1. ChemE 260 Equations of State April 4, 2005 Dr. William Baratuci Senior Lecturer Chemical Engineering Department University of Washington TCD 2: E & F CB 2: 6 – 8, Supplement

2. Equations of State Relationship between Ideal Gas EOS: Universal Gas Constant:R –R = 8.314 J/mol-K = 0.082054 L-atm/mol-K = 1.987 Btu/lbmole- o R When does the IG EOS apply ? –When molecules interact very little with each other –At high T and low P –Generally: –Diatomic gases are especially unlikely to interact Baratuci ChemE 260 April 4, 2005

3. Advanced Equations of State Compressibility Factor EOS (graphical) Virial EOS Van der Waals EOS Redlich-Kwong EOS Soave-Redlich-Kwong EOS Baratuci ChemE 260 April 4, 2005

4. Compressibility Factor EOS Compressibility Factor: Principle of Corresponding States Reduced Properties: Compressibility Charts –Z vs P R –Curves of constant T R –Curves of constant Baratuci ChemE 260 April 4, 2005

5. Virial EOS Uses a power series expansion to describe deviations of Z from 1, the IG value B, C, D, etc are the Virial “constants” –functions of T, only –Determined experimentally Truncated Virial EOS: –Estimating B: Baratuci ChemE 260 April 4, 2005

6. Van der Waals EOS First cubic EOS Constants have physical interpretation Baratuci ChemE 260 April 4, 2005

7. RK & SRK EOS’s Redlich-Kwong Soave-Redlich-Kwong Baratuci ChemE 260 April 4, 2005

8. Applications of EOS’s Given any 2 of the 3 variables, determine the value of the unknown Cubic EOS’s and other even more sophisticated EOS’s can be used to… –predict properties of liquids –Estimate molar internal energies, enthalpies and entropies of gases and liquids –In this way, sophisticated EOS’s are used to generate the Thermodynamic “Data” Tables that we use Baratuci ChemE 260 April 4, 2005

9. Next Class Problem Session ! After that… –Chapter 3 – Heat Effects Internal Energy and Enthalpy Using the NIST Webbook Baratuci ChemE 260 April 4, 2005

10. Example #1 An Application of Equations of State –Estimate the pressure of ammonia at a temperature of 22 o C and a specific volume of 0.600 m 3 /kg. The Ideal Gas EOS The Virial EOS The van der Waal EOS The Soave-Redlich-Kwong EOS The Compressibility Factor EOS The Steam Tables Baratuci ChemE 260 April 4, 2005

11. Example #1 – Answers Ideal Gas: Ans.: P = 288.2 kPa Virial: Ans.: P = 280.6 kPa van der Waal:Ans.: P = 283.6 kPa SRK:Ans.: P = 281.5 kPa Z-Factor:Ans.: P = 282.0 kPa P = 281.0 kPa Steam Tables:Ans.: P = 281.7 kPa Baratuci ChemE 260 April 4, 2005