Joule-Thomson effect for a van der Waals gas

Another relationship can be obtained by defining an ideal pressure P as 

If we substitute from Equation (10.72) into Equation (10.71), we obtain 

the fugacity can be estimated from the observed pressure, P, and the ideal pressure can be calculated from the observed volume. The error (6, p. 198) in Equation (10.73) is less than 1% for oxygen up to a pressure of 10 MPa. For carbon dioxide, the error is 1% at 2.5 MPa and 4% at 5 MPa [6]. If a P C RT, the numeric value of f/P is relatively insensitive to variations in the value of a as large as 30%. 

Although the van der Waals equation is not the best of the semi-empirical equations for predicting quantitatively the PVT behavior of real gases, it does provide excellent qualitative predictions. We have pointed out that the temperature coefficient of the fugacity function is related to the Joule-Thomson coefficient p,j x.- Let us now use the van der Waals equation to calculate p,j.T. from a fugacity equation. We will restrict our discussion to relatively low pressures. 

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