Joule Thomson Effect - Lab Report PDF

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Joule-Thomson Effect Massimo Ruscitti Partner: Jaci SilvaSa October 31, 2018

Ruscitti 1 Abstract: In this experiment, the Joule-Thompson coefficients of three gases were found through graphical analysis. To find the coefficients, each gas was passed through an experimental apparatus, and the temperature difference from the trial was plotted against the negative pressure difference. The resulting slope of the linear trendline possessed the same magnitude as the JouleThomson coefficients. The three gases, helium, nitrogen, and carbon dioxide were found to have Joule-Thomson coefficients of -0.0887 K/bar, 0.1987 K/bar, and 0.9606 K/bar. When compared to values found in literature, the percent error of these experimental coefficients was found to be 42.1%, 10.4%, and 12.7%, respectively. Introduction: The purpose of this experiment is to determine the Joule-Thomson coefficient for three gases: helium, nitrogen, and carbon dioxide. The Joule-Thomson coefficient of a gas is a representation of the experimental ratio between temperature difference and pressure difference at a constant enthalpy1, shown in Eq. (1), where µ is the Joule-Thomson coefficient, ∂T is the difference in temperature, ∂p is the difference in pressure, and H is the enthalpy.

μ≡

( ∂∂ Tp ) (1) H

Since the Joule-Thomson coefficient for a perfect gas is zero, the Joule-Thomson coefficients for real gases can be used to represent how well these gases follow perfect gas behavior as they undergo isenthalpic expansion2. Within the context of this experiment, the value of µ for the three gases can be taken from the linear slope of a temperature difference versus pressure difference graph, considering that the change in temperature should be proportional to the change

Ruscitti 2 in pressure. The apparatus used in this experiment is composed of a spiraling copper tube connected to a pressurized gas cylinder and a digital multimeter. While the temperature change is not recorded, the multimeter is able to record the change in voltage in microvolts, which can be converted to temperature difference in degrees Kelvin using Eq. (2), where ΔT is the change in temperature and ΔV is the change in voltage. ∆T=

∆V (2) μV 40.6 K

Experimental Method: To begin, the digital multimeter was switched on and allowed to warm up. The thermocouple lead was connected to the red terminal of the multimeter, and the “null” button was pressed to ensure that the multimeter was zeroed properly. For the helium gas trial, a canister of pressurized helium was connected to the apparatus using a length of flexible tubing. The gas valve was opened, and the regulator on the canister was used to allow helium gas to flow through the apparatus at a pressure of 0.5 bar. This purging process lasted a few minutes, and then the pressure was inside the apparatus was increased by 0.5 bar intervals. As the pressure was increased, the multimeter reading was recorded in microvolts. Upon recording a reasonable number of readings, the gas cylinder valve was shut off, and the tubing was removed from the helium gas and attached to the nitrogen gas cylinder. In the nitrogen gas trial, the same procedure was used as with the helium gas after allowing the nitrogen gas to purge the apparatus for a few minutes. Once the multimeter readings were recorded for the nitrogen gas, the same procedure was repeated with the carbon dioxide gas.

Ruscitti 3 Results: Apparatus Identifier: A

Ruscitti 4

Ruscitti 5

Sample Calculation of ΔT for Helium Trial: ∆T=

6 μV =0.147783 K (3) μV 40.6 K

Sample Calculation of Percent Error for Carbon Dioxide Trial: ¯¿ ¯¿−1.10 K ¿ K 0.9606 ¿ ¿ K 1.10 ¯ ∗100 %=12.7 % Error (4) ¿ ¿ ¿ Discussion: Overall, the experimental findings indicate that the Joule-Thomson coefficients for helium, nitrogen, and carbon dioxide were -0.0887 K/bar, 0.1987 K/bar, and 0.9606 K/bar. Figures 1-3 show the difference in temperature with respect to changes in pressure. For convenience in plotting, the negative pressure differences were graphed, meaning that the slope of the trendline possesses the opposite sign of the Joule-Thomson coefficient for the gases. In drawing the lines of best fit for the data, some readings were deemed as outliers and were not included to increase the accuracy of the Joule-Thomson coefficients. Table 4 contains all the necessary findings from the experimental data, including R2 values for the trendlines, experimental Joule-Thomson coefficients of the gases, literature values for the Joule-Thomson coefficients3, and the percent error. The R2 values for all three trendlines are very high, proving that the data follows a linear regression.

Ruscitti 6 However, the experimental Joule-Thomson coefficients for helium, nitrogen, and carbon dioxide possessed errors of 42.1%, 10.4%, and 12.7%, respectively, showing that there must have been a systematic error in the experiment. One potential source of error lies within the accuracy of the multimeter. If the multimeter could detect smaller changes in voltage, then the data could form a trendline that better reflects the Joule-Thomson coefficients found in the literature. Furthermore, the gases may not have been given enough time to equilibrate within the apparatus, which would contribute to the error present in the experiment. If the multimeter readings were recorded at equilibrium, then the line of best fit from the data would possess the same Joule-Thomson coefficeint as what is found in the literature.

References: 1

Garland, Carl W., et al., Experiments in Physical Chemistry Eighth Edition, 98-105, 2009.

2

Atkins, Peter, de Paula, Julio, Physical Chemistry: Thermodynamics, Structure, and Change, 10th Edition, 95-98, 2014. 3

A.M. Halpern and S. Gozashti, J. Chem. Educ. 63, 1001 (1986)....