(b) The molecular interpretation of the Joule–Thomson effect
The kinetic model of gases (Section 1.2b) and the equipartition theorem (Section F.5)
jointly imply that the mean kinetic energy of molecules in a gas is proportional to the
temperature. It follows that reducing the average speed of the molecules is equivalent
to cooling the gas. If the speed of the molecules can be reduced to the point that neighbours
can capture each other by their intermolecular attractions, then the cooled gas
will condense to a liquid.
To slow the gas molecules, we make use of an effect similar to that seen when a ball
is thrown into the air: as it rises it slows in response to the gravitational attraction of
the Earth and its kinetic energy is converted into potential energy. We saw in Section
1.3 that molecules in a real gas attract each other (the attraction is not gravitational,
but the effect is the same). It follows that, if we can cause the molecules to move apart
from each other, like a ball rising from a planet, then they should slow. It is very easy
to move molecules apart from each other: we simply allow the gas to expand, which
increases the average separation of the molecules. To cool a gas, therefore, we allow
it to expand without allowing any energy to enter from outside as heat. As the gas
expands, the molecules move apart to fill the available volume, struggling as they do
so against the attraction of their neighbours. Because some kinetic energy must be
converted into potential energy to reach greater separations, the molecules travel
more slowly as their separation increases. This sequence of molecular events explains
the Joule–Thomson effect: the cooling of a real gas by adiabatic expansion. The cooling
effect, which corresponds to μ > 0, is observed under conditions when attractive
interactions are dominant (Z < 1, eqn 1.17), because the molecules have to climb apart
against the attractive force in order for them to travel more slowly. For molecules
under conditions when repulsions are dominant (Z > 1), the Joule–Thomson effect
results in the gas becoming warmer, or μ < 0.