Lecture_05

Under those conditions the maxwell relation p s 3124

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Unformatted text preview: r region. Under those conditions, the Maxwell relation æ ¹P ö = æ ¹S ö , (3.124) è ¹T ø V è ¹V ø T (3.124) can be modified as follows: dP = dS j S m,v − S m,l = , vap S m (5.8) dT dV V m,v − V m,l , vap V m Substituting the definition of entropy change for a phase change, we obtain dP = , vap H m . (5.9) dT T, vap V m This is called the Clapeyron equation. Similar equations can be written for the solid-vapor boundary (enthalpy of sublimation!) and the solid-liquid boundary (enthalpy of fusion!). Note that, since enthalpy is a state function, ∆subHm = ∆fusHm + ∆vapHm. The Clausius-Clapeyron Equation: Eq. (5.9) may be written as , vap H m , vap H m , vap H m dP = l TV j P, RT 2 dT T æ V − V ö m,g m,l ø è m,g (5.10) (5.11) where we have assumed that the vapor behaves ideally to get the last equality. This equation may be rearranged and integrated to give −, vap H m ln P u = + C, or (5.14) RT , vap H m æ 1 P 1ö ln æ P 2 ö = (5.16) R è T1 − T2 ø . è 1ø The...
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