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Lecture note 11 (10-11-2011)

# Lecture note 11 (10-11-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 11 Phase equilibrium and structure Gibbs’s Phase Rule P + F = C +2 where P is the number of phases in thermodynamic equilibrium with each other and C is the number of components . Typical phases are solids, liquids and gases. A system involving one pure chemical is an example of a one-component system. Two-component systems, such as mixtures of water and ethanol, have two chemically independent components. F is the number of degrees of freedom, which means the number of intensive properties such as temperature or pressure, which are independent of other intensive variables. Pure substances For pure substances C = 1 so that F = 3 – P . In a single phase ( P = 1) condition of a pure component system, two variables ( F = 2), such as temperature and pressure , can be controlled to any selected pair of values. However, if the temperature and pressure combination ranges to a point where the pure component undergoes a separation into two phases ( P = 2), F decreases from 2 to 1. When the system enters the two phase region, it becomes no longer possible to independently control temperature and pressure. In the phase diagram shown below, the boundary curve between the liquid and gas regions maps the constraint between temperature and pressure when the single component system has separated into liquid and gas phases at equilibrium. If the pressure is increased by compression, some of the gas condenses and the temperature goes up. If the temperature is decreased by cooling, some of the gas condenses, decreasing the pressure. Throughout both processes, the

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