1 Introduction to Chemical Engineering Thermodynamics Ji-Sheng Chang Chapter 10-1 The concepts and laws for binary vapor-liquid equilibrium problems

2 Equilibrium between phases  The nature of equilibrium Equilibrium: the all values of the thermodynamic properties of the system had been fixed. By macroscopic view: static equilibrium By microscopic view: dynamic equilibrium  平衡的本質 在平衡時， 熱力變數的 數值為定值 巨觀觀點： 靜態平衡 微觀觀點： 動態平衡

3 The phase rule  The size of system The size of the system, we have to given an extensive property of the system. Given each one of extensive property V total, H total, U total,..., or total mass  系統的大小 系統大小由 一個示量性 質界定之

4 The phase rule  The phase rule The Gibbs phase rule, tell us that how many properties or variables can to fix the system? For a  phases and N components system at equilibrium F = 2 -  + N  相律 Gibbs phase rule 提供界定系 統之自由度 的計算式 自由度隨系 統之總成份 數與總平衡 相數而變

5 The phase rule  The phase rule The Duhem ’ s theorem, tell us that how many variables can given the information of the size distribution between equilibrium phases? F = 2 F: the degrees of freedom of a system.  相律 Duhem’s theorem 提 供平衡相間 確知相分佈 未的自由度 自由度為定 值等於 2

6 Simple models for VLE  Simple models for vapor/liquid equilibrium Dalton ’ s law; ideal solution behavior for gas phase P i = y i P Raoult ’ s law; ideal solution behavior for liquid phase P i = x i P i sat Henry ’ s law; ideal solution behavior for liquid phase P i = x i H i,j  氣液平衡有 關之模式 道爾吞分壓 定律 勞特定律 拉午耳定律 亨利定律

7 Simple models for VLE  Simple models for vapor/liquid equilibrium Ideal gas behavior PV=RT; For pure components vapor/liquid system, at equilibrium, P = P i sat  氣液平衡有 關之模式 理想氣體 純成份氣液 平衡系統， 系統壓力為 成分飽和蒸 汽壓

8 Thermodynamic variables  The variables T: Temperature P: Pressure : chemical potential f: fugacity P i : partial pressure  the suffix and superscript V: vapor phase; L: liquid phase; 1,2: species  變數 / 熱力性 質

9 VLE problems  For a binary VLE problems Variables  T, P, x 1, x 2, y 1, y 2 ; ( P 1 sat, P 2 sat ) The degrees of freedom from the Gibbs phase rule  F = = 2  雙成分氣液 平衡問題 未知變數有 六個因勞特 定律之適用 增加二個變 數 計算得雙成 份氣液平衡 系統之自由 度為 2

10 Independent equations(1)  Independent equations as from the state at equilibrium, T V = T L P V = P L P 1 V =P 1 L ; ( 1 V = 1 L ; f 1 V =f 1 L ) P 2 V =P 2 L ; ( 2 V = 2 L ; f 2 V =f 2 L )  獨立方程式 溫度 壓力 成份 1 的分 壓 成份 2 的分 壓

11 Independent equations(2)  Other equations The physical law The other thermodynamic models  Antoine equation  獨立方程式 物理定律與 定義定律 其他之熱力 學模式  安東尼方 程式

12 Kind of VLE calculation  The cases of binary VLE problems Bubble pressure calculation Dew pressure calculation Bubble temperature calculation Dew temperature calculation Compositions calculation States property calculation  雙成分氣液 平衡計算類 型 泡點壓力計算 霧點壓力計算 泡點溫度計算 霧點溫度計算 組成計算 狀態性質計算

13 Vapor-liquid equilibrium  Equation of vapor/liquid equilibrium When the liquid phase is an ideal solution, when the gas phase is an ideal solution, and which of each species in vapor phase is an ideal gas behavior. The partial pressure of species could be given by Dalton ’ s law P i = y i P and Raoult ’ s law P i = x i P i sat y i P = x i P i sat  氣液平衡方 程式 成份之蒸氣 遵守理想氣 體行為 氣相為理想 氣體理想混 合 液相為理想 溶液

14 Vapor-liquid equilibrium  Equation of vapor/liquid equilibrium When the liquid phase is not an ideal solution Modified by Raoult ’ s law y i P =  i x i P i sat ;by  氣液平衡方 程式 若液相混合 物不是理想 溶液行為 用活性係數 修正勞特定 律

15 Vapor-liquid equilibrium  Equation of vapor/liquid equilibrium When the gas phase is not an ideal solution Additional modified of Dalton ’ s law  i y i P =  i x i P i sat  氣液平衡方 程式 若氣相不是 理想氣體混 合 用逸壓係數 修正道爾吞 分壓定律

16 Vapor-liquid equilibrium  Equation of vapor/liquid equilibrium When each of species in vapor phase is a real gas, using the fugacity of pure species thermodynamic properties replaced the saturated pressure.  i y i P =  i x i f i,pure  氣液平衡方 程式 成份之蒸氣 為真實氣體 行為 用逸壓替代 飽和蒸氣壓

17 Fugacity  A thermodynamics properties Fugacity ; f i,pure  純成分逸壓由體積性質計算之計算式

18 Binary vapor/liquid equilibrium 劇情如何發展？ 敬請期待！