The Clausius-Clapeyron Equation
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1 The Clausius-Clapeyron Equation stepwise Frank W Seeberger The Clausius-Clapeyron Equation 1 / 8
2 Outline 1 Application Abbreviations 2 3 Frank W Seeberger The Clausius-Clapeyron Equation 2 / 8
3 Application Abbreviations Application of the For calculating... Bsp.: phase diagram of water the phase boundary line H (melt pressure curve given) the melting point at p 2 (T = constant) with given p 1 and H f 221 bar pressure 1,013 bar 0,006 bar ice triple point water vapour critical point 0,01 C 100 C temperature 374 C Frank W Seeberger The Clausius-Clapeyron Equation 3 / 8
4 Abbreviations Application Abbreviations G V p S T Free Enthalpy Volume Pressure Entropy Temperature Frank W Seeberger The Clausius-Clapeyron Equation 4 / 8
5 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
6 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
7 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
8 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
9 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
10 dg = V SdT (1) dg 2 = V 2 S 2 dt and V 1 S 1 dt = dg 1 (2) V 2 S 2 dt = V 1 S 1 dt (3) V 2 V 1 = S 2 dt S 1 dt (4) (V 2 V 1 ) = (S 2 S 1 ) dt (5) dt = S 2 S 1 Frank W Seeberger The Clausius-Clapeyron Equation 5 / 8
11 dt = S 2 S 1 G = H T S and G = 0 leads to (7) S = H T dt = H T V and (8) (9) Frank W Seeberger The Clausius-Clapeyron Equation 6 / 8
12 dt = S 2 S 1 G = H T S and G = 0 leads to (7) S = H T dt = H T V and (8) (9) Frank W Seeberger The Clausius-Clapeyron Equation 6 / 8
13 dt = S 2 S 1 G = H T S and G = 0 leads to (7) S = H T dt = H T V and (8) (9) Frank W Seeberger The Clausius-Clapeyron Equation 6 / 8
14 dt = S 2 S 1 G = H T S and G = 0 leads to (7) S = H T dt = H T V and (8) (9) Frank W Seeberger The Clausius-Clapeyron Equation 6 / 8
15 of the p2 dt = H T V p 1 = H V T2 T 1 dt T (9) and (10) p 2 p 1 = H V ln T 2 T 1 (11) Frank W Seeberger The Clausius-Clapeyron Equation 7 / 8
16 of the p2 dt = H T V p 1 = H V T2 T 1 dt T (9) and (10) p 2 p 1 = H V ln T 2 T 1 (11) Frank W Seeberger The Clausius-Clapeyron Equation 7 / 8
17 of the p2 dt = H T V p 1 = H V T2 T 1 dt T (9) and (10) p 2 p 1 = H V ln T 2 T 1 (11) Frank W Seeberger The Clausius-Clapeyron Equation 7 / 8
18 Walter J. Moore, Dieter O. Hummel Physikalische Chemie, 4. Aufl., S. 250f Walter de Gruyter, Clausius-Clapeyron-Gleichung Frank W Seeberger The Clausius-Clapeyron Equation 8 / 8
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