Cylinder filling thermodynamics

Equation (4.23) is known as the first law of thermodynamics for a closed system.] Keep in mind that a system may do work, or have work done on it, without some obvious mechanical device such as a pump, shaft, and so on, being present. Often the nature of the work is implied rather than explicity stated. For example, a cylinder filled with gas enclosed by a movable piston implies that the surrounding atmosphere can do work on the piston or the reverse a batch fuel cell does no mechanical work, unless it produces bubbles, but does deliver a current at a potential difference electromagnetic radiation can impinge on or leave a system and so forth. 

It is widely accepted that two mechanisms contribute to the observed hysteresis. The first mechanism is thermodynamic in origin [391,392], It is illustrated in Fig. 9.14 for a cylindrical pore of radius rc. The adsorption cycle starts at a low pressure. A thin layer of vapor condenses onto the walls of the pore (1). With increasing pressure the thickness of the layer increases. This leads to a reduced radius of curvature for the liquid cylinder a. Once a critical radius ac is reached (2), capillary condensation sets in and the whole pore fills with liquid (3). When decreasing the pressure again, at some point the liquid evaporates. This point corresponds to a radius am which is larger than ac. Accordingly, the pressure is lower. For a detailed discussion see Ref. [393],... 

As a consequence of the second law of thermodynamics, the average work required to change an external parameter (for instance the position of a piston sliding in or out of a gas-filled cylinder) is larger than the Helmholtz free energy difference between the two equilibrium states corresponding to the initial and final value of the external parameter [34,44] ... 

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