In thermodynamics, the state postulate sometimes also called state principle is the minimum number of independent properties necessary to completely describe a thermodynamic system in a state of balance .
In this article we will explain the concept of the state postulate and the Gibbs phase rule, a rule that allows us to know the number of properties necessary to describe a system.
State postulate concept
The state of a system is defined by the value of its thermodynamic properties, such as pressure, temperature, volume, heat, etc.
The value of some properties depends on the value of other properties. These properties are the dependent properties ; if the value of one property changes, so does the value of the other.
For example, if we keep the volume of a fluid constant, increasing the temperature will increase the pressure.
Other properties, on the other hand, are independent properties . Changing these properties does not affect the value of other properties. For example, him intensive properties of matter they are all independent properties.
So state postulate is defined as the number of independent properties that are necessary, as a minimum, to be able to describe the condition equilibrium of a thermodynamic system.
Knowing the value of these properties, we can calculate the value of the rest of the properties of the system.
To describe the state of a system it is always necessary to know the relative mole fraction of each chemical component and each phase, in addition to pressure, temperature and volume, although pressure, temperature and volume can be independent or dependent depending on the type of system.
Once the values of the independent properties have been fixed, that is, once the state postulate has been described, the rest of the properties can be calculated and derived automatically using the equation of state .
State Postulate in Simple Systems
EITHER state postulate by simple systems and always north + 1 independent properties, where Hey? the number of quasi-static works presented by the system (electromagnetic, gravitational, surface tension, elastic, movement,…).
EITHER system simpler simpler is the simple compressible system. In these systems there are no electromagnetic and gravitational fields, no surface tension and no movement. The state postulate for these systems is 2.
This means that a simple compressible system is completely described by two intensive or independent properties all other properties are deductible from these two.
In multiphase systems on the contrary, it is necessary to measure a larger number of properties in order to fully describe the state of the system and to be able to calculate the value of other properties.
THE specific temperature is he specific volume are always independent properties. Other properties, however, can be independent or dependent, depending on the study system.
For example, temperature Y Pressure are properties independent in single-phase systems But they are dependent on multiphase systems .
For example, liquid water in equilibrium with its vapor is a multiphase gas-liquid system. The boiling point of the liquid phase is 100°C at 1 atm pressure, but if the pressure decreases, the boiling point will also decrease, and vice versa, if the pressure increases, the boiling point will also increase.
Gibbs phase rule
As we saw earlier, the number of phases of a thermodynamic system influences state postulate that is, it influences the number of independent variables in the system.
In addition to the number of phases, the number of chemical components also influences.
THE gibbs phase rule Or simply the phase rule list all these variables:
number of independent variables either degrees of freedom (L)
number of phases (F)
number of components (C)
Through the following formula:
L = C – F + 2
If we take the previous example of liquid water in equilibrium with gaseous water, we have a system with 2 phases and 1 chemical component. The number of independent properties required for the state postulate will be:
L = 1 – 2 + 2 = 1
In this system, which has two phases, pressure is a function of temperature and vice versa. With one of them and the relative molar fraction of each phase, the system would be completely described.
However, if the system had only one phase (single-phase system), the pressure and temperature would be independent, so the system would have two degrees of freedom (L = 2):
L = 1 – 1 + 2 = 2
In systems with 1 component and 3 phases in equilibrium, the system is invariant (L = 0, this is called triple stitch of the phase diagrams):
L = 1 – 3 + 2 = 0
Example: Postulate of State in Ideal Gases
THE ideal gas law is a equation of state which describes the behavior of a gas in an ideal state in which the gas forms a closed system:
The ideal gas equation is:
VP = nRT
done:
P is the pressure
v is the volume
T is the absolute temperature (degrees Kelvin)
No is the number of moles of gas
R is the universal ideal gas constant
If we apply the Gibbs phase rule that we saw earlier, we have a system with 1 phase and 1 component, so it will have two degrees of freedom.
That’s the ideal gas state postulate requires the definition of two thermodynamic properties .
This can be verified with the ideal gas equation. If we know two of the properties that appear in the equation, we can describe the system.
For example, if we know the pressure and temperature, we can calculate the volume:
V = nRT/P
Or if we know the volume and pressure, we can know the temperature:
T = PV / nRT
In the same way, one can define the state postulate for any other system and, with a minimum number of independent properties, calculate the other properties of the system.
