# The Joule-Thomson Effect

**Stephanie Ng: 5/5/2016**

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The Joule-Thomson coefficient is a measurable quantity that results from observing the expansion of a gas under adiabatic conditions, corresponding to the Joule-Thomson effect. When adiabatic conditions are met, heat does not enter or leave the system. In the Joule-Thomson effect, upon expansion, a temperature change should result, which allows one to observe deviation from ideal gas behavior. For an ideal gas, the Joule-Thomson coefficient should be zero.

Attractive forces will contribute more in determining behavior than the repulsive forces in reality, and therefore, most real gases will cool upon expansion. The cooling results from the van der Waals attractive forces between the molecules of the gas. Since the attractive forces need to be overcome before the molecules can move away from each other and expand, energy must be put into the system, resulting in cooling of the surroundings. Cooling upon expansion yields a Joule-Thomson coefficient that is positive. In contrast, small-molecule and nearly ideal gases will not have very strong van der Waals attractive forces and therefore will exhibit the opposite behavior upon expansion: they will cause heating. This difference can be illustrated with tests using gases such as helium and carbon dioxide. Due to its small size, helium generally exhibits a negative Joule-Thomson coefficient, while carbon dioxide yields a positive value. In addition, helium will have a coefficient closer to zero, demonstrating that it is closer to an ideal gas than carbon dioxide.

In order to model the Joule Thomson effect, different theoretical equations can be used, each with their own set of assumptions. One common model is the use of the van der Waals equation. This equation takes into account the attractive forces between the molecules and the volume occupied by the molecules as it becomes smaller and smaller. In addition, the molecules are modeled as small spheres, and the smallest distance between two molecules is the sum of their van der Waals radii. Since the van der Waals equation is a very simplistic view of the system, it does not give the most accurate estimation of the Joule Thomson coefficient. Another equation that can be used for modeling is the Beattie-Bridgeman equation, which yields an accurate measurement over a wide range of temperatures and other variables. The theoretical basis for this equation is the kinetic theory of gases and the differences in the pressure based upon the kinetic energy and potential energy of the gas. The Beattie-Bridgeman equation yields a more accurate approximation than the van der Waals equation.

Moreover, the Joule-Thomson effect is of particular interest because the Joule-Thomson cooling has a practical basis for the Linde method of gas liquefaction. This method allows the operation of refrigerators and heat pumps for the most part. It can also be utilized in the cooling of small infrared and optical detectors on space probes. As the Joule-Thomson coefficient becomes increasingly large, the process of cooling will become more efficient. Understanding the Joule-Thomson effect can therefore contribute to increasing the effectiveness of different technologies. The wide range of applications theoretically, experimentally, and practically illustrates the Joule-Thomson effect as an interesting area of study.