Questions and answers

Here are a few questions that I received through email and responses that may be useful to you.

I was just wondering how much of the virial expansion we will need to know. I am assuming everything we learned, to be safe. But I was wondering if there was a certain emphasis you wanted us to have, such as where the equation comes from or solving a problem like the example we had in class.

What we covered in lecture should be sufficient for understanding the virial equation. Generally, anything presented in lecture is what you should know very well, especially since we are covering a lot of material in just 10 weeks.

When do you know where to use the virial expansion? In the book example and the one in lecture the values for B and C were given, indicating that the virial equation would be used. Is there a table in the book for the values?I couldn't find one. Or would we be given the values if they were needed?

Second (and sometimes third) virial coefficients are tabulated for a wide range of systems because they are often easy to measure experimentally, but I don't think the book has a table. Generally if we work a problem these values will be given. In your later courses, you may see a lot more of the virial equation because it is frequently used to model dilute suspensions and colloidal solutions. But for the purposes of modeling fluids, the cubic equations of state and, even more so, the generalized correlations are usually more accurate.

Are the isothermal compressibility and the thermal volume expansivity generally constant for a specific material, or do they vary with temperature and pressure? For an ideal gas can we assume they are constant?

In general, these parameters are state-dependent, and thus depend on the specific pressure and temperature of the system. They do depend on state for an ideal gas. I believed we derived the ideal gas expressions for these parameters in lecture, but it should also be in the book if you want a second perspective.

MSS