Jednačina stanja

Jednačina stanja je jednačina koja preko pritiska, temperature i zapremine opisuje ponašanje gasa i izražava se u obliku   f ( p , V , T ) = 0 . {\displaystyle {\ f(p,V,T)=0}.}

Jednačine stanja za posebne modele

  • Jednačina stanja idealnog gasa:   p V = n R T . {\displaystyle {\ pV=nRT}.}
  • Jednačina stanja Van der Valsovog gasa: ( p + a V m 2 ) ( V m − b ) = R T {\displaystyle {\left(p+{\frac {a}{V_{m}^{2}}}\right)\left(V_{m}-b\right)=RT}}
  • Redlih-Kvongova (Redlich-Kwong) jednačina stanja: p = R T V m − b − a T V m ( V m + b ) {\displaystyle {p={\frac {R\,T}{V_{m}-b}}-{\frac {a}{{\sqrt {T}}\,V_{m}\left(V_{m}+b\right)}}}}
  • Soaova modifikacija Redlih-Kvongove jednačine stanja: p = R T V m − b − a α V m ( V m + b ) {\displaystyle p={\frac {R\,T}{V_{m}-b}}-{\frac {a\,\alpha }{V_{m}\left(V_{m}+b\right)}}}
  • Peng-Robinsonova jednačina stanja: p = R T V m − b − a α V m 2 + 2 b V m − b 2 {\displaystyle p={\frac {R\,T}{V_{m}-b}}-{\frac {a\,\alpha }{V_{m}^{2}+2bV_{m}-b^{2}}}}
  • Peng-Robinson-Strajek-Vera (Peng-Robinson-Stryjek-Vera) jednačina stanja: κ = κ 0 + [ κ 1 + κ 2 ( κ 3 − T r ) ( 1 − T r 0.5 ) ] ( 1 + T r 0.5 ) ( 0.7 − T r ) {\displaystyle \kappa =\kappa _{0}+\left[\kappa _{1}+\kappa _{2}\left(\kappa _{3}-T_{r}\right)\left(1-T_{r}^{0.5}\right)\right]\left(1+T_{r}^{0.5}\right)\left(0.7-T_{r}\right)}
  • Eliot-Sureš-Donohova (Elliott, Suresh, Donohue) jednačina stanja: p V m R T = Z = 1 + Z r e p + Z a t t {\displaystyle {\frac {pV_{m}}{RT}}=Z=1+Z^{\rm {rep}}+Z^{\rm {att}}}
  • Dietrići (Dieterici) jednačina stanja:   p ( V − b ) = R T e − a / R T V {\displaystyle \ p(V-b)=RTe^{-a/RTV}}
  • Virialova jednačina stanja: p V m R T = 1 + B V m + C V m 2 + D V m 3 + … {\displaystyle {\frac {pV_{m}}{RT}}=1+{\frac {B}{V_{m}}}+{\frac {C}{V_{m}^{2}}}+{\frac {D}{V_{m}^{3}}}+\dots }
  • Benedikt-Veb-Rubinova jednačina stanja: p = ρ R T + ( B 0 R T − A 0 − C 0 T 2 + D 0 T 3 − E 0 T 4 ) ρ 2 + ( b R T − a − d T ) ρ 3 + α ( a + d T ) ρ 6 + c ρ 3 T 2 ( 1 + γ ρ 2 ) exp ⁡ ( − γ ρ 2 ) {\displaystyle p=\rho RT+\left(B_{0}RT-A_{0}-{\frac {C_{0}}{T^{2}}}+{\frac {D_{0}}{T^{3}}}-{\frac {E_{0}}{T^{4}}}\right)\rho ^{2}+\left(bRT-a-{\frac {d}{T}}\right)\rho ^{3}+\alpha \left(a+{\frac {d}{T}}\right)\rho ^{6}+{\frac {c\rho ^{3}}{T^{2}}}\left(1+\gamma \rho ^{2}\right)\exp \left(-\gamma \rho ^{2}\right)}

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Literatura

  • Elliot & Lira, (1999). Introductory Chemical Engineering Thermodynamics, Prentice Hall.