The Wilson “cloud chamber” is used to detect and visualize trajectories of charged particles or x–rays. Water vapor mixed with air and other gases is first subjected to a rapid, undisturbed expansion to a volume about 25% greater than the volume at which condensation of vapor would occur. Initiation of condensation requires a small but finite disturbance such as a nucleation center. When the rapid expansion occurs in the absence of disturbances, condensation does not occur. After the expansion, the state of the system does not change with time until some disturbance promotes the condensation. A charged particle crossing the amber with sufficient energy causes ionization of the water vapor along its trajectory. the disturbance promotes condensation along the trajectory, that is, the formation of liquid droplets around the ionized molecules. these liquid droplets provide an observable trace of the trajectory of the charged particle crossing the chamber. If the charged particle collides with other particles while in the Wilson chamber, the trajectory bends and so the trace of liquid droplets shows the mechanics of the collisions. Due to the surface tension between liquid and vapor, there is a critical droplet size — of the order of a few water molecules — below which a droplet collapses and above which it grows indefinitely. Thus if all the droplets happen to have formed with size below the critical, they will all collapse and the chamber return to its initial state. (a) What kind of equilibrium state is that of the Wilson chamber just after the rapid undisturbed expansion? (b) What kind of equilibrium state is that of the Wilson chamber with only one droplet of exactly the critical size?
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