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Lecture 10 Classical description of a single component system

Explore Gibbs free energy & phases at different temperatures, molar properties, Clapeyron equation, and phase diagrams of single component systems. Learn about vapor-liquid-solid equilibrium, latent heat, and phase transitions. Solve problems using Clapeyron and Gibbs-Duhem equations.

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Lecture 10 Classical description of a single component system

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  1. Lecture 10 Classical description of a single component system • Gibbs free energy and equilibrium phases as a function of temperature • Phase diagram • Molar properties and Clapeyron equation • Problem 11.4

  2. Gibbs free energy Typically we control pressure and temperature - therefore for a single component system to find equilibrium phase we need to consider Gibbs free energy, G (P, T). In general for each phase, : From chapter 4 we know that

  3. G as a function of T for a given pressure Entropy of vapor > entropy of liquid > entropy of solid vapor liquid solid At the melting point Gsolid = Gliquid At the boiling point Gliquid = Gvapor

  4. Enthalpy Since G = H-TS also vapor liquid H solid Latent heat - heat of fusion Heat of vaporization

  5. Phase diagram solid liquid vapor

  6. Molar properties - converting extensive into intensive variables Mole fraction Molar entropy etc.

  7. Gibbs-Duhem equation The original equation for each phase Dividing by Gives for two phases,  and 

  8. Clapeyron equation Along the coexistence line Also for a single component in  and  phases Therefore From which Since in equilibrium coexistence

  9. Coexistence with vapor slope

  10. Problem 11.4 Calculate the vapor pressure at 300 K of an element for which melting point is 1000 K, the normal boiling point is 2500 K, the heat of vaporization is 240, 000 J/mol and the heat of fusion is 12,000 J/mol.

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