PD-OneComp

PD-OneComp - Phase Transitions and Phase Diagrams...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei Phase Transitions and Phase Diagrams One-component systems Enthalpy and entropy dependence on P and T Gibbs free energy dependence on P and T Clapeyron equation Understanding phase diagrams for one-component systems Polymorphic phase transitions Driving force for a phase transition First order and second-order phase transitions Reading: 1.2 of Porter and Easterling Chapter 7.1 ± 7.4 of Gaskell
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei A pure substance is heated at constant pressure T T b V P
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei H and S as function of T at constant P In a closed one-component system equilibrium, at temperature T and pressure P, corresponds to the state with minimum Gibbs free energy G. Therefore, in order to predict what phases are stable under different conditions we have to examine the dependence of G on T and P. Let±s use thermodynamic relations to predict the temperature dependence of H, S, and G at constant P. For H(T) we have ±² ³ ´ T 298 P 298 dT C H T H P P C T H ¸ ¹ · ¨ © § w w For S(T) we have ³ T 0 P dT T C T S T C T S P P ¸ ¹ · ¨ © § w w 0 0 0 C P H S T, K T, K T, K 298 Slope = C P Slope = C P /T
Background image of page 4
MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei G as function of T at constant P For G = H ± TS we have dG = -SdT +VdP and for P = const S T G P ± ¸ ¹ · ¨ © § w w for the slope T c T S T G P P P 2 2 ± ¸ ¹ · ¨ © § w w ± ¸ ¸ ¹ · ¨ ¨ © § w w for the curvature 0 H T, K TS Slope = C P Slope = -S G G(T) for a single phase at P = const
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei G as function of T at constant P for liquid and solid phases At all temperatures the liquid has a higher internal energy U and enthalpy H as compared to the solid. Therefore G l > G s at low T. The liquid phase, however, has a higher entropy S than the solid phase at all T. Therefore G l decreases more rapidly with T as compared to G s . At T m G l (T) crosses G s (T) and both liquid and solid phases can co-exist in equilibrium (G l = G s ) 0 H l T, K T m G l At T m the heat supplied to the system will not rise its temperature but will be used to supply the latent heat of melting ' H m that is required to convert solid into liquid. At T m the heat capacity C p = ( w H/ w T) P is infinite ±addition of heat does not increase T .
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

PD-OneComp - Phase Transitions and Phase Diagrams...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online