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PROPERTIES OF GASES. Introduction. 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.

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slide2

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.
slide3

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 liquids.

  • Changes in gas density directly related to changes in pressure and temperature through the Clapeyron equation:
  • p =  R T (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 idealor perfectgas law,or the equation of statefor an ideal gases. It is known to closely approximate the behavior of real gases under normal conditions (when the gases are not approaching liquefaction).
slide4

Gas

Molecular mass

R,

Normal state

Standard state

rn,

kg/m3

nn 106,

m2/s

r,

kg/m3

n106,

m2/s

Hydrogen

Water vapor

Air

Oxygen

Methane

Propane

2,016

18,02

28,96

32,00

16,04

44,10

4124

461

287

260

518

189

0,0899

0,80

1,29

1,43

0,72

2,02

13,3

14,3

3,71

0,084

0,75

1,20

1,34

0,67

1,88

108,00

13,62

14,96

14,98

16,33

4,25

  • 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
slide5

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  R T (3)
  • Where: z  1.0 – an empirical coefficient for real gasses (see Table)
slide6

Pressure, MPa

0,2

1,0

2,0

3,0

5,0

z

1,002

1,000

0,956

0,930

0,883

Table.The values of gas compressibility coefficient z.

  • 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 as:
  • E = - (4)

Where:dp – the differential change in pressure needed to create a differential change in volume, dV or V

slide7

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)

  • Liquids are usually considered to be incompressible, whereas gases are generally considered to be compressible.When gases are compressed (or expanded) the relationship between pressure and 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:
  • (6)
slide8

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:

(8)

  • 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)
slide9

The bulk modulus E for gases in an isentropic process:

  • E = k p (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  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 water.
  • All gases are dissolved in liquids. When the pressure is increased, the volume of dissolved gases in liquids is also increased, and vice versa.
gas equilibrium
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 process)
  • 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)
slide11

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 process

z

z, p, r, T

p = const

h

z0= 0, p0 , r, T0

0

Equilibrium equation of isoxoric process
  • 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)

The scheme of free surface of gases

slide13

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:

(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
Equilibrium equation of polytropic process

This is an universal thermodynamic process when all parameters are variable:

(16)

Where:

n – index of politropy;

c – constant;

After the substitution of Eg.(11) it follows:

(17)

slide15

After the integration yield :

(18)

After the embedded from Clapeyron p / = R T:

(19)

  • 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 gases