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Phase rule
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Phase rule
In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium. For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N):
Examples of intensive properties that count toward F are the temperature and pressure. For simple liquids and gases, pressure-volume work is the only type of work, in which case N = 1.
The rule was derived by American physicist Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878.
The number of degrees of freedom F (also called the variance) is the number of independent intensive properties, i.e., the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and independently of each other.
An example of a one-component system (C = 1) is a pure chemical. A two-component system (C = 2) has two chemically independent components, like a mixture of water and ethanol. Examples of phases that count toward P are solids, liquids and gases.
The basis for the rule is that equilibrium between phases places a constraint on the intensive variables. More rigorously, since the phases are in thermodynamic equilibrium with each other, the chemical potentials of the phases must be equal. The number of equality relationships determines the number of degrees of freedom. For example, if the chemical potentials of a liquid and of its vapour depend on temperature (T) and pressure (p), the equality of chemical potentials will mean that each of those variables will be dependent on the other. Mathematically, the equation μliq(T, p) = μvap(T, p), where μ, the chemical potential, defines temperature as a function of pressure or vice versa. (Caution: do not confuse p as pressure with P, number of phases.)
To be more specific, the composition of each phase is determined by C − 1 intensive variables (such as mole fractions) in each phase. The total number of variables is (C − 1)P + 2, where the extra two are temperature T and pressure p. The number of constraints is C(P − 1), since the chemical potential of each component must be equal in all phases. Subtract the number of constraints from the number of variables to obtain the number of degrees of freedom as F = (C − 1)P + 2 − C(P − 1) = C − P + 2.
The rule is valid provided the equilibrium between phases is not influenced by gravitational, electrical or magnetic forces, or by surface area, and only by temperature, pressure, and concentration.
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Phase rule
In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium. For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N):
Examples of intensive properties that count toward F are the temperature and pressure. For simple liquids and gases, pressure-volume work is the only type of work, in which case N = 1.
The rule was derived by American physicist Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878.
The number of degrees of freedom F (also called the variance) is the number of independent intensive properties, i.e., the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and independently of each other.
An example of a one-component system (C = 1) is a pure chemical. A two-component system (C = 2) has two chemically independent components, like a mixture of water and ethanol. Examples of phases that count toward P are solids, liquids and gases.
The basis for the rule is that equilibrium between phases places a constraint on the intensive variables. More rigorously, since the phases are in thermodynamic equilibrium with each other, the chemical potentials of the phases must be equal. The number of equality relationships determines the number of degrees of freedom. For example, if the chemical potentials of a liquid and of its vapour depend on temperature (T) and pressure (p), the equality of chemical potentials will mean that each of those variables will be dependent on the other. Mathematically, the equation μliq(T, p) = μvap(T, p), where μ, the chemical potential, defines temperature as a function of pressure or vice versa. (Caution: do not confuse p as pressure with P, number of phases.)
To be more specific, the composition of each phase is determined by C − 1 intensive variables (such as mole fractions) in each phase. The total number of variables is (C − 1)P + 2, where the extra two are temperature T and pressure p. The number of constraints is C(P − 1), since the chemical potential of each component must be equal in all phases. Subtract the number of constraints from the number of variables to obtain the number of degrees of freedom as F = (C − 1)P + 2 − C(P − 1) = C − P + 2.
The rule is valid provided the equilibrium between phases is not influenced by gravitational, electrical or magnetic forces, or by surface area, and only by temperature, pressure, and concentration.