Departure function
Encyclopedia
In thermodynamics
, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the species as it exists in the real world, for a specified temperature T and pressure P. Common departure functions include those for enthalpy
, entropy
, and internal energy
.
Departure functions are used to calculate real fluid extensive properties (i.e properties which are computed as a difference between two states). A departure function gives the difference between the real state, at a finite volume or non-zero pressure and temperature, and the ideal state, usually at zero pressure or infinite volume and temperature.
For example, to evaluate enthalpy change between two points h(v1,T1) and h(v2,T2) we first compute the enthalpy departure function between the v1 and infinite volume at T=T1, then add to that the ideal gas enthalpy change due to the temperature change from T1 to T2, then subtract the departure function value between v2 and infinite volume.
Departure functions are computed by integating a function which depends on an equation of state
and its derivative.
H, the Entropy
S and the Gibbs Energy G are given by
Where
is defined in the Peng-Robinson equation of state, Tr is the reduced temperature, Pr is the reduced pressure, Z is the compressibility factor
, and
Typically, one knows two of the three state properties (P, Vm, T), and must compute the third directly from the equation of state under consideration. To calculate the third state property, it is necessary to know three constants for the species at hand: the critical temperature Tc, critical pressure Pc, and the acentric factor
ω. But once these constants are known, it is possible to evaluate all of the above expressions and hence determine the enthalpy and entropy departures.
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the species as it exists in the real world, for a specified temperature T and pressure P. Common departure functions include those for enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
, entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, and internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...
.
Departure functions are used to calculate real fluid extensive properties (i.e properties which are computed as a difference between two states). A departure function gives the difference between the real state, at a finite volume or non-zero pressure and temperature, and the ideal state, usually at zero pressure or infinite volume and temperature.
For example, to evaluate enthalpy change between two points h(v1,T1) and h(v2,T2) we first compute the enthalpy departure function between the v1 and infinite volume at T=T1, then add to that the ideal gas enthalpy change due to the temperature change from T1 to T2, then subtract the departure function value between v2 and infinite volume.
Departure functions are computed by integating a function which depends on an equation of state
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
and its derivative.
General Expressions
General Expressions for the EnthalpyEnthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
H, the Entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
S and the Gibbs Energy G are given by
Departure functions for Peng-Robinson equation of state
The Peng-Robinson equation of state relates the three interdependent state properties pressure P, temperature T, and molar volume Vm. From the state properties (P, Vm, T), one may compute the departure function for enthalpy per mole (denoted h) and entropy per mole (s):Where
is defined in the Peng-Robinson equation of state, Tr is the reduced temperature, Pr is the reduced pressure, Z is the compressibility factorCompressibility factor
The compressibility factor , also known as the compression factor, is a useful thermodynamic property for modifying the ideal gas law to account for the real gas behavior. In general, deviation from ideal behavior becomes more significant the closer a gas is to a phase change, the lower the...
, and
Typically, one knows two of the three state properties (P, Vm, T), and must compute the third directly from the equation of state under consideration. To calculate the third state property, it is necessary to know three constants for the species at hand: the critical temperature Tc, critical pressure Pc, and the acentric factor
Acentric factor
The acentric factor \omega is a conceptual number introduced by Pitzer in 1955, proven to be very useful in the description of matter. It has become a standard for the phase characterization of single & pure components...
ω. But once these constants are known, it is possible to evaluate all of the above expressions and hence determine the enthalpy and entropy departures.