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This equation can be used to obtain Joule–Thomson coefficients from the more easily measured isothermal Joule–Thomson coefficient. It is used in the following to obtain a mathematical expression for the Joule–Thomson coefficient in terms of the volumetric properties of a fluid.
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
Isothermal ΔT = 0 Adiabatic = ... Coefficients Equation Joule-Thomson coefficient
Using isoenthalpic-isobaric ensemble of Lennard-Jones fluid, it was shown [4] that the Joule–Thomson coefficient and inversion curve can be computed directly from a single molecular dynamics simulation.
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]
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
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.
In thermodynamics, Bridgman's thermodynamic equations are a basic set of thermodynamic equations, derived using a method of generating multiple thermodynamic identities involving a number of thermodynamic quantities.