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yflK 544.015:514.12
Application of graphic and graphic-analytic geometry systems on the liquid and gas phases of matter
Beycan Ibrahimoglu1, Gozde Tekeli2*
1 Gazi University department of mechanical engineers, Rektorlugu 06500, Ankara, Turkey
2 Plasma Technology Center, Anatolia, Ankara, Turkey. * E-mail: gozdettkl@gmail.com
Abstract. If we investigate the past, we will discover that the teachers of thermodynamics were always trying to interpret an important part of their science by using geometry. The relation between geometry and thermodynamics is of great interest and importance in teaching thermodynamics. In this respect, graphic system has been used extensively in fields such as physics, chemistry, mathematics, astronomy, space engineering, crystallography etc. Graphic system determines specifications of matter like its real dimensions or its geometry. Additively, it offers methods with simple operations. In our studies, it was possible to determine dissociation and ionization temperature of substances, pressure-dependent boiling and critical temperature, temperatures of freezing and triple point, the boundary range depending on the pressure in the liquid phases of the substance by applying graphic and graphic-analytic geometry system to the liquid and gas phases of matter.
For a long time, experimental results of many researches from fields of physics and chemistry have caused numerous misunderstandings owing to the existence of abundant number of terms, but in time an agreement was reached over the thermodynamic parameters. Ones, those have been accepted available for the energy and mass exchange, which are temperature, density, volume, enthalpy and some other thermodynamic parameters.
By applying the graphic system to the thermodynamic parameters like temperature, pressure, volume and density, it is possible to get information on the basic thermodynamic points of the matter. Also, it is possible to get different information on the matter by applying the graphic-analytic geometry system to the both gas and liquid phases of matter [1-8].
Graphic system has been used extensively in fields such as physics, chemistry, mathematics, astronomy, space engineering, crystallography etc. Graphic system determines specifications of matter like its real dimensions or its geometry. Additively, it offers methods with simple operations.
For this purpose, in 1840's William Kelvin Thomson determined a new scale of temperature (T = 0 K) of the gas phase of the matter under the condition of constant pressure (P) on P-T diagram (fig. 1). There are no negative numbers on the Kelvin scale, and so, 0 K is the lowest temperature possible in nature.
Keywords:
graphic,
graphic-analytic geometry system, dissociation and ionization temperature, pressure-dependent boundary range of liquid phase, critical pressure.
Fig. 1. Gas phase data in V = const (P-T) diagram shows the absolute zero point on the T axis
In P-T diagram, the linear isochore line that passes through P(0) and P(100) intersect the T axis at a point. Research showed that this point is the absolute temperature (T = -273,15 °C) and this diagram is same for all substances [7-10].
As given in fig. 1, the isochores were obtained from the application in (P-T), V = const dependence of a gas phase and showed a fundamental point of a solid phase. This indicates that the atoms of a gas phase have memory, and this information can only be obtained by using graphical method.
By analogy, applying the graphic system to the gas phase under the context of density-temperature
(p-T), P = const, it was observed that all isobars intersect the T axis in the direction of temperature increase [8]. Conducted studies showed that the isobars intersect on the T axis in the direction of increasing temperature, and intersection point coincides with the temperature which matter starts to dissociate or ionize (table 1). The point where the isobars intersect the temperature axis in the direction of increasing temperature differs for each gas. Differences in between dissociation and ionization energies for each gas substances cause them to gather at different points where the isobars intersect the T axis in the direction of temperature
Table 1
Dissociation temperatures for various gases, K
Gas Graphic-analytic method Measurements
Oxygen 2550 2573 [11]
Argon 2920 -
Air 2690 -
Nitrogen 3700 35001
Carbon dioxide 2223 22731
Xenon 2500
1 See: NIKOLSKIY, B.P. et al. (eds.). Chemist's Handbook [Spravochnik khimika]: in 7 volumes. Moscow & Leningrad: Khimiya (Leningrad department), 1965-1968. (Russ). = Справочник химика: в 7 т. / под. ред. чл.-кор. АН СССР Б.П. Никольского (глав. ред.) и др. - 2-е изд., перераб. и доп. - М.-Л.: Химия [Ленингр. отд-ние], 1965-1968.
T, K
Fig. 2. (p-T), P = const diagram for Xenon
T, K
Fig. 3. Correlation of (V-T), P = const and (p-T), P = const for Argon
Ö ö
te .a Solid я -£3 ta ГЛ Liquid J
'G и о О
Gas
Plasma
83,8 87,3 V 2950 T, K
Fig. 4. Phase diagram of Argon with respect to temperature
increase. Fig. 2 illustrates the p-T diagram of the Xenon gas. Experimental data to plot this diagram was taken from literature [7, 8].
With the application of the graphic system, (V-T), P = const and (p-T), P = const diagrams were obtained. Direct extrapolation of isobars in directions of both the increase and the decrease in temperature provided two basic points for absolute temperature: dissociation and ionization points. Determination of absolute temperature by William Kelvin and our studies in assignment of dissociation or ionization temperature using graphical method led us to show all the phases of a certain substance together as given in figs. 3 and 4.
Analytic Geometry System
Analytic geometry offers methods to determine real dimensions of matters. With simple operations, they can determine some points', lines' or geometrical objects' specifications like their location or real geometry by graphic method. Graphic method provides a better technique for pressure, temperature, constant density lines or constant viscosity lines, increasing visibility of physical processes, abstract thinking, intuition, analysis and comparison problems, by bringing the basic principles and methods of analytic geometry. By applying a graphic system to the thermodynamic parameters of matter in gas phase, information can be gathered on the basic thermodynamic
points of the matter, such as absolute temperature, dissociation and ionization temperatures.
A graphic-analytic geometry system created by the merger of the graphic method and an analytic geometry system provides incredible opportunities. This system allows to obtain wide amount of information on triple points of matters in high pressure and temperature, critical parameters, freezing and boiling temperatures and other basic points. For example, this system under (V-T ), P = const condition made it possible to find a pressure value that coincide with the critical temperature of a certain matter.
Method for determination of the pressure fitting the critical temperature
Graphic analytic geometry system applied to the (V-T ), P = const condition enables to determine the pressure (Pcr) matching the critical temperature (Tcr). For this purpose, V1 axis is drawn parallel to the V axis, and the projection of AB isobaric line on the V axis is drawn. In comparable way, projections of CD and EF lines on the V are determined (fig. 5). After that, a point where the isotherm line that passes through Au, Cu, and E11 points intersects V1 axis is the pressure point that coincides with the Tcr value of a given gas (table 2). More detailed information is given in references [4, 5].
Table 2
The comparison of experimental pressure values at critical temperatures, determined with the graphic analytic method vs the literature values
Gas Pcr, bar Deviation, %
graphic-analytic method [12]
O2 47,5 5Q,1 5,2
N2 33,Q 33,6 1,78
CO2 75,8 73,8 -2,71
CH4 48,3 46,4 -4,52
0
Fig. 5. Pressure that coincides with the critical temperatures of gases in (V-T), P = const condition
Applying graphic system to the liquid phase of matter
The graphic system was applied to the liquid ortho, meta and para toluidines. Density and viscosity experimental results for para toluidine at elevated temperatures and pressures are given in tables 3 and 4.
Experimental results of the viscosity of para toluidine under high pressure and temperature were plotted [11], and with the application of graphic analytic geometry system method (fig. 6) to the (q-P), T = const diagram it was possible to determine Tcr value of the para toluidine, depending on the pressure (fig. 7).
Experimental results of the density p, kg/m3, [11, 13] of para toluidine under high pressure and
temperature were drawn, and graphic analytic geometry system method was applied (fig. 8) to the (p-P) diagram. Thus, the freezing and absolute temperatures of the para toluidine depending on the pressure were determined (fig. 9).
Application of (p-P), T = const dependence on substances in the liquid phase indicates the presence of a new point. (p-P), T = const dependence was applied to liquids such as hydrocarbons, alkanes, nitriles, paraffin carbohydrate (table 5). This new point that on the liquid-solid phase needs explanation. As an example, benzene (p-P) under T = const condition graph is represented in fig. 10.
The Pcr on the liquid-solid phase curve obtained from the application of (P-p) dependence
Table 3
Dynamic viscosity values n, 106 Pa-s, for para toluidine at high temperatures and pressures
P, MPa T, K
323 348 373 398 423 448 473 498 523
0,1 1518,0 1022,4 749,4 587,6 498,0 414,4 - - -
5 1554,1 1028,2 768,6 609,3 504,6 422,0 350,5 301,6 265,2
10 1612,4 1068,4 794,0 630,2 520,8 438,2 364,0 318,4 381,1
20 1723,3 1172,0 861,2 672,0 557,0 469,4 393,0 340,6 304,3
30 - 1262,6 922,3 716,2 594,8 487,0 428,0 368,2 331,4
40 - 1354,8 987,0 759,6 623,0 514,2 459,6 397,4 355,2
50 - 1442,1 1051,0 801,4 659,6 559,8 489,5 422,0 381,6
Table 4 Density values p, kg/m3, for para toluidine at high temperatures and pressures
P, MPa T, K
323 348 373 398 423 448 473 498 523
0,1 951,9 907,9 847,8 797,7 745,7 685,7 - - -
5 953,9 908,9 851,8 803,8 751,7 703,7 643,6 565,5 485,4
10 955,9 909,9 855,8 811,8 763,7 714,9 667,6 607,6 551,5
20 957,9 912,9 870,8 823,8 779,7 737,7 695,6 649,6 609,6
30 - 915,9 875,8 835,8 795,7 755,7 715,7 675,6 635,6
40 - 918,9 880,8 844,0 816,7 778,7 740,0 709,5 650,0
50 - 921,9 899,8 853,9 839,0 803,2 771,5 740,0 700,0
273
й СМ
1450-
1200
950
700
450
200
323
373
423
AT, K 473
P = 15
P = 20
10
\ T= 298 K P = 0,1 a, Pmax
P = 5
P = 10 rr^^
P = 30
P = 40
P = 50
423К
Г\ 448 K \ 473 K
20
30
40 50 P, MPa
Fig. 6. Experimental results for the viscosity Fig. 7. Analytical geometry diagram of para toluidine, of para toluidine (n-P), T = const (P-n), T = const
273
323
373
423
T, K 473
■ 1000
M
900
800
700
600
500
10 20 30 40 50
P, MPa
Fig. 8. Experimental results for the density of para toluidine, (p-P), T = const
Fig. 9. Analytical geometry diagram of para toluidine, (P-p), T = const
on the liquid phase of the substance is as given in the P-T phase diagram in fig. 11.
The application of graphical and graphical-analytical geometry to the gas and liquid phases of various substances has led to the determination of important thermodynamic parameters. In addition, the existence of the critical pressure of the liquid phase at higher pressures with the application of (P-p), T = const dependence for
the liquid phases of the substances will lead to different studies for the researchers, namely:
• determination of absolute temperature with the graphic method for the gas phase of a matter in (P-T), V = const condition;
• determination of dissociation and ionization temperatures with the graphic method for the gas phase of matter in (p-T), P = const condition;
• determination of pressure values coincide with the critical temperature of the matter
Table 5
Critical pressures obtained from (P-p), T = const dependence for substances in liquid phase
Liquid substance Pressure, bar
C7H9N (meta toluidine) 1450
C7H9N (ortho toluidine) 1400
C7H5N (benzonitrile) 1273
C8H10 (o-ksilenin) 2000
C8H10 (n-ksilenin) 2000
C9H20 (n-nonane) 1550
C10H22 (n-decane) 1360
C6H6 (benzene) 2200
C7H5 (tolol) 2161
P, bar
Fig. 10. Under the condition of T = const, Fig. 11. P-T phase diagram of liquid phase
benzene isotherms intersect on the P axis in (P-p), T = const dependence
at the point where P = 2200 bar
by applying the graphic analytic geometry system to the gas phase of matter in (V-T ), P = const condition;
• determination of critical temperature and boiling point temperature depending on pressure by applying the graphic analytic geometry system to the liquid phase of matter in (P-q), T = const condition;
• determination of absolute temperature and freezing point temperature depending on pressure by applying the graphic analytic geometry system to the liquid phase of matter in (p-P), T = const condition.
By applying the graphic analytic geometry system on the liquid phase of matter in (p-P), T = const condition it was observed that isotherms gather on a single point on the P axis. This point was very similar to the absolute, dissociation and
ionization temperatures. This indicates that there is a fundamental point on the P axis that depends on the liquid phase of matter.
Examinations showed that it was possible to state that the point which isobars gather on the T axis on the V-T diagram was absolute temperature; the point which the isobars collected on the T axis on the p-T diagram was dissociation or ionization temperature; and the point which the isotherms intersect on the P axis in the p-P diagram was the critical pressure of the liquid phase Pcrl.
Discussion of results
"Experimental Determination of Dynamic Viscosity and Density of Benzonitrile, Ortho, Meta, and Para Toluidine under High Pressure and Temperature" was taken as the main reference due to be the thesis subject of the author.
323
348
373
398
423
448
473
498
523
T, K
Fig. 11. Viscosity-temperature graph of para toluidine
To determine the densities and dynamic viscosities of benzonitrile, ortho, meta, and para toluidine, a special, combined experimental set up was designed and experiments under high pressure and temperature were conducted [11, 13, 14].
Experiments with light load method were conducted at P =50 MPa and at T = 523 K for density p, hydrostatic lifting method and dynamic viscosity. The melting point for para toluidine at normal pressure is 45 °C [11, 14]. It was decided to run the experiments under 500 atm. For this purpose, the system was heated above the melting temperature and melting point under high pressure was determined:
1) viscosity isobars show critical temperature in the direction of temperature increase;
2) density isobars show absolute temperature in the direction of temperature decrease (see figs 7-9).
The reason why isobars are in different directions of temperature for viscosity and density parameters
Even though the viscosity of liquids does not get affected by the pressure, it is a function of temperature, and as a result, when the temperature increases, the viscosity decreases. At the same time, for the gas phase of matter as temperature increases the viscosity also increases. In other words, viscosity shows different behavior for gas and liquid phases (fig. 12).
In liquid phase the gathering of isobars in one point in (P-q), T = const shows the critical temperature and the critical viscosity (see fig. 7). The critical temperature and the critical viscosity are also the points where the liquid phase turns into the gas phase. By the effect of temperature, the viscosity that was decreasing in liquid phase starts to increase, after it changes into the gas phase. It can be said that the viscosity corresponds to this temperature is the critical temperature. The Viscosity-Temperature graph of para-toluidine, as given in fig. 12, shows that the critical temperature is 448 K. In addition to that, at this temperature, viscosity values drop as matter changes from liquid phase to gas phase.
References
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of phase changes in fluids [Issledovaniye fazovykh perekhodov v zhidkostyakh]. Izvestiya Akademii Nauk Azerbaydzhanskoy SSR. 1984, vol. 12. (Russ.).
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A. HÜSEYNOV et al. Study of thermodynamic parameters of hydrogen gas by graph-analytic method. In: Hydrogen Materials Science and Chemistry of Carbon Nanomaterials: Proc. of the NATO Advanced Research Workshop, 2004, pp. 225-232.
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A. HUSEYNOV. Study of thermodynamic parameters of hydrogen gas by grapho-analytic method. International Journal of Hydrogen Energy. 2005, no. 30, pp. 515-519.
ISSN 0360-3199.
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et al. Determination of 1V-T (P, constant) diagrams of hydrogen gases by graph-analytical methods. Journal of Thermal Engineering. 2017, vol. 3, no. 1, pp. 1071-1077. ISSN 2148-7847.
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of Thermometry. 1990, vol. 1, no. 1, pp. 1-18.
11. IBRAHIMOGLU, B. Benzonitrile and O-, M-, Para toloudins: Thesis studies. Baki, Azerbaijan, 1983. (Russ.)
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po teplofizicheskim svoystvam gazov i zhidkostey]. Moscow: Nauka, 1972. (Russ.).
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Применение графических и графоаналитических геометрических систем для изучения жидкого и газообразного фазовых состояний вещества
Беджан Ибрагим оглы Фарзалиев1, Гёзде Текели2*
1 Университет Гази, отделение машиностроения, Турецкая Республика, Анкара, Rektorlugu 06500
2 Plasma Technology Center, Турецкая Республика, Анкара, Анатолия. * E-mail: gozdettkl@gmail.com
Тезисы. Известно, что в прошлом преподаватели термодинамики всегда старались дать основополагающим положениям своей науки геометрическую интерпретацию. Взаимосвязь между геометрией и термодинамикой представляет большой интерес с точки зрения изучения последней. Также графические средства широко
использовались в физике, химии, математике, астрономии, космическом приборостроении, кристаллографии и др. Графическое представление предмета исследования точно характеризует его размеры и форму. Кроме того, графикой легко оперировать.
При помощи графических и графоаналитических методов авторам удалось определить температуры диссоциации и ионизации веществ, зависимости температуры кипения и критической температуры от давления, температуры тройной точки и точки застывания, граничные условия существования жидкой фазы веществ в зависимости от давления.
Ключевые слова: графические и графоаналитические геометрические системы, температура диссоциации, температура ионизации, граничный диапазон давлений жидкой фазы, критическое давление.
Список литературы
1. Фарзалиев, Б.И. Исследование фазовых переходов в жидкостях / Б.И. Фарзалиев, А.М. Рагимов // Известия Академии наук Азербайджанской ССР. 1984. - Т. 12.
2. Гусейнов С.О. Обработка и математическое описание экспериментальных данных вязкости жидкостей в зависимости от температуры и давления / С.О. Гусейнов, Б.И. Фарзалиев, А.М. Рагимов и др.; депонент ред. Инженерно-физического журнала. - Минск, 1985. - 14 с.; Аннотация // Инженерно-физический журнал. - 1985. - Т. 49. - № 3. - С. 498.
3. Фарзалиев Б.И. Графическое определение параметров тройной точки фазового равновесия / Б.И. Фарзалиев, А.М. Рагимов, А.Т. Гаджиев // Изв. вузов. Нефть и газ. - 1985. - № 12. - С. 57-59.
4. Ibrahimoglu, B. Gazlarda Kritik Basincinin Grafoanalitik Yöntemle Bulunmasi = Критическое давление газа. Исследование графоаналитическим методом / B. Ibrahimoglu // Türk Isi Bilmi ve Teknigi Dergisi. - 1994. -Т. 17. - № 2.
5. Ibrahimoglu B. Erime Egrisi Uzerinde Bir Uf Noktanin Belirlenmesi / B. Ibrahimoglu, O.E. Ataer // Ulusal Isi Bilim ve Teknigi Kongresinin Bildirimleri. - Ankara, 1997. - № 33 (11).
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B. Ibrahimoglu, N. Veziroglu, A. Huseynov // International Journal of Hydrogen Energy. - 2005. - № 30. -
C. 515-519.
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B. ibrahimoglu, Q.K. Dindar, H. Erol et al. // Journal of Thermal Engineering. - 2017. - Т. 3. - № 1. -
C. 1071-1077.
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