Theory
The Joule-Thomson effect cannot be described in the theory of ideal gases, in which interactions between particles are ignored. Instead, one must use a theory that accounts for the Van der Waals force between interacting particles that becomes much stronger as a gas becomes a liquid.
For a van der Waals gas we can calculate the enthalpy H using statistical mechanics as
,
where is the number of molecules, is volume, is temperature (in the Kelvin scale), is Boltzmann's constant, and and are constants depending on intermolecular forces and molecular volume, respectively.
From this equation, we note that if we keep enthalpy constant and increase volume, temperature must change depending on the sign of . Therefore, our inversion temperature is given where the sign flips at zero, or
,
where is the critical temperature of the substance. So for, an expansion at constant enthalpy increases temperature as the work done by the repulsive interactions of the gas is dominant, and so the change in energy is negative. But for, expansion causes temperature to decrease because the work of attractive intermolecular forces dominates, giving a positive change in energy.
Read more about this topic: Inversion Temperature
Famous quotes containing the word theory:
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)
“The theory [before the twentieth century] ... was that all the jobs in the world belonged by right to men, and that only men were by nature entitled to wages. If a woman earned money, outside domestic service, it was because some misfortune had deprived her of masculine protection.”
—Rheta Childe Dorr (1866–1948)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (1805–1872)