Thermodynamic equilibrium

Properties such as temperature, pressure, and enthalpy are defined only for an equilibrium state. For a system to be in equilibrium, we require that the system be simultaneously in thermal equilibrium, mechanical equilibrium, phase equilibrium, and chemical equilibrium.

Thermal equilibrium is achieved when temperature is uniform within each homogeneous region of the system and does not change with time.

Mechanical equilibrium is achieved when the pressere thoughout the system is uniform and there are no unbalanced forces at the system boundaries.

Phase equlibrium

related to conditions in which a substance can exist in more than one physical state (as H₂ that can be liquid, solid, or vapor). Phase equilibrium requires that the amount of a substance in any on phase not change with time.

These are the necessary conditions for thermodynamic equilibrium, teh system has everywhere the same constant temperature, the same pressure and the same chemical potential,

$$\{\begin{array}{l}\mathrm{\nabla }P=0\\ \mathrm{\nabla }T=0\\ \mathrm{\nabla }{\mu }_i=0\end{array}$$

With ∇ is the gradient (nabla) operator, ∇ = (∂,∂x) + (∂/∂y) + (∂/∂z)

Chemical potential: A difference in chemical potential between two locations or a chemical potential gradient is the driving force for the migration of the corresponding chemical species from high chemical potential regions to lower chemical potential regions. It will be investigated in details in further chapters.

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