•The gas are divided into “real” and “ideal”. The last ones (do not
exist in reality) are when intermolecular bombardment forces is
equal to 0.
•The pressure in the ideal gas law must be expressed as an absolute
pressure (a pressure that would only occur in a perfect vacuum).In
engineering it is common practice to measure pressure of real gas
relatively to local atmospheric pressure (it is called “gage
pressure”Pm ). Thus, the absolute pressure Pa can be obtained from
gage pressure Pm by adding the value of the atmospheric pressure Pat

            Pa = Pat + Pm ;
•The behavior of real gas under normal conditions (temperature t =00
C and absolute pressure Pa = Pat = 101.3 kPa) is known closely
approximate for an ideal gases. However, when the real gases are
getting cool and under pressure( Pa > 1MPa) their behavior is
different from that of the ideal gases.(liquefaction of gases).
Thus,properties of gases are like those for the liquids, only changes
of gas state is different.
• In the gases(air,oxygen,etc.)spacing between molecules is on the
order of 10-6 mm, and for the liquids it is on the order of 10 –7 mm.This
is because the intermolecular cohesive forces for gases are smaller and
their molecules have more kinetic energy and more freedom of motion
than liquids. Thus, gases are highly compressible in comparison to
• Changes in gas density directly related to changes in pressure and
temperature through the Clapeyron equation:
                    p=RT                                    (1)

Where: p- absolute pressure, in Pa;
         -density,
        T – the absolute temperature, 0 K(T = Tc +273.15 )
        R – gas constant related to the molecular weight of the gas(for
Air R = 287 J/kg K,for Hydrogen- 4120,for Oxygen-260)
• Equation (1) is commonly termed as ideal or perfect gas law,or the
equation of state for an ideal gases. It is known to closely approximate
the behavior of real gases under normal conditions (when the gases are
not approaching liquefaction).
•State of real gases is called as “normal” when the temperature t =
00C, and absolute pressure p = Pat = 101.3 kPa (standard sea-level
atmospheric pressure);
•State of gases is called as “standard” when the temperature t = 200 C
and p = Pat ;
Table. Approximate Physical Properties of Some Common Gases
                                     Normal state       Standard state
     Gas          cular     R,
                  mass              n,      nn 106,     ,       n106,
                            J      kg/m3               kg/m3
                                              m2/s                m2/s
                          kg  K
Hydrogen         2,016      4124   0,0899              0,084     108,00
Water vapor      18,02       461   0,80                0,75       13,62
Air              28,96       287   1,29      13,3      1,20       14,96
Oxygen           32,00       260   1,43                1,34       14,98
Methane          16,04       518   0,72      14,3      0,67       16,33
Propane          44,10       189   2,02       3,71     1,88        4,25
•The R for an ideal gases can be expressed:
        R = cP – cV = cV (k – 1)                              (2)

      Where: k = cP /cV – adiabatic factor(it depends on density of
atoms in the molecule. For example, k = 1.67 for one-atom gases,
1.4-for double-atom , 1.33-for triplex-atom. k = 1.4 for air,1.33-for
water vapor);
               cP – specific heat of gases when pressure is constant,
               cV – specific heat of gases when volume is constant.
•When the pressure of gases is high (mostly in the mains of gas
pipelines network) and p > 1.0 MPa, the impact of compressibility in
the equation (1) must be estimated by coefficient z as follows:

          p=zRT                                                (3)

         Where: z  1.0 – an empirical coefficient for real gasses (see
Table.The values of gas compressibility coefficient z.

  Pressure,       0,2        1,0       2,0        3,0      5,0
        z         1,002      1,000     0,956      0,930    0,883

•An important question to answer when considering the behavior of
gases is how easily the volume (and then- the density) of a given
mass of gases can be changed when there is a change in pressure?
That is, how compressible is the gas? A property that is commonly
used to characterize compressibility is the bulk modulus E defined
      E=-                                                     (4)
              dV / V
Where:dp – the differential change in pressure needed to create a
differential change in volume, dV or V
The negative sign is included since an increase in pressure will cause
a decrease in volume of a given mass, m =  V, will result in an
increase in density, Eq.(3) can be expressed as|
            E=                                               (5)
                    d / 
     •Liquids are usually considered to be incompressible, whereas
     gases are generally considered to be compressible.When gases are
                                     relationship between pressure and
     compressed (or expanded) theconst
     density depends on the nature of the process.If the compression or
     expansion takes place under constant temperature conditions
     (isothermal process), then from the Clapeyron equation:

                     const                                    (6)
The bulk modulus E for gases can be determined by obtaining the
derivative dp/d :
                   E = p;                             (7)

If the compression is frictionless and no heat is exchanged with the
surroundings (isentropic process), then:

                              const                        (8)
                        k

   Where :            k=cP/cV ;

                   cP – ratio of the specific heat at constant pressure;
                   cV – ratio of the specific heat at constant volume.
   •Therefore, the 2 specific heats are related to the gas constant R,
   through the equation:

                   R =cP – cV                                 (9)
The bulk modulus E for gases in an isentropic process:

                    E=kp                                  (10)
Note: In both isothermal and isentropic processes the bulk modulus
varies directly with pressure. However, real gases can often be
treated as incompressible if the changes in pressure are
comparatively small, and when the flow velocity v < 100 m/s;
•The kinematics viscosity of real gases n is increasing when the
temperature t is increasing (opposite when of the liquids). This is
because viscosity of molecular turbulence of gases is much more
than laminar viscosity of atomic gravity.
•When the pressure is increasing, the viscosity of real gases is
decreased.The kinematics viscosity of gases is more than that of
•All gases are dissolved in liquids. When the pressure is increased,
the volume of dissolved gases in liquids is also increased, and vice
                  Gas equilibrium
•The same differential equations for equilibrium and motion, like
those applied for uncompressible liquids, can be applied for
compressible gases. Only the impact of compressibility on the
pressure and density of gases must be estimated.
•The state of gases is changing because of their heat capacity and
under the mechanical or thermal condition (thermo dynamical
•For liquids or gases at rest the pressure gradient in the vertical
direction at any point in a fluid depends only on the specific
weight of the fluid at that point.The static equilibrium equation
         dp/ +g dz = 0                                       (11)
  Since p depends only on z, the Eq. (11) can be written :
          dp/dz = -                                           (12)
•Equation (12) is the fundamental equation for fluids at rest. It can
be used to determine how pressure changes with elevation.
However, to proceed with the integration of Eq. (12) it is necessary
to stipulate how the specific weight varies with z.
   Equilibrium equation of isoxoric
•When density of gases  = const,the isoxoric process is going on.
After integration of Eq. (11), we have found:
          p + g z = const, or z + p /  g =const ;         (13)

                           z, p, , T
                           p = const


                      z0= 0, p0 ,  , T0         The scheme of free
                                             0   surface of gases
•In the free surface of the sea (sea plain line):
        z0 = 0 , p = p0 ,

        p = p0 +  g (z0 – z) = p0 -  g h ;                    (14)
   Where :
            h- point height from the sea plain;
Since p = RT, from the Eq.(14), after substitution we can find the
vertical distribution of temperatures of the gases:
                       T  T0     .                            (15)
  As it can be seen, when the point height in the gases is increased
  both the pressure and temperature is decrease.
  •For the real gases in the closed space,   const when the height
  is  80 m. A mistake in that case is less than 1 %.
           Equilibrium equation of
             polytropic process
This is an universal thermodynamic process when all parameters
are variable:
                 p1 / n              1   c
                         const;        1/ n ,           (16)
                                     p

               n – index of politropy;
               c – constant;
 After the substitution of Eg.(11) it follows:
                 gdz  c      1/ n
                                      0.                  (17)
After the integration yield :
            1/ n                1
           p        1     1                   n p
    gz                   p     n    gz            const.   (18)
                  1
                      1                      n 1 
After the embedded from Clapeyron p / = R T:
               gz       RT  const.                           (19)
                    n 1

•The both (18) and (19) equations are similar like those for the
liquid(the difference is only coefficient in the second number)They
are describe pressure and temperature (dynamic laws) changes of the

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