The Joule-Thomson Effect

As preparation for this experiment, you should read the section in your physical chemistry text which deals with the thermodynamic principles involved in understanding the Joule-Thomson effect. You must also read the experimental setup and procedure as given in your physical chemistry lab text¹. A basic outline is as follows.

Gas in an insulated vessel is caused to pass through a "throttle". In our apparatus, a stainless steel frit acts as the throttle, and the pressure drop across the frit is from a regulated constant pressure to atmospheric. Thermodynamic analysis shows that the adiabatic nature of the expansion through the frit leads to the conclusion that the process is carried out at constant enthalpy. The Joule-Thomson coefficient is defined as:

Procedure

The apparatus is on the benchtop where the large water bath and CO₂ cylinder are located. The bath temperature should be maintained at 25^oC throughout the course of the experiment; a few hours before collecting your data, switch on the immersion circulator and let the bath warm to the desired temperature.

The gas is brought to a constant temperature before reaching the frit by passing it through about 200 feet of copper tubing which is immersed in a water bath. The temperature difference across the frit is very small. We will use a thermocouple circuit in which one junction is located on the high-pressure side of the frit, while the second junction is positioned just above the porous frit on the atmospheric pressure side. The Agilent 34970A is used to measure the voltage difference between the two junctions, which, for the largest pressure difference, will be about 40-70 microvolts. The corresponding temperature drop across the frit is very small. Over a temperature range this small, it is not necessary to use a cubic (or higher) polynomial to convert voltage to temperature. We will use the published Seebeck coefficient for the type T thermocouple at 25^oC (40 mvolt/K.)

A set of observations is obtained by choosing several pressure differences, starting with approximately 40-45 psi difference across the frit (i.e., 40-45 psi above atmospheric pressure) as read on the Bourdon gauge fitted to the Joule-Thomson cell. At each pressure, wait for constant voltages from the thermocouple circuit before collecting data and selecting a new pressure. Start at the largest pressure difference and work downwards in increments of about 5 psi toward zero pressure difference. It should be possible to obtain four or five pairs of readings.

Configure the 34970A read the voltage across the thermocouple circuit. Connect the copper leads from the thermocouples to the multiplexer and record the channel. Configure the channel to make a DC voltage measurement (do not configure for a thermocouple measurement!) Before the experiment begins, collect and average an adequate number of voltages to be stored as the offset voltage (there will be a small potential difference between the two thermocouple junctions.) Record this voltage as the offset voltage. When the pressure has been raised/lowered to the desired value, make sure that the thermocouple voltage is stable, and collect and average an adequate number of voltages. Record the average voltage and the corresponding pressure in your lab notebook. To convert the averaged voltage to a temperature, subtract the offset voltage from the observed voltage and multiply the result by the Seebeck coefficient.

The data sets in their final form can be plotted as the temperature differences vs. the pressure differences. Over the range in pressure accessible to us, the data can be expected to form a straight line. The slope of the line is our experimental value of the Joule-Thomson coefficient for the gas. Calculate the Joule-Thomson coefficient for CO₂ at 25^oC, and include quality estimates. Compare your results to literature values. In your report, explain why the temperature difference develops across the frit, and compare the Joule-Thomson coefficient for carbon dioxide to that for nitrogen and helium. Explain the differences in these quantities. Also, explain how one could calculate a Joule-Thomson coefficent from an equation of state (e.g., the van der Waals or Redlich-Kwong equation.)

References

1. D.P. Shoemaker, C.W. Garland, and J.W. Nibler, "Experiments in Physical Chemistry", 6th ed, McGraw-Hill, New York (1996) and references contained therein.

2. Agilent 34970A Data Acquisition/Switch Unit User's Guide, Agilent Technologies Inc., 2003.