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V2 -

(2.7)

This is why the transition is called "first-order." The behavior of gl(P, T) and g2(P, T) are qualitatively sketched in Fig. 2.5. To determine the vapor pressure we proceed as follows. Let

(2.8)

where all quantities are evaluated at the transition temperature T and vapor pressure P. The condition for equilibrium is that T and P be such as to make I1g = O. Dividing (2.6) by (2.7), we have

18 D

By the chain relation,

(2.9)

FIGURE 5.26 A very clean RSI buy signal, since the RSI line went plainly below and then above the 30 mark.

(2.10)

The reason the chain relation is valid here is that I1g is a function of T and P,

and hence there must exist a relation of the form f(T, P, dg) =

(2.11)

is precisely the derivative of the vapor pressure with respect to temperature under equilibrium conditions, for dg is held fixed at the value zero. Combining (2.11), (2.10), and (2.9), we obtain dP(T) ds ---=(2.12) dT dv The quantity (2.13) 1= Tds is called the latent heat of transition. Thus

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(2.14) dT Tdv This is known as the Clapeyron equation. It governs the vapor pressure in any first-order transition. It may happen in a phase transition that S2 - SI = 0 and v2 - VI = O. When this is so the first derivatives of the chemical potentials are continuous across the transition point. Such a transition is not of the first order and would not be governed by the Clapeyron equation, and its isotherm would not have a horizontal part in the P- V diagram. Ehrenfest defines a phase transition to be an nth-order transition if, at the transition point,

dP(T)

You can further customise a report using Design view. You can change the formatting of fields, move fields around and more. You can even apply conditional formatting to the report by clicking the Conditional Formatting button in the Format tab. (For more about conditional formatting, refer to the section Use Conditional Formatting earlier in this chapter.)

FIGURE 5.27 Some securities are so volatile that they provide multiple entry and exit points in a relatively short timeframe.

whereas all lower derivatives are equal. A well-known example is the second-order transition in superconductivity. On the other hand many examples of phase transitions cannot be described by this scheme. Notable among these are the Curie point transition in ferromagnets, the order-disorder transition in binary alloys, and the .\ transition in liquid helium. In these cases the specific heat diverges logarithmically at the transition point. Since the specific heat is related to the second derivative of g these examples cannot be characterized by the behaviors of the higher derivatives of g, because they do not exist. Modem usuage distinguishes only between first-order and higher-order transitions, and the latter are usually indiscriminately called "second-order" transitions.

L L f(r;) g(r) '1'0

(13.25)

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