1. MOLAR VOLUME AND COMPRESSIBILITY FACTOR FROM VAN DER WAALS EQUATION
1.1 Numerical Methods
Solution of a single nonlinear algebraic equation.
1.2 Concepts Utilized
Use of the van der Waals equation of state to calculate molar volume and compressibility factor for a
gas.
1.3 Course Useage
Introduction to Chemical Engineering, Thermodynamics.
1.4 Problem Statement
The ideal gas law can represent the pressure-volume-temperature (PVT) relationship of gases only at
low (near atmospheric) pressures. For higher pressures more complex equations of state should be
used. The calculation of the molar volume and the compressibility factor using complex equations of
state typically requires a numerical solution when the pressure and temperature are specified.
The van der Waals equation of state is given by
(1)
where
(2)
and
(3)
The variables are defined by
P = pressure in atm
V = molar volume in liters/g-mol
T = temperature in K
R = gas constant (R = 0.08206 atm.liter/g-mol.K)
Tc = critical temperature (405.5 K for ammonia)
Pc = critical pressure (111.3 atm for ammonia)
1.1 Numerical Methods
Solution of a single nonlinear algebraic equation.
1.2 Concepts Utilized
Use of the van der Waals equation of state to calculate molar volume and compressibility factor for a
gas.
1.3 Course Useage
Introduction to Chemical Engineering, Thermodynamics.
1.4 Problem Statement
The ideal gas law can represent the pressure-volume-temperature (PVT) relationship of gases only at
low (near atmospheric) pressures. For higher pressures more complex equations of state should be
used. The calculation of the molar volume and the compressibility factor using complex equations of
state typically requires a numerical solution when the pressure and temperature are specified.
The van der Waals equation of state is given by
(1)
where
(2)
and
(3)
The variables are defined by
P = pressure in atm
V = molar volume in liters/g-mol
T = temperature in K
R = gas constant (R = 0.08206 atm.liter/g-mol.K)
Tc = critical temperature (405.5 K for ammonia)
Pc = critical pressure (111.3 atm for ammonia)
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