null,0.06,{"$f":"rho_tp1($E$6,D13*1000000)","v":1.0167489588272483}]
[null,null,null,7.0000000000000007E-2,{"$f":"rho_tp1($E$6,D14*1000000)","v":1.1867106849570142}]
[null,null,null,0.08,{"$f":"rho_tp1($E$6,D15*1000000)","v":1.3568170844967571}]
[null,null,null,0.09,{"$f":"rho_tp1($E$6,D16*1000000)","v":1.5270684586674714}]
[null,null,null,0.1,{"$f":"rho_tp1($E$6,D17*1000000)","v":1.6974651096886666}]
[null,null,null,0.2,{"$f":"rho_tp1($E$6,D18*1000000)","v":3.4094890578906929}]
[null,null,null,0.4,{"$f":"rho_tp1($E$6,D19*1000000)","v":6.8784595125847527}]
[null,null,null,0.6,{"$f":"rho_tp1($E$6,D20*1000000)","v":10.409511777712831}]
[null,null,null,0.8,{"$f":"rho_tp1($E$6,D21*1000000)","v":14.005431138984997}]
[null,null,null,1,{"$f":"rho_tp1($E$6,D22*1000000)","v":17.66920576640797}]
[null,null,null,1.2,{"$f":"rho_tp1($E$6,D23*1000000)","v":21.404046990125394}]
[null,null,null,1.4,{"$f":"rho_tp1($E$6,D24*1000000)","v":25.213412193431139}]
[null,null,null,1.6,{"$f":"rho_tp1($E$6,D25*1000000)","v":29.101030743136597}]
[null,null,null,1.8,{"$f":"rho_tp1($E$6,D26*1000000)","v":33.070933458930057}]
[null,null,null,2,{"$f":"rho_tp1($E$6,D27*1000000)","v":37.127486223480005}]
[null,null,null,2.2000000000000002,{"$f":"rho_tp1($E$6,D28*1000000)","v":41.275428458768765}]
[null,null,null,2.4,{"$f":"rho_tp1($E$6,D29*1000000)","v":45.519917347973717}]
[null,null,null,2.6,{"$f":"rho_tp1($E$6,D30*1000000)","v":49.866578874654607}]
[null,null,null,2.8,{"$f":"rho_tp1($E$6,D31*1000000)","v":54.321566993330123}]
[null,null,null,3,{"$f":"rho_tp1($E$6,D32*1000000)","v":58.891632552788607}]
[null,null,null,3.2,{"$f":"rho_tp1($E$6,D33*1000000)","v":63.58420398594243}]
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