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I'm reading The Physics and Mathematics of the Second Law of Thermodynamics and have a question about the definition of the adiabatic accessibility.

It is defined as follows in page 16:

A state $Y$ is adiabatically accessible from a state $X$, in symbols $X \prec Y$, if it is possible to change the state from $X$ to $Y$ by means of an interaction with some device (which may consist of mechanical and electrical parts as well as auxiliary thermodynamic systems) and a weight, in such a way that the device returns to its initial state at the end of the process whereas the weight may have changed its position in a gravitational field.

Can you give me some examples of this kind of devices?

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A reversible adiabatic transformation example would be a two-phase system in a thermally isolated cylinder with a piston controlling the volume of the gas phase. The piston is attached to a weight through a pulley, and as you lower the weight the volume of the cylinder is increased thereby changing the phase equilibrium pressure and temperature of the system, too. Ignoring friction and some such if we return the weight to the original position the system will also return to its starting sate.

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