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