1. Advance Chemical Engineering Thermodynamics By Dr.Dang Saebea

2. Part III Real gas

3. 4. Real gas 2. The equation of state is not given by 1. Real gas can be liquefied and solidified by reducing temperature T < Tcrit  Real gas behavior

4. Experimetation has demostrated the following general features of the behavior of pure gases:

5. (2) At the critical point on the critical isotherm, the first and second derivatives of pressure with respect to volume are zero.

6. (3) Boyle temperature is the temperature at which a non ideal gas behaves most like an ideal gas.  It is at this temperature that the attractive forces and the repulsive forces acting on the gas particles balance out.  The compressibility factor approaches 1 at low pressures, but does so with different slopes. Gas approaches ideality

7.  Analytical 1) Virial equation 2) Van der Waals 3) Redlich Kwong 4) Peng-Robinsion  Graphical and tabular- third parameter 1)Critical compressibility 2)Acentric factor Equation of state 1.Representation of PVT data. 2.Prediction of gas phase properties of pure fluids and their mixture from the experimental data. 3.Prediction of vapor-liquid equilibrium of mixtures, especially at high pressure.

9. Example A certain gas behaves according to the EOS Where a and b are constants, Does the EOS predict the possibility of liquefying the gas

10. 1. Virial Equation

11.  The parameters B, C, D, etc. are virial coefficients, accounting of interactions between molecules. Ex. B = the second virial coefficient, is interpreted as the sum of the interact of custers of two molecules. C = the third virial coefficient, is interpreted as the sum of the interact of custers of three molecules. Clearly truncation will depend on the pressure range being analyzed: P distance between molecules more terms 5-6 atm --- > B 15-20 atm ---> B, C 50 atm ---> B, C, D

12. Reciprocal volume Reciprocal pressure 2 3 Their coefficients may be correlated as follows: Correlation of coefficients in both equation The volume expansion is more accurate than the pressure expansion, when an equal number of terms is considered. For example, if we consider C = 0 then we obtain C’ 0, hence more terms are require by the pressure expansion

13. Coefficients at critical point at the critical point If we apply the condition at the critical point and solve the three relations for the value of B(T c ), C(T c ) and D(T c )