The Ideal Gas Law and the Superheated Region

Last post we talked about using the ideal gas law on the right side of the steam dome and found that it could be used as a decent approximation for very low pressures, even when the vapor is about to start condensing into liquid.  Today we’ll look at the accuracy of the ideal gas approximation out in the superheated region.

This figure shows the steam dome (red and blue lines) along with constant pressure lines for 15, 1500, and 4000 psia across the superheated region.

This figure compares steam table data with ideal gas approximation calculations for 4000 psia. 

The red line represents the actual v-T data from the superheated tables for water, while the green line represents temperatures calculated from tabulated pressure and specific volume data using the ideal gas approximation, and the blue symbols represent specific volumes calculated from tabulated pressure and temperature data.  

At this very high pressure, the ideal gas approximation never works well, although it is starting to get into the right neighborhood at the highest temperatures.

This figure shows the same comparison between steam table data and the ideal gas approximation in the superheated region for 1500 psia.

  While the ideal gas approximation is still not great, this lower pressure shows much better agreement at the highest temperatures than the data from 4000 psia.

This figure compares the steam table date with the ideal gas approximation for superheated water vapor at 15 psia. 

 The differences between steam table data and the ideal gas approximation were not discernable on a plot, so the percent error is plotted instead.  As before, the best agreement occurs at the highest temperatures (highest specific volume), but in this case the ideal gas approximation might be reasonable across the entire 15psia line.