Question

Example 4.6 The fugacity of a van der Waals gas Using the expression for the compressibility factor Z of a van der Waals gas given in equa- tion 1.26, what is the expression for fugacity of a van der Waals gas? As an approximation, terms in P2 and higher in the series expansion are omitted 2-1-0-(0)0r P RT RT Z In P dP P C'P 1 dP RTRT a b P a b RT RT 1Forfe-r a f P exp b RT RT

Answer 1

AD By definition 4 - γρ = f/ X fugacity coefficient. JL unitless Deviation from ideality waha can be representated by the nato of fugacity coefficient We know, AL Const Ti dell= TdP u P& pred with سلام uzu, ident - Videal p = d Foridealgas Р. Forsidenegas -> duint- vidutip halen. Svep wat vir jouse For real gass du read. I real de P P2 Nowe Mid uit Tulp = RT in P o Mount super ang tagal = RT in fz -0 P2 (trade vikend) df = RT In (fex P) ideally, When peo recal gazes behana fugacity co lefficient r ol in fap.

Nou and id) al = RT ln() Compressibility faclox z = Traal Videal Treal = z videad 1 (24) Videal df = RI Infle Z compreserbilines factor |(24) RT dp = RTin f[p (2-1) dpa in fp = lne JE-)102 for real gas (P+ 942) (v=b) - RT puta - pb- ab = RT pu = RT +Pb-q taba T= RT tba at table

اهلم We know da SdTtude Fool ideal gas; M (TP) = M (T) + RTlm (6) (d) = (2) + Rls (on) -5= - O'ta Lo P/abom. 15 = 30 _ R ln (9/16) M(+1) = M(+) + RT intre) ()+ - RTL Diuiding by da= -sdt tv de du = -5dTtu de 1 helmohtz free energy in I AFU-TS 0% Ārū-15 =(M+75°-RT) - T(5-RInf) A = M = Rinp -RT] the know, a = HTS AL = - T3 = a + T5 Ta Mo + RT lm. (P/2ben) + T5 - RT ln / P/an] Gabbo focee every Th= l + Tool (3Rinph G=HTS ot, ñ = 5 T 5 os ã = Mit T3 of CE M - RIP Acum Ha ut PN M = ū + pu ū a Ta pü M7 15°- PART Tu= M+TSORT