Example 02.08_d Pressure of Steam Using a High Precision Equation of State


A pressurized vessel (V = 0.5 m3) contains 5 kg steam (H2O) at = 220°C. Calculate the pressure in the vessel

a) according to the ideal gas law

b) using the virial equation

c) using the Soave-Redlich-Kwong equation

d) using a high-precision equation of state

molar mass: M = 18.015 g/mol

2nd virial coefficient: B = - 293 cm3/mol

critical temperature: Tc = 647.096 K

critical pressure: Pc = 220.64 . 105 Pa (220.64 bar)

acentric factor: w = 0.3443

Definitions and Constants:

IAPWS95 Parameters:

IAPWS95 refers to the Revised Release on the "Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use" (September 2009) as published on the website www.iapws.org of the International Association for the Properties of Water and Steam.

The names of the various constants were transferred to valid MathCad variable names with minor modifications. Details and parameter values can be found in the document:

http://www.iapws.org/relguide/IAPWS95-Rev.pdf (Ref.1)

Critical Data and Gas Constant (Ref.1, page 3):

Ideal Gas Parameters (Ref.1, Table 1):

Dimensionless Helmholtz Free Energy (Ideal Gas) (Ref.1, Equation 5):

Residual Part Parameters (Ref.1, Table 2):

Residual Part of the Dimensionless Helmholtz Free Energy (Ref.1, Equation 6):

Total Dimensionless Helmholtz Free Energy (Ref.1, Equation 4):


The pressure can easily be calculated using the following function (Ref.1, Table 3) :

Expressions for further properties are given in Ref.1, Table 3. Analytical derivatives are reported in Ref.1, Tables 4 and 5.