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

Problem:

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:

2nd virial coefficient:

critical temperature:

critical pressure:

acentric factor:

Definitions and Constants:

Solution:

5 kg of water correspond to a molar quantity of

The volume is

and the temperature is

This leads to a molar volume of

Ideal Gas Law

Using the ideal gas law, the pressure is calculates as:

Virial Equation

As obvious from the unit of the second virial coefficient B, the following form of the equation has to be used (Leiden form):

Solving the right hand side formulation for the pressure P using Symbolics - Variable - Solve leads to:

Soave-Redlich-Kwong Equation of State

In case of the Redlich-Kwong-equation the parameters a and b need to be first calculated from the critical temperature and pressure

The pressure can then be calculated directly from the pressure explicit form of the equation:

The three results are thus:

The second virial coefficient is directly fitted to PvT-data and therefor should give reliable results. On the other hand the total pressure is too high for a reliable calculation using only the second virial coefficient. Also in case of the SRK equation, the result might not be reliable at this high pressure.

The correct result calculated via a high precision equation of state is

The vollowing plot shows the compressibility factor as function of reciprocal volume calculated by the three equations above:

A plot as function of pressure can be generated in the following way: