I understand one of the benefits of the Hampson-Linde cycle is that there are no cold-side moving parts, but isn't one losing an awful lot of energy in the throttling process? There must be something basic I'm missing here, because it looks almost like this cycle destroys energy: pressure drops while volume increases, and temperature drops at the same time. The expansion is isentropic (How does that differ from an adiabatic expansion? I thought the condition that dS = 0 constrained a gas to a unique trajectory - an adiabat - along which it does work. But unless I'm mistaken, a Joule-Thomson expansion does no external work, despite not being an expansion into an evacuated space. Where did the work "go"?

Maybe an example might illustrate. If I let air out of my car's tyres, is that a Joule-Thomson expansion? If so, doesn't the expansion do work in lifting the atmosphere by 20 attometers? If not, what is an everydayish example?