See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/292616497 Critical behavior of refractive index of binary mixture cyclohexane phenol ARTICLE · JANUARY 2016 READS 20 3 AUTHORS, INCLUDING: Mohammed Abu-Jafar An-Najah National University 42 PUBLICATIONS 208 CITATIONS SEE PROFILE Issam Ashqer An-Najah National University 113 PUBLICATIONS 1,119 CITATIONS SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Issam Ashqer Retrieved on: 17 February 2016
The dynamic viscosity of binary mixture of cyclohexane - phenol was measured over the entire range of tempera-tures and at concentration range (0.00% � 39.70%) by weight of phenol. The results above the critical tempera-
ture and critical concentration were analyzed by the mode coupling theory of one phase. The anomaly of dynamicviscosity was detected as a function of temperature and concentration. Dynamic viscosity anomaly was clearlyobserved near the critical temperature T
c = 17.0 C and the critical concentration ÷
c= 2.70% by weight of phenol.
The value of noncritical part of refractive index was found to be = 1.4276. The universal critical exponentfor refractive index is also calculated to be 0.00156. The behavior of refractive index of cyclohexane - phenolobeys power law universality above the phase transition. The isobaric specific heat for the critical binary
mixture was found to be 106.6 using twoscale factor universality. Joule�s constant for cyclohexane -
phenol binary mixture was found to be 4.15 . 2015 Trade Science Inc. - INDIA
INTRODUCTION
Cyclohexane and phenol are two hazardous sub-stances widely utilized in different industries. There-fore, the identification of their physico-chemicalproperties is highly crucial. Cyclohexane is a col-orless organic solvent produced by reacting benzenewith hydrogen. Cyclohexane is fractionated frompetroleum and exists as a liquid at standard tem-perature and pressure (STP). It causes central ner-vous system depression as a result of acute expo-sures and may additionally cause irreversible dam-age to the liver and kidneys over prolonged expo-sure
The organic compound phenol is known as car-
bolic acid and phenic acid. It is a colorless whitecrystalline solid at room temperature and naturallyavailable. Besides its uses in chemical laboratories,phenol is used in manufacturing plastics, fertilizers,paints, rubber, adhesives, and paper. Phenol and itsvapors are corrosive and toxic to the eyes, the skinand the respiratory tract. It is very toxic to neuronsand if injected into the blood stream it can lead toinstant death by blocking the neural transmission sys-tem[3].
THE CRITICAL POINT
A critical point is the term coined when bothtemperature and concentration are stabilized at their
Physical CHEMISTRYPhysical CHEMISTRYAn Indian Journal
critical values. The two liquids behave as one liq-uid with new physical characteristics. The tempera-ture and concentration at which the two liquids be-come completely miscible at all proportions arecalled critical temperature T
c and critical concen-
tration ÷c, respectively. A pure liquid has a critical
point at the end of the vapor-liquid coexistencecurve.
Many properties for different binary mixtureshave been studied near their critical points, includ-ing the dynamic shear viscosity, bulk viscosity, ther-mal expansion coefficient, heat capacity at constantpressure and constant volume, ultrasonic propaga-tion, sound attenuation, ultrasonic velocity, refrac-tive index and other physical properties[9, 25].
REFRACTIVE INDEX
Refractive index of a given medium is a physi-cal property for that medium. It is a dimensionlessvalue which describes how light or any radiationscan propagate through the medium.
Refractive index determines how much light isrefracted. It can be defined as the ratio between thespeed of light in vacuum and the speed of light inmedium as expressed in equation (1):
= (1)Where is the refractive index of the medium atwavelength 589.29 nm (The Fraunhofer D line), c isthe speed of light in vacuum, and is the speed oflight in medium.
Refractive index is affected by factors such asdensity and temperature of the medium. The speedof electromagnetic waves (light) decreases for me-dium with high density causing a decrease in refrac-tive index[4]. The refractive index is inversely pro-portional to the temperature[18]. In addition, it de-pends on the wavelength of the incident light[16].
The refractive index is one of the most impor-tant physical properties of a transparent solid, liq-uid and gas. Accurate knowledge of refractive in-dex is correlated to the concentration, temperature,wavelength and pressure for transparent fluids. Itcan be used for the identification and characteriza-tion of pure materials. Concentrations of multi-
component mixtures can be measured using valuesof refractive indices[23].
To our knowledge, the physic-chemical proper-ties of the cyclohexane-phenol binary mixture werenot identified. Therefore, here we measured the vis-cosity of cyclohexane-phenol binary mixture as afunction of temperature over the entire possible con-centration range to determine the critical point. Thiswas followed by the determination of the criticaltemperature and critical concentration of cyclohex-ane-phenol binary mixture. The data extrapolatedwill be employed in setting up the power law forthe refractive index and calculating the critical ex-ponent ÷
n of the critical binary mixture. The critical
isobaric heat capacity for the mixture will also de-termine at the critical point. Finally, the Joule�s con-
stant for the binary mixture will be identified.
THEORY
Viscosity
Viscosity measures the resistance of a fluid togradual deformation by shear stress or tensile stress.For liquids, it corresponds to the informal notion of�thickness�. Viscosity is due to friction between
neighboring particles of the fluid that are moving atdifferent velocities[27].
The shear viscosity of a fluid can be expressedin two distinct forms:
The dynamic or absolute shear viscosity
The dynamic shear viscosity is defined as theratio of shear stress (force over cross section area)to the rate of shear deformation or shear velocity.
(2)Where dynamic shear viscosity in (Pa.s) is, is
shear stress in (N/m2), and is rate of deformation
(shear rate) in (s-1)[8].The dynamic shear viscosity unit is the centi-
poise (cP).
Kinematic viscosity
The kinematic viscosity is the dynamic viscos-ity divided by the mass density of the fluid
Full PaperCritical behavior of refractive index of binary mixture cyclohexane � phenol PCAIJ, 10(2) 2015
An Indian JournalPhysical CHEMISTRYPhysical CHEMISTRY
(3)Where, is kinematic viscosity in centistokes (cSt),and is mass density[8].
Dynamic shear viscosity of pure liquids
The viscosity of a pure liquid is affected by tem-perature, pressure, density and surface tension of thatliquid. The dynamicshear viscosity of liquids de-creases with increasing temperature and decreasingpressure[8].
Liquids have complex nature; therefore, severaltheories were proposed to describe the viscosity.Like the theoretical methods of calculating liquidviscosities, the molecular dynamic approaches, semi-empirical and empirical methods. The equation thatexplains the correlation between the dynamic vis-cosity and the temperature is in the form of anArrhenius-type equation[6].
(4)Where is the measured dynamic shear viscosity in(cP),
is the dynamic shear viscosity at some ref-
erence temperature, is the activation energy in
(J/mol), R is the universal gas constant (J/mol.K)and T is the absolute temperature (K).
The logarithm of liquid viscosity varies linearlywith the reciprocal of the absolute temperature Tbelow the normal boiling point which is describedby the empirical model.
(5)Where Ặ and B are constants determined empiri-cally.
At temperatures above the normal boiling point,
the versus relationship becomes nonlinear
and is described by a number of semi empiricalmethods.
Dynamic shear viscosity of mixtures
Viscosity is studied by several methods for so-lutions (homogeneous products of dissolution of sol-ids or gases in liquids) and for liquid mixtures (ho-mogeneous mixtures resulting from mixing of two ormore liquids). Some of the methods are developedusing excess Gibbs free energy models include Wil-
son, non-random two-liquid (NRTL) and universalquasi chemical (UNIQUAC)[8].
Far from the critical point (under or above) of abinary liquid mixture, the behavior of the viscosityis like pure liquids, but around the critical point thesituation becomes more complicated.
The mode coupling theory is used to study thecritical anomaly of the dynamic shear viscosity andthe coefficients.
The mode coupling theory
The �mode� refers to eigenmodes of an ideal-
ized, �unperturbed�, linear system. The superposi-
tion principle indicates that eigenmodes of linearsystems are independent of each other. In most realsystems, there are at least some perturbations thatcause energy transfer between different modes. Thisperturbation is interpreted as an interaction betweenthe modes. Therefore, the term �mode coupling� is
coined to describe this theory[13].Mode coupling theory is applied when the modes
of one fluid are perturbed by the modes of the otherfluid. Such perturbations lead to coupling and ex-change of energy[19], which indicates the start of theinteraction between the fluids layers. It started origi-nally by Fixman who proposed mechanisms by whichthe relaxation time and the kinetic coefficients, suchas viscosity and density, could diverge at a criticalpoint[9]. These ideas were more fully developed byKawasaki, Kadanoff and Swift[15, 14].
Reichman and Charbonneau derived the mode-coupling equations for the description of density fluc-tuations from microscopic considerations. In addi-tion, they derived schematic mode-coupling equa-tions of a similar form from a field-theoretical per-spective. They reviewed the successes and failuresof the mode-coupling theory, and discussed recentadvances in the applications of the theory[24].
The theories that describe the critical absorp-tion of the binary mixture are based on the mode-coupling theory which considers the effect of twomode states. These theories are based on understand-ing fluctuations that occur in those binarymixturesrather than focusing on microscopic aspects[9]. Theavailable theories can thus give important informa-tion about how binary mixtures act at their critical
Physical CHEMISTRYPhysical CHEMISTRYAn Indian Journal
points[10].Dynamic shear viscosity near the critical point:The critical anomaly of the dynamic shear vis-
cosity coefficient by Kawasaki and Perl and Ferrellis given according to the equation (6)[21]:
= (6)Where is the noncritical part of the measured dy-namic shear viscosity, is the mode-coupling theoryuniversal constant predicted to have the theoretical
value = 0.054[7], is the correlation lengthand q
D is the Debye momentum cutoff.
Mode coupling theory predicts a divergence ofthe kinetic coefficients near the critical point. Oneof the kinetic transport coefficients is the dynamicshear viscosity ç. The divergence of ç can be de-scribed near the critical point. However, two con-tributions must be considered: the critical part; whichis dominant near the critical point, and the regularpart; which is dominant far away from critical point.The dynamic shear viscosity ç is temperature de-pendent at the critical concentration which is givenby the power law equation (7):
(7)Where is the reduced temperature, ç
0 is the noncriti-
cal part of the dynamic shear viscosity in cP, and is the critical exponent for the dynamic shear
viscosity anomaly which equals 0.04[17, 2].The correlation length is the average distance
between two molecules at temperatures near the criti-cal temperature. The correlation length expressionis given by equation (8):
(8)This is related to the reduced temperature T
C near
the critical temperature and critical concentrationX
C.Van der Waals intermolecular forces act between
stable molecules or between functional groups ofmacromolecules. The intermolecular force range isthe reciprocal of the correlation length at =
[5].The mode-coupling theory has important appli-
cations such as fiber optics, lasers, and condensed-matter physics, to describe the slowing down of thecritical behavior.
Refractive index of a binary mixture
The refractive index nD
of any mixture can becalculated from the knowledge of the refractive in-dex and the mass density of pure components. n
D
can be measured in all ranges of existing tempera-tures and can also be deduced theoretically[26]. TheLorentz and Lorenz mixing rule in the form reportedhave been verified for the system under investiga-tion[28]. This rule was used to calculate the refrac-tive index for the phenol-cyclohexane binary mix-ture theoretically. The rule is given by equation (9):
(9)Where is given by equation (10):
(10)Where and are the pure components refrac-tive indices, and are the weight fractions, is the mixture mass density at critical temperatureand critical concentration, and are the purecomponents mass densities[20].
Power law of refractive index
Specific heat, thermal expansion coefficient and thermalconductivity and other thermodynamic properties, divergeas the critical temperature is approached with thedivergence obeying a power-law in |T - Tc |. Otherthermodynamic properties show a non-divergent power-law.The exponents that go with these power laws are called criticalexponents[22].
The refractive index is expected to be tempera-ture dependent, as viscosity and density of binarymixture, as given by the power law shown in equa-tion (11):
(11)Where is reduced temperature, which is given
by , is the universal critical exponent for
the refractive index, and is critical exponent whichequals to 0.64[7, 17].
Two � scale � factor universality:
The two � scale � factor universality has been
used in some theories to explain the critical phe-nomena of binary liquid mixtures by prediction of[11].This quantity is defined in equation (12):
Full PaperCritical behavior of refractive index of binary mixture cyclohexane � phenol PCAIJ, 10(2) 2015
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(12)Where is the universal quantity that equals0.270[11], is the critical exponent that equals 0.11,
is the mass density at the critical temperature, is the critical amplitude of the isobaric specific heat,
is the Boltzmann�s constant, is the criticalamplitude of the thermal expansion and is thepressure derivation of the critical temperature alongthe critical line[1, 11].
The specific heat at constant pressure is givenby the equation (13):
(13)Where is the critical amplitude of the isobaricspecific heat that is calculated from equation (12)and is the background isobaric specific heat.
METHODOLOGY
The characteristics of the binary mixture compo-nents
Cyclohexane and phenol
Cyclohexane and phenol substances with purity(99.5%) were used in this work. The molecularstructure of cyclohexane is shown in Figure (1).
Some physical and chemical properties for purecyclohexane and pure phenol are given in TABLE(1).
Viscosity apparatus
A Glass capillary U-tube viscometer is used for
viscosity measurement. It consists of a U-shapedglass tube held vertically in a controlled tempera-ture bath. One of the U-tube arms is vertically ori-ented with a narrow bore that consists of two bulbs.The other arm has a large bulb lower down the twobulbs on the first arm.
Temperature controller
Julabo F25-MV Refrigerated and Heating Cir-culator with temperature range (-28 to 200 °C) of
accuracy ±0.5is used to control the temperature of
the sample in the glass capillary viscometer.
Digital thermometer
A digital thermometer with accuracy ±0.5% is
used to measure the temperature of the water pathfor the samples.
Refractive index apparatus
Digital abbe refractometeris used to measure therefractive indices ( ) of the samples with accu-racy ±0.00005% at the entire range of temperatures.
Incident light with visible wavelength of D linewavelength (589.29 nm) is used.
Calorimeter
The specific heat of cyclohexane-phenol sampleis measured using the calorimeter. Glass capillaryviscometer, calorimeter cup and pycnometer arecleaned twice using ethanol alcohol (99.9%) anddried completely.
SAMPLES PREPARATION
Density measurements
A volume of 10.0 ml is measured by a 10.0 mlpycnometer, and weighed using an HR-200 analyti-
Property Phenol (Lide, 1993) Cyclohexane (Colette et al, 2003)
Physical CHEMISTRYPhysical CHEMISTRYAn Indian Journal
cal balance with accuracy of ±0.00005%.
Concentration of samples
Samples of different concentrations are preparedin the range 0.00% to 39.70% by weight of phenol.The concentration of phenol in a given sample ofcyclohexane and phenol in a given volume V can becalculated from equation (3.2):
(14)The volume of phenol is changed to enable its
addition to the sample. One component volume isfixed to find the volume of the other component for aspecific concentration.
Viscosity measurements
The sample of cyclohexane-phenol mixture is putinto the upper bulb by suction. It is then allowed toflow down through the capillary into the lower bulb.Two marks (one above and one below the upperbulb) indicate a known volume. The time taken forthe level of the liquid to pass between these marksis proportional to the dynamic shear viscosity. Thetime required for the test liquid to flow through acapillary of a known diameter of a certain factorbetween two marked points is measured. The ex-periment is performed three times for each concen-tration.
Viscosity of binary mixture can be calculatedusing equation (3.3):
(15)Where the dynamic is shear viscosity of binarymixture; is the time and is the mass densityof binary mixture at certain temperature andconcentration; is the dynamic shear viscosityof water, is the time and is the massdensity of water at certain temperature.
Water viscosity at temperature range (0.0 °C �
20.0 °C) can be calculated using equation (3.4.1)
(David, 1985):
(16)
Water viscosity at temperature range (20.0 °C �
100.0 °C) can be calculated using equation (3.4.2)
(David, 1985):
(17)
Refractive index measurements
A sample of 20.0 ml of cyclohexane-phenol isincubated in a water bath until its temperature isequilibrated with the water bath. The temperatureof the abbe refractometer prism is controlled usinga thermo stated bath. Two drops of the sample aretaken to measure n
D at certain temperature. Refrac-
tive indices are measured at temperature rang (14.0� 12.0 °C).
Isobaric specific heat measurement
The calorimeter is connected with the powersupply, digital ammeter, and digital voltmeter. The150.0 ml of critical binary mixture is weighted be-fore being placed inside the calorimeter. The ap-plied voltage is changed from power supply untilthe temperature 25.0 °C is reached for the binary
mixture. The power supply is then cut off from theset and temperature started decreasing. The timeneeded to reach the certain temperature is measuredusing stopwatch.
The work done on the binary mixture is calcu-lated using equation (3.5):Work = current × volt × time
(18)Joule�s constant (J) is calculated for cyclohex-
ane-phenol mixture using equation (19):
J = (19)Where is the quantity of heat in calorie.
Heat quantity ( can be calculated using equation(20):
= ( + + + ) ÄT (20)Where: is the mass of calorimeter cup (pyrexbeaker), is the mass of stirring rod, is themass of heater, is the mass of the binarymixture, is the specific heat of calorimeter cup, isthe specific heat of stirring rod, is the specific heatof heater and is the specific heat of the binary mix-ture at critical concentration, and ÄT is temperaturedifference.
52
Full PaperCritical behavior of refractive index of binary mixture cyclohexane � phenol PCAIJ, 10(2) 2015
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RESULTS
High-purity samples of cyclohexane and phenolwere used in this work. The shear viscosities at tem-peratures ranging from 14.0 to 21.0 ºC are measured
for cyclohexane-phenol binary mixtures, over theentire composition range. The dependence of theshear viscosity on the concentration and tempera-ture is determined. Refractive indices are measuredat temperatures in the range 14.0 to 21.0 ºC of dif-
ferent concentrations of cyclohexane - phenol binarymixture.
Viscosity measurements
The dynamic viscosity values for cyclohexane-phenol mixture are measured for a concentrationrange (0.00% � 39.70%) by weight of phenol at tem-
perature range (14.0 °C � 21.0 °C).
The dynamic shear viscosity of cyclohexane-phe-nol binary mixture depends on temperature. A posi-tive relationship was found between the dynamicshear viscosity and the concentration of phenol in
the sample. This is due to the high viscosity of phe-nol in the mixture.
The dynamic shear viscosity of cyclohexane-phe-nol of different concentrations (0.00% - 39.70%)by weight of phenol is plotted as a function of tem-perature, as shown in Figures (1)�(4).
The dynamic shear viscosity behaves anoma-lously near the concentration 2.70% by weight ofphenol and at the temperature 17.0 C. This gives anindication that this is possibly the critical point (T
c
= 17.0 °C, ÷c= 2.70% by weight of phenol) for the
binary mixture cyclohexane-phenol.Figures (2) - (4) show that at each concentration
of phenol the dynamic shear viscosity continuouslydecreases as the temperature increases. This is nor-mal, because when temperature is applied to liq-uids the molecules their average kinetic energy in-creases. The molecules can then slide over each othermore easily. The liquid thus becomes less viscous.Moreover, for each temperature the dynamic shearviscosity increases as the concentration of phenolincreases because phenol substance is more viscous
Figure 2 : Thedynamic shear viscosity of cyclohexane-phenol as a function of temperature of concentrations (2.00%- 6.70%) by weight of phenol
Figure 3 : Thedynamic shear viscosity of cyclohexane-phenol as a function of temperature of concentrations (9.90%- 17.90%) by weight of phenol
Issam Abdelraziq et al. 53
Full PaperPCAIJ, 10(2) 2015
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Figure 4 : The dynamic shear viscosity of cyclohexane-phenol as a function of temperature of concentrations (19.46%- 31.00%) by weight of phenol
Figure 5 : The dynamic shear viscosity of cyclohexane-phenol as a function of temperature of concentrations (34.00%- 39.70%) by weight of phenol
Figure 6 : Dynamic shear viscosity measured at different temperatures of 2.00%, 2.70% and 6.70% by weight ofphenol
than cyclohexane. The viscosity dependence on thetemperature at the critical concentration is different
from the other concentrations; there are no anoma-lous behaviors for these concentrations.
54
Full PaperCritical behavior of refractive index of binary mixture cyclohexane � phenol PCAIJ, 10(2) 2015
An Indian JournalPhysical CHEMISTRYPhysical CHEMISTRY
The anomaly can be clearly noticed by plottingthe dynamic shear viscosity vs. temperature for theconcentrations 2.00%, 2.70% and 6.70% by weightof phenol, as shown in Figure (6).
Figures (1) through (5) show a cusp at concen-tration ÷
c = 2.70% by weight of phenol and tempera-
ture Tc= 17.0ºC. This point is considered to be a
critical point. Mode coupling theory for the dynamicshear viscosity is used to fit the data near the criti-cal point.
The noncritical part of refractive index ( )
The Lorentz and Lorenz mixing rule can be usedto verify the refractive index values for different bi-nary mixtures. However, employing this rule for phe-nol is difficult to achieve for its solid state charac-teristic at room temperature.
The power law of the refractive index is usedto determine the background refractive index . Italso shows the reliance of refractive index on the
temperature. The data of refractive indices are fit-ted in the power lawequation ,where the noncritical part of is refractive index,
and is critical exponents, and is the reduced
temperature .
The measured refractive indices of the criticalconcentration above the critical temperature aregiven in TABLE (2).
Equation (14) gives relation between refractiveindex as a function of temperature. It can be re-writ-ten as shown in equation (15).
(14)
(15)Figure (7) shows a linear relation between( ) and (t) which can be noticed from equa-
tion (15). Therefore, the determination of the valueof the critical exponent and the noncritical partof refractive index is achieved. The values for
(°C) = ( ) ( )
17.3 0.3 0.0176 1.431 0.3583 -4.0372
17.5 0.5 0.0294 1.4306 0.3580 -3.5264
18.0 1.0 0.0588 1.4304 0.3579 -2.8332
18.5 1.5 0.0882 1.4299 0.3576 -2.4277
19.0 2.0 0.1176 1.4297 0.3574 -2.1401
19.5 2.5 0.1470 1.4296 0.3573 -1.9169
20.0 3.0 0.1764 1.4295 0.3573 -1.7346
20.5 3.5 0.2058 1.4294 0.3572 -1.5805
21.0 4.0 0.2352 1.4292 0.3571 -1.4469
TABLE 2 : Themeasured refractive index values of critical binary mixture above critical temperature
Physical CHEMISTRYPhysical CHEMISTRYAn Indian Journal
the slope equals to = 0.001, but as ,the universal constant for refractive index =0.00156. The intercept value = 0.356 is alsoneeded to calculate the background refractive in-dex = 1.4276. A least square fit gives the bestvalue for .
Calculation of specific heat
The specific heat under constant pressure at thecritical temperature is calculated using the two scalefactor universality.
The universal constant is given by equation (16)
= 0.270 (16)Where the critical exponent á = 0.11, dimension d =3, the mass density of binary mixture cyclohexan-phenol at the critical temperature = 0.7627gm/
that is found in this work, Boltzmann�s constant
is given by = 1.38 × J/k, is the noncriti-cal part of correlation length for critical binary mix-ture and it is equal to 3.12 Å[2]. The value for can
be calculated to be 106.6 .
(17)The isobaric specific heats values can be cal-
culated at different temperatures close to the criti-cal temperature (17.0 °C) are given in TABLE (3).
The average value for is 135.2 for cyclo-hexane / phenol binary mixture.
Joule�s constant for cyclohexane-phenol binary
mixture
The specific heat at constant pressure of the criti-cal cyclohexane/phenol binary mixture is calculated
to be 135.2 .
Joule�s constant J for cyclohexane-phenol binary
mixture can be calculated from equation (18):
J = (18)
Where H is heat quantity and it can be calculatedfrom equation (19):
= ( + + + ) ÄT (19)W is the work done on the binary mixture, it can
be calculated from equation (20):(20)
The values of different masses and different spe-cific heats are given in TABLE (4):
Full PaperCritical behavior of refractive index of binary mixture cyclohexane � phenol PCAIJ, 10(2) 2015
An Indian JournalPhysical CHEMISTRYPhysical CHEMISTRY
Constant measured or calculated Value
Tc 17.0 C
÷c 2.70% by weight of phenol
1.4276
0.00156
106.6 J 4.15 Calorie/J
TABLE 6 : Summary of values of constants measured or calculated in this work
ranges are given in TABLE (5).The average Joule�s constant value is 4.15 Calo-
rie/J. The average value for Joule�s constant for cy-
clohexane-phenol binary mixture is less than theJoule�s constant for water (4.1860 Calorie/J). This
small deviation between the two values is due to thechange in temperature ranges at which Joule�s con-
stants are calculated.
CONCLUSION
The mode coupling theory of the anomalous dy-namic shear viscosity near the critical point has beenstudied for cyclohexane - phenol binary liquid mix-ture.
The critical temperature Tc and critical concen-
tration ÷cvalues have been measured of cyclohex-
ane-phenol binary mixture.Shear viscosity coefficients and some thermo-
dynamic properties about the binary mixtures areimportant for the scientists working on the improve-ment of molecular theories.
The behavior of refractive index of cyclohex-ane-phenol obeys power law universality above thephase transition. The noncritical part of refractiveindex has been obtained; the universal critical ex-ponent for refractive index has also been calcu-lated.
The isobaric specific heat for the critical binarymixture has been calculatedusing two scale factoruniversality. The value of Joule�s constant J of cy-
clohexane-phenol binary mixture has been calcu-lated.
The experimental values Tc, ÷
c, , , and
Joule�s constant of cyclohexane-phenol are
calculated in this work to the first time. Such values
give more characteristic properties for cyclohexane/phenol binary mixture.
The results of the different properties that havebeen calculated and measured of the binary liquidmixture cyclohexane-phenol are summarized inTABLE (6).
REFERENCES
[1] I.Abdelraziq; �Concentration and temperature de-
pendence of shear viscosity of the critical mixtureof nitroethane and 3-methylpentane�, An-Najah
University Jounal for Research, 16(2), 117-124(2002).
[2] I.Abdelraziq; �Two � scale � factor universality of
binary liquid critical mixtures�, Pakistan journal of
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