Volume 02 Issue 12-2022
192
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
A
BSTRACT
This article discusses all the laws considered for an ideal gas, taking into account the interactions of real
gas molecules and their individual sizes.
K
EYWORDS
Ideal gas, radius, molecule, temperature, wave, enthalpy, pressure, volume.
I
NTRODUCTION
When we studied molecular-kinetic theory, we
dealt with ideal gases. In this, the molecules were
simplified to the point that they did not interact
with each other and their sizes and volumes were
incalculably small [1,2,3,4].
When working with real gases, it is necessary to
take into account the specific volumes of
molecules. The size of one molecule
=
−
V
r
4
3
4 10
3
30
м
3
. The specific volume of
Journal
Website:
http://sciencebring.co
m/index.php/ijasr
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Research Article
THE INTERACTION FORCES BETWEEN MOLECULES
Submission Date:
December 14, 2022,
Accepted Date:
December 19, 2022,
Published Date:
December 24, 2022
Crossref doi:
https://doi.org/10.37547/ijasr-02-12-27
Sh.Sh. Abdullayev
Assistant, Department Of Physics, Fergana Polytechnic Institute, Fergana, Uzbekistan
Volume 02 Issue 12-2022
193
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
molecules in 1 m
3
volume under normal
conditions.
nV
= 2,69
.
10
25
.
4
.
10
-30
m
3
This is a very small volume, but when the
pressure increases several thousand times, the
specific volume of the molecules becomes
comparable to the volume occupied by the gas.
Failure to take into account the specific volume
of molecules in such cases leads to large errors
[5,6,7,8,9].
Figure 1
The second simplification in an ideal gas was the
assumption that there are no interaction forces
between the molecules. In real gases, there are
mutual attraction and repulsion forces between
molecules
The values of these forces depend on the distance
between the molecules. The repulsive force F
1
and the repulsive force F
2
act simultaneously.
Repulsive forces are positive and attractive forces
are negative. The sum of these two forces is equal
to F shown by the continuous line in the figure, at
r = r
0
F
1
and F
2
balance each other and the
resultant force is zero [10-15].
At r < r
0
, the resultant force is repulsive, and at
r>r
0
, it is attractive. When the molecules approach
each other to the distance d
eff
(the distance
between the centres of the molecules), they begin
to move away from each other due to mutual
repulsion forces.
Thus, taking into account the interactions of real
gas molecules and their individual sizes makes all
the laws considered for an ideal gas invalid for a
real gas.
van der Waals equation.
If we recall the equation of the state of one mole
of an ideal gas, that is, the Mendeleev-Clapeyron
equation
M
V
RT
P
=
were expressed in relation.
Volume 02 Issue 12-2022
194
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
In order to derive the "mass equation" of a real
gas, corrections must be made to this equation to
take into account the specific volumes of the
molecules and the forces of attraction and
repulsion [16-18].
When a real gas is under the influence of very
strong pressure, the molecules condense and
form some kind of "forbidden" "
b
" in the
container corresponding to the nature of this gas.
b
” occupies the volume. Because two molecules
of a real gas can approach each other only up to a
certain distance where the forces of mutual
repulsion become apparent. In other words, the
size of a sphere d
ef
whose radius is
4
3
3
d
эфф
there is a "forbidden size" for the centres of two
interacting molecules. This volume is the specific
volume V of the molecule
is 4 times greater than
b
= 4NAV
will be. The total volume through
which molecules can move is V
m
-
b
will appear.
Using this, we write in the following form:
b
V
RT
P
M
−
=
the expression is the pressure exerted by the real
gas molecules on the container wall.
Now let's determine the effect of mutual
attraction between molecules.
The pressure exerted by real gas molecules on the
container wall is smaller than the pressure
exerted by ideal gas molecules. The number of
molecules approaching the container wall and
colliding with it is proportional to n, and the
number of molecules pulling molecules
approaching the container wall to the inside of the
container is also proportional to n. So, the
reduced part of the real gas pressure due to the
effect of the mutual attraction of molecules is R
i
n
2
will be proportional. The number of molecules
per unit volume is n
M
V
1
if we take into account
that (n=N
A
/V
M
) and introduce a coefficient in
order to convert proportionality into equality, the
internal pressure caused by gravity is determined
as follows:
2
M
i
V
a
P
−
=
in this, (
−
) indicates that the internal pressure is
in the opposite direction to the real gas pressure
R.
Volume 02 Issue 12-2022
195
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
Figure 2.
Thus, the pressure of a real gas based on Eqs
2
M
M
V
a
b
V
RT
P
−
−
=
is equal to, from which a mole of a real gas is the
equation of
(
)
RT
b
V
V
a
P
M
M
=
−
+
2
can be written in the form. This relationship is
called the Van der Walps equation,
а
and
в
are
constants characterizing certain gas molecules,
which are called Van der Walps corrections. since
the equation is of the third degree with respect to
V
M
, it will have three roots, i.e. three volume nets
for one pressure (Fig. 2). These graphs are called
Van der Walps isotherms. At low temperatures,
all three roots of the Van der Walps equation are
real but have different values. The isotherm
corresponding to the temperature T
1
is cut by a
straight line corresponding to R
1
at points A, V,
and C. These three points represent different
isothermal states.
These conditions are characterized by the R
1
value of pressure, and different V
A
, V
V
, and V
S
values of volume. On the isotherm corresponding
to T
k
at a higher temperature, all three points
overlap. Often, T
k
is called the critical
temperature, and the isotherm corresponding to
it is called the critical isotherm. When the gas
volume is reduced below the critical point, it
begins to condense. When the gas volume reaches
V=b, it goes into the full liquid phase.
If the temperature of the gas is higher than the
temperature of the isotherm passing through
point K, it will not condense into a liquid. Values
of volume and pressure corresponding to the
critical point are called critical volume (V
k
), and
critical pressure (R
k
). For example, the critical
parameters of nitrogen gas,
N
K
V
= 9. 10-2
m
3
/K.molp;
N
K
P
=33.5. 105 Pa;
N
K
T
= 126 K. If we
Volume 02 Issue 12-2022
196
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
consider that the parameters of one k.moll of
nitrogen gas under normal conditions are V
0
=
22,414 m
3
/K.molp, r
0
= 105 Pa, T
0
= 273 K, we see
that nitrogen gas needs to be strongly cooled in
order to transfer it to the liquid phase. If we
compare these with the critical parameters, the
volume is 250 times smaller, and the pressure is
33.5 times larger. If we continue in the gas at a
temperature of 126 K, nitrogen will begin to
condense.
The internal energy of a real gas. Joule-Thomson
effect
We derived the following expression for the
internal energy of one mole of gas assuming that
molecules of an ideal gas do not interact with each
other
T
C
RT
i
U
V
=
=
2
Real gas molecules interact with each other
except for thermal motion, so their internal
energy consists of the sum of the kinetic energy of
the thermal motion of molecules and interaction
potential energy.
In order to determine the potential energy of
molecules, let's determine the work done when
the volume of one mole of gas is expanded from
V
M1
to V
M2
:
1
2
2
1
2
1
2
M
M
V
V
M
M
V
V
M
M
V
a
V
a
dV
V
a
dV
P
A
M
M
M
M
−
=
−
=
−
=
This work is equal to the change in the potential
energy of the system. Therefore, the potential
energy of one mole of gas
−
M
V
a
equal to Given
the above, one mole is for the internal energy of a
real gas
M
V
т
p
V
a
T
С
U
−
=
.
.
we form a relationship.
So, the internal energy of a real gas depends on
both temperature and volume. When an ideal gas
expands adiabatically (dQ=0), the external work
done is zero. According to the first law of
thermodynamics, the internal energy of the
system does not change during such adiabatic
expansion, i.e.
Volume 02 Issue 12-2022
197
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
Figure 3.
2
1
U
U
=
In the adiabatic expansion of ideal gases, apart
from the internal energy, the temperature also
remains unchanged.
In an adiabatic process, when real gases expand
without doing work against the external pressure,
the gas can heat up or cool down. The change in
gas temperature during the adiabatic expansion
of a real gas is called the Joulep-Thomson effect.
As the temperature of the gas decreases (
T<0)
positive Joulep-Thomson effect, on the contrary,
in cases of increased temperature (
T>0)
negative Joulep-Thomson effect occurs. A positive
Joulep-Thomson effect is observed for most gases
at room temperature. A negative Joulep-Thomson
effect was observed only for hydrogen and
helium.
Joule and Thomson conducted the following
experiment. Two frictionless pistons P
1
and P
2
are
placed inside the insulated cylinder. A cotton plug
(cotton plug) is placed between the pistons. If the
parameters of the gas located on the left side of
the barrier are R
1
, V
1
, and T
1
then the parameters
of the gas passing through the open barrier to the
right are R
2
, V
2
, and T
2
respectively. When the first
piston moves, the gas passes through the valve to
the right and the work done is A
1
= R
1
V
1
. And the
work done when the second piston moves are A
2
=
R
2
V
2
. Putting this work done expressions into the
first law of thermodynamics written for an
adiabatic process:
2
2
2
1
1
1
V
P
U
V
P
U
+
=
+
It can be seen that in the Joulep-Thomson
experiment, the magnitude of U+RV remains
unchanged. This quantity is called the heat
function or enthalpy of the gas. Equal enthalpy in
real gases does not mean equal temperatures.
C
ONCLUSION
In conclusion, it should be said that the Linde
machine is widely used in technology for the
liquefaction of gases. Its working principle can be
interpreted as follows. A gas, for example, is
Volume 02 Issue 12-2022
198
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
12
Pages:
192-199
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
compressed to a pressure of about 200 atm in an
air compressor and cooled by running water in a
cooler, since most gases heat up when
compressed. Then two layers of compressed air
pass through the inner nozzle of the tube, and in a
wide container at the end of the tube, 1 atm in the
condenser expands to pressure. In this case, the
gas cools down to about 20
℃
. Expanded air is
sucked back into the compressor through the
outer tube of the wave-shaped tube, which in turn
cools the second part of the compressed air in the
inner tube at the distance to the compressor.
Thus, the second part of the gas cools by 20
℃
in
the corrugated tube itself and then cools another
20
℃
as it expands in the condenser. This process
is repeated many times. As a result, the air is
cooled from the critical temperature to a lower
temperature.
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Pages:
192-199
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