1. REAL GAS RELATIONSHIPS How can we predict behavior of gases at such conditions ? There are FOUR methods: 1) Compressibility Charts 2) Equations of State 3) Estimated properties 4) Actual Experimental Data

2. 2) Equations of State I- Van der Waals Equation {p+( a )}{V-b}=RT ; a= 27 R 2 T c 2. b=(1/8)RT c V 64 P c P c where V is the specific volume And P c, T c and V c are critical pressure, temp and volume respectively

3. Notes: It is a semi-empirical Equation It is developed from theory ( effects of attractive forces & volume occupied by gases themselves are taken into consideration) But the constants a, b are found from experiments for each gas. To solve for V the Equation is rearranged as:

4. Example: A cylinder 0.150 m 3 in volume containing 22.7 kg of propane. A pressure gauge shows that the pressure is 4790 KPa gauge. Estimate the temp of propane in the cylinder using Van der Waals equation For propane : a=9.24x10 6 atm cm3 b = 90.7 cm 3 / gmol 2 g mol

5. II - VIRIAL Form of the equation of State: : Other form of equations of state can be seen in the textbook