Thermodynamical expressions for open systems

However, if the solution is saturated previously, and we add the same amount of salt to this solution, then we form a salt precipitate in the solution forming two phases, and thus the change in internal energy is different for this case from the first process. 

The internal energy for a single homogeneous open system, which can exchange matter as well as energy with its surroundings, is a function of S, V and also composition, 

a new parameter called the chemical potential, fi of a substance, i, present in the system, in terms of constant volume and entropy is defined as 

similar to Equation (141), it is possible to define the chemical potential in terms of other thermodynamic parameters from Equations (143)—(145), so that 

It should be pointed out that there are many one-phase open systems in which the composition is changing due to irreversible chemical reactions. Two or more-phase open systems are also present if the irreversible interphase transport of matter takes place in the closed system. In chemistry, the independent variables of T and P are mostly used. Consequently, the chemical potential is generally expressed as the partial molar 

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