Page 59 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch06 Elementary Physical Chemistry

44 Elementary Physical Chemistry

Pressure–temperature phase diagram of a one-component system.
Fig. 6.1

For example, in a one-component system,
F =1 − 1+2 = 2 when p =1 (in the areas)

F =1 − 2+2 = 1 when p = 2 (along the lines)
F =1 − 3+2 = 0 when p = 3 (at the triple point)

The phase rule tells us that in areas you can choose both the temperature
and pressure. Along lines you can specify either the temperature or pressure
but not both. At the triple point you cannot choose any variable: the
variables are fixed.

6.1.2. The Clapeyron Equation
The slopes of the phase diagram lines can also be predicted thermodynam-
ically, and must obey the Clapeyron equation:
dP/dT =∆H trans/(T ∆V trans) (6.2)

where the subscript trans refers to the particular transition, say liquid–
vapor or solid–liquid.
The Clapeyron equation is easy to derive. From

G = H − TS

we get the differential form
dG =dH − T dS − SdT (6.3a)

=dU + PdV + V dP − T dS − SdT (6.3b)