Major ideas
1. The Pressure versus Volume curve at constant temperature (isothermal) for SF6 allows us to investigate a gas-liquid phase change at reasonable (experimentally accessible) conditions. Phase transitions are pervasive in everyday life (ice-water-vapor for example) and have provided a rich field of study in physics and chemistry for a long time. Phase transitions are an example of what are now called critical phenomena. In 1982 Kenneth G. Wilson was awarded the Nobel Prize in Physics “for his theory for critical phenomena in connection with phase transitions.”
2. One of the properties of a gas-liquid phase transition is that the gas and liquid can coexist in various proportions at the same pressure over a volume interval at constant temperature. Your PV data should show this coexistence region. In this critical region the gas-liquid mixture will exhibit critical opalescence, a critical phenomenon, which you may observe in your sample chamber.
Major equipment
1. 3B Scientific Physics Critical Point Apparatus – see "CriticalPointInstructions.pdf" below.
2. A heat exchanger is used to keep the SF6 at a constant temperature while you measure the pressure as a function of volume. How does the heat exchanger work? What are some applications of heat exchangers?
Data analysis
1. The phenomenological van der Waals equation of state extends the Ideal Gas equation to account for the excluded volume due to the size molecules and the attractive interaction of molecules. Know how to account for these corrections.
a. Law of corresponding states: once you know the critical pressure, critical volume, and critical temperature you can write the van der Waals equation of state in “reduced” form. All van der Waals gases have the same “reduced” form. This is called the “Law of Corresponding States.” Know how to derive the reduced van der Waals equation.
b. Maxwell construction: If you were to plot P vs V at a constant temperature using the van der Waals equation your plot would look nothing like your data. Why not? How does the “Maxwell construction” allow you to identify the coexistence region of your PV curve?
2. Nonlinear curve fitting: The van der Waals equation is a nonlinear equation. You cannot use Linear Regression to fit your data to find the critical pressure, critical temperature, or critical volume. Look into a typical “nonlinear” fitting routine. What does it do?
Here is a link to the attached document containing prelab questions.
See the documents below.
Valderrama, J. O. (2010), "The legacy of Johannes Diderik van der Walls, a hundred years after his Nobel Prize for physics," J. of Supercritical Fluids 55, 415-420; doi: 10.1016/j.supflu.2010.10.026