Calculate change in thermodynamic property \(M\):

\[\Delta M = M_2 – M_1 = (M_2 – M^{ig} _2) + (M^{ig} _2 – M^{ig} _1) – (M_2 – M^{ig} _1)\]

where \(M\) is any state function

\(M_1\) is the value of the state function for the real gas at state 1

\(M_2\) is its value at state 2

\(M^{ig} _1\) and \(M^{ig} _2\) are the values of the state function if it were an ideal gas at the same temperature and pressure as the real gas.

The change in entropy of an ideal gas when pressure changes from \(P_1\) to \(P_2\) is:

\[\Delta S^{ig} = -R\hspace{1mm}ln\frac{P_2}{P_1}\]