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The Differential Relationships of Thermodynamic Variables for the Equilibrium of Heterogeneous Substances
Zhang Shimin,Huang Kelong,Zhou Debi
Author NameAffiliationE-mail
Zhang Shimin College of Chemistry and Chemical Engineering, Central South University, Changsha 410083 zsz@csu.edu.cn 
Huang Kelong College of Chemistry and Chemical Engineering, Central South University, Changsha 410083  
Zhou Debi College of Chemistry and Chemical Engineering, Central South University, Changsha 410083  
Abstract:
For the system without adiabatic walls, rigid walls or semi-permeable walls and without chemical reactions or without other restrictions except restrictions of phase equilibrium conditions, if the number of components of the system is k and the number of phases is φ, the degree of freedom of the system at equilibrium is f=k-φ+2. Because the degree of freedom is incapable of being negative, f=k-φ+2≥0, viz.φ≤k+2. For the heterogeneous equilibrium, the number of phases is at least 2, so φ=k+2-f≥2, viz. f≤k. Hence the range of change of φ and f is 2≤φ≤k+2,0≤f≤k, respectitvely. If φ=k+2, there are no independent variables in the system at equilibrium. If φ=k+1, there is one independent variable; if the temperature is selected as the independent variable, the other dependent variables can be expressed as the function of the temperature. If φ=k, there are two independent variables; if the temperature and pressure are selected as the independent variables, the other dependent variables can be expressed as the function of the temperature and pressure. If 2≤φ≤k-1, there are more than two independent variables; if the temperature, pressure and some concentrations are selected as independent variables, the other dependent variables can be expressed as the function of the temperature, pressure and these concentrations. The differential relationships of dependent variables and independent variables are educed out according to the principle of phase equilibriums for 2≤φ≤k-1. In any phase the number of the variables is(k+1), viz. temperature T, pressure p and (k-1) mole fractions x1, x2,…, xk-1. The temperature and pressure are common variables of every phase. The number of independent variables is at best k for the heterogeneous equilibriums of k components. The temperature, pressure and (k-2) concentrations are selected as independent variables. The independent concentration variables are selected entirely from the first phase and the concentration variables of the other phases all act as dependent variables. There is at least one dependent concentration variable in the first phase.
Key words:  Systems of heterogeneous substances, Phase equilibrium, Degree of freedom, Phase rule
FundProject:
多元复相平衡体系热力学变量的微分关系
张世民*,黄可龙,周德壁
摘要:
根据相平衡原理,导出了无绝热壁、刚性壁和半透壁及无化学反应、除相平衡条件约束外无其他约束的k组分和φ相(2≤φ≤k-1)的多元复相平衡体系非独立变量与独立变量之间的微分关系.任一相有温度、压力和(k-1)个摩尔分数共(k+1)个变量,其中温度和压力是各相的公共变量; k组分复相平衡体系的独立变量个数最多为k,把温度和压力作为首选的独立变量,独立的浓度变量最多为(k-2);把独立的浓度变量全部选在第一相,而把其他相的浓度变量都做非独立变量,第一相至少有一个非独立的浓度变量.
关键词:  多元系  相平衡  自由度  相律
DOI:10.1088/1674-0068/16/1/30-40
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