By Hitchcock F.L.

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We draw P as a function of v at a fairly low constant temperature T in Fig. 7 and notice that same P occurs with two or three diﬀerent volumes v. What does that mean? First remember the stability condition (p. 18): 1 ∂V ∂P < 0, >0⇒ V ∂P T,N ∂V so P has to decrease with V and points like B are completely unstable. 8 Van der Waals ﬂuid 33 P PC PB C'' C B' B B'' A'' PA A VB V VB’’ Fig. 7. Pressure as a function of molecular volume v according to the van der Waals equation of state at a fairly low temperature.

12 must be equal to area A1 . Now we return to the ﬂat surface case and study how temperature aﬀects the phase equilibrium. 14). If we plot points A and C for diﬀerent temperatures we get a curve called spinodal, which restricts the forbidden area where the system is unstable. When temperature T increases the valley A becomes less deep and at T = Tc it vanishes. With T ≥ Tc there is only one v for each P . Tc is the critical temperature above which gas and liquid are not separable phases. Spinodal and binodal meet at the highest point of both of these curves, and this point corresponds to the critical temperature Tc and pressure pc above which liquid and vapour are not distinguishable phases.

Now we return to the ﬂat surface case and study how temperature aﬀects the phase equilibrium. 14). If we plot points A and C for diﬀerent temperatures we get a curve called spinodal, which restricts the forbidden area where the system is unstable. When temperature T increases the valley A becomes less deep and at T = Tc it vanishes. With T ≥ Tc there is only one v for each P . Tc is the critical temperature above which gas and liquid are not separable phases. Spinodal and binodal meet at the highest point of both of these curves, and this point corresponds to the critical temperature Tc and pressure pc above which liquid and vapour are not distinguishable phases.