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The temperature of this point, the Joule–Thomson inversion temperature, depends on the pressure of the gas before expansion. In a gas expansion the pressure decreases, so the sign of is negative by definition. With that in mind, the following table explains when the Joule–Thomson effect cools or warms a real gas:
This temperature change is known as the Joule–Thomson effect, and is exploited in the liquefaction of gases. Inversion temperature depends on the nature of the gas. For a van der Waals gas we can calculate the enthalpy using statistical mechanics as
For real gasses, the molecules do interact via attraction or repulsion depending on temperature and pressure, and heating or cooling does occur. This is known as the Joule–Thomson effect. For reference, the Joule–Thomson coefficient μ JT for air at room temperature and sea level is 0.22 °C/bar. [7]
It yields an analytic analysis of the Joule–Thomson coefficient and associated inversion curve, which were instrumental in the development of the commercial liquefaction of gases. It shows that the specific heat at constant volume c v {\displaystyle c_{v}} is a function of T {\displaystyle T} only.
The body of the tables contain the characters in the respective irreducible representations for each respective symmetry operation, or set of symmetry operations. The symbol i used in the body of the table denotes the imaginary unit: i 2 = −1. Used in a column heading, it denotes the operation of inversion.
This Thomson effect was predicted and later observed in 1851 by Lord Kelvin (William Thomson). [9] It describes the heating or cooling of a current-carrying conductor with a temperature gradient. If a current density J {\displaystyle \mathbf {J} } is passed through a homogeneous conductor, the Thomson effect predicts a heat production rate per ...
On the other hand, real-gas models have to be used near the condensation point of gases, near critical points, at very high pressures, to explain the Joule–Thomson effect, and in other less usual cases. The deviation from ideality can be described by the compressibility factor Z.
This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph Louis Gay-Lussac in 1807 with similar results as obtained by Joule. [1] [2]
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