In the treatment that follows this section, we eschew the details of molecular
motion and intermolecular forces by describing relevant effects in terms of macroscopic
thermodynamic variables: pressure p, density ρ, and absolute temperature
T . These variables relate to each other through an equation of state
p = p(ρ, T )
which is usually established experimentally. The implication of the equation of
state is that only two of the variables are independent; this is to say if the values
of two of the independent thermodynamic variables are given for a fluid, the
specific value of any other thermodynamic property is automatically established.
The equation of state for an ideal gas,
p
ρ
= RT (2.5)
can be derived from simple kinetic theory. Here,
R = gas constant, energy per unit mass per degree
R = /M
=universal gas constant, energy per mole per degree
= 8.314.3 kJ/kg mol K = 1545.5 ft lbf/lb mol R
= 1.986 Btu/lbmmol R
M = molecular weight of gas, kg/kg mol or lbm/lbm mol
Each kilogram-mole of the gas contains N0 = 6.02 × 1026 molecules. N0 constitutes
Avogadro’s number for the MKS system of dimensional units.With η representing
the mass of a single-gas molecule, M = N0
η, the number of molecules
per unit volume is N = ρ/ η. The equation of state for the ideal gas can now be
rewritten as:
p = N
N0
T = NkT
where k is the Boltzmann constant= /N0 = 1.38 ×10–26 kJ/K.
In liquids and gases under extreme pressures, the relationships between the
thermodynamic variables p, T , ρ, X (here X is the quality or the fractional mass
of gas comprising a saturated liquid–gas mixture, e.g., X = 1.00 represents a fully
saturated gaseous state and X = 0 represents the fully saturated liquid state) are
not so simple, but the fact remains that these parameters are fully dependent upon
each other, and specifying two thermodynamic parameters (including enthalpy,
entropy, etc.) will fully specify the thermodynamic state of the fluid.
motion and intermolecular forces by describing relevant effects in terms of macroscopic
thermodynamic variables: pressure p, density ρ, and absolute temperature
T . These variables relate to each other through an equation of state
p = p(ρ, T )
which is usually established experimentally. The implication of the equation of
state is that only two of the variables are independent; this is to say if the values
of two of the independent thermodynamic variables are given for a fluid, the
specific value of any other thermodynamic property is automatically established.
The equation of state for an ideal gas,
p
ρ
= RT (2.5)
can be derived from simple kinetic theory. Here,
R = gas constant, energy per unit mass per degree
R = /M
=universal gas constant, energy per mole per degree
= 8.314.3 kJ/kg mol K = 1545.5 ft lbf/lb mol R
= 1.986 Btu/lbmmol R
M = molecular weight of gas, kg/kg mol or lbm/lbm mol
Each kilogram-mole of the gas contains N0 = 6.02 × 1026 molecules. N0 constitutes
Avogadro’s number for the MKS system of dimensional units.With η representing
the mass of a single-gas molecule, M = N0
η, the number of molecules
per unit volume is N = ρ/ η. The equation of state for the ideal gas can now be
rewritten as:
p = N
N0
T = NkT
where k is the Boltzmann constant= /N0 = 1.38 ×10–26 kJ/K.
In liquids and gases under extreme pressures, the relationships between the
thermodynamic variables p, T , ρ, X (here X is the quality or the fractional mass
of gas comprising a saturated liquid–gas mixture, e.g., X = 1.00 represents a fully
saturated gaseous state and X = 0 represents the fully saturated liquid state) are
not so simple, but the fact remains that these parameters are fully dependent upon
each other, and specifying two thermodynamic parameters (including enthalpy,
entropy, etc.) will fully specify the thermodynamic state of the fluid.
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