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Phase equilibrium refers to the state in a thermodynamic system where all its phases are present and unchanging over time. A phase is a region of a system that is uniform in chemical composition and physical state. For example, in a closed container of water, liquid water, ice, and water vapor can coexist in equilibrium. This means that the rate at which water molecules freeze to ice is equal to the rate at which ice melts to water, and similarly for evaporation and condensation.

The conditions for phase equilibrium are typically defined by temperature and pressure. For a given substance, there are specific combinations of temperature and pressure at which two or more phases can coexist stably. These points are often represented on a phase diagram, which plots the stable phases of a substance as a function of temperature and pressure. The lines on a phase diagram represent the conditions where phase transitions occur, such as melting, boiling, or sublimation.

At a given temperature and pressure, a system will tend towards equilibrium. If a system is not in equilibrium, spontaneous processes will occur to reach it. For instance, if you heat ice above its melting point, it will melt into liquid water, moving towards a more stable phase at that temperature. Understanding phase equilibrium is crucial in many scientific and engineering fields, including chemistry, materials science, and geology, for predicting the behavior of substances and designing processes.