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Fig. 8 shows the situation when we have swapped the roles of x and y-axes compared to Fig. 7 . Now the molecular volume v is not a well-defined function of pressure P , since several values of v can be obtained with a single P . 8 Van der Waals fluid 35 P Pl (r) Pe (r) Pe (¥)=Pl (¥) =Pv (¥) V Fig. 11. Liquid pressure Pl (r) and saturation vapour pressure Pg (r) for a spherical droplet compared to the flat surface saturation vapour pressure Pg (∞). V 4 A2 P 3 2 Pl (r) 1 A1 Pe (r) 0 A3 Pe (r) P A3 0 3 4 A1 2 A2 1 Pl (r) V Fig.
Minimum B corresponds to liquid (higher ρ). It is the true equilibrium when S > 1. But it can be seen that the system can be trapped behind a barrier. If we plot the free energies corresponding to the minima in Fig. 3 as functions of saturation ratio, we obtain Fig. 4, where A is the equilibrium free energy curve with vapour density, B with liquid density. Phase change should happen at S = 1 because nature should settle to the global minimum of free energy. Saturation ratio S > 1 drives the phase transition from vapour to liquid.
The intensive properties of the bath (P0 , T0 , µi,0 ) do not change even if the system exchanges heat, volume and/or particles with the bath. The extensive properties (V0 , Ni,0 , S0 , U0 ) of the bath can change. The system is so small that anything coming out of it or going into it is a drop in the ocean for the bath. SYSTEM BATH T0, P0, m0 Fig. 2. The combination of the system and the bath is isolated. The system is much smaller than the bath. Heat bath: Exchanges heat with the system, heat flows in and out so that the temperature of the system stays constant and equal to that of the bath in quasi-static processes.