Measurement and model validation of specific heat of xanthan gum using joules calorimeter method

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 09 | Sep-2013, Available @ http://www.ijret.org 232
MEASUREMENT AND MODEL VALIDATION OF SPECIFIC HEAT OF
XANTHAN GUM USING JOULES CALORIMETER METHOD
K. Muthamizhi1
, P. Kalaichelvi2
, A. Arunagiri3
, A. Rudhra4
1
Researchscholar, 2, 3
Associate Professor, 4
B. Tech, Chemical EnggDept, National Institute of Technology, Tamil Nadu,
India,tamilkrypal@gmail.com.,kalai@nitt.edu,aagiri@nitt.edu,rudhra.nitt@gmail.com.
Abstract
The purpose of this paper is to examine the concentration and temperature influence on the specific heat of xanthan gum and to
propose a model equation for estimating the specific heat of xanthan gum at different concentration and temperature usingthe Joules
calorimeter method. Joules calorimeter method was tested with distilled water for accuracy and reliability before applying to xanthan
gum samples which varied in concentration. The specific heat of xanthan gum needs to be known for evaluating the design and
modeling aspects of heat transfer processes of refrigeration, freezing, heating, pasteurization and drying. The specific heat of xanthan
gum increases with an increase in temperature (293.15 - 333.15K) and concentration (0.1 - 0.6 %w/w). The minimum value of specific
heat of xanthan gum was 4.133 KJ/kg K at 300.25K with a concentration of 0.2 %w/w, whereas the maximum value of specific heat of
xanthan gum was 7.459 KJ/kg K at 333.95K with a concentration of 0.5 %w/w. The specific heat capacity of xanthan gum is compared
with that of pure water at 308.15, 318.15 and 328.15 K and literature available model at 293.15 - 333.15 K for 0.1 - 0.6 %w/w
concentration of xanthan gum. The influence of operating parameters on the specific heat of xanthan gum was determined by
employing a central composite rotatable design in response surface methodology (CCRD-RSM). The new model equation obtained for
estimating the specific heat using RSM possesses good agreement with experimental data with a regression coefficient of 0.9774.
Index Terms: Specific heat, Xanthan gum, Pseudo plastic fluid and Response surface methodology etc.…
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1. INTRODUCTION
Xanthan gum is a high molecular weight polysaccharide,
produced by the bacterium Xanthomonas campestris [1-3] and
it can be used to add texture to food [4]. Texture is one of the
most vital properties to characterize the quality of food
products.
Xanthan gum is soluble in cold and hot water and the powder
of xanthan gum has a strong tendency to form lumps when
added with water.
This specific property of the gum needs intensive agitation in
order to avoid the formation of lumps like hydrocolloids [5].
The xanthan gum primary structure is a linear β-(1-4) -D-
glucose, which is the backbone of xanthan gum and it has
similar characteristics as cellulose [6-7]. Xanthan gum forms a
twin stranded, right-handed fivefold helix and the stability of
the helix is strongly affected by the Ionic environment [8].
Xanthan gum is used in food, chemicals, petrochemicals,
polymers, cosmetic and pharmaceutical industry, for a number
of key reasons, including emulsion stabilization, temperature
stability, and compatibility with food ingredients [5-9].
Xanthan gum has pseudo-plastic fluid property - both two- and
three-dimensional behavior – which is different from the
behavior of a Newtonian fluid. The particle of pseudo-plastic
fluid contains dissolved or dispersed particles, which have
random orientations in the fluid at rest, but get lined up when
the fluid is sheared. This property allows it to pour, pump and
facilities ease of swallowing [10].
The heating and cooling of foods are the most important unit
operations in food processing industries [11-15]. Due to the
need for the information about the thermo-physical properties
of foods, the design of food products has been limited
[12&16]. Specific heat, thermal conductivity, density,
viscosity, surface tension and coefficient of thermal expansion
are the most important thermo-physical properties of pseudo-
plastic fluids. As of now, the limited value of thermo-physical
measurement has been conducted for dilute and aqueous
solutions of moderate concentration of typically used
polymers such as polyethylene oxide, carbopol,
polyacrylamide, and carboxymethyl cellulose [17]. The
specific heat of the food products strongly depends upon their
temperature and concentration [18-21].
Total heat required to raise 1 g of substance temperature by 1°
C is called specific heat [22]. Specific heat is the most
important thermodynamic parameter in heat transfer
calculations and it increases when the temperature increases. It
is case sensitive to the composition of the ingredients (if the
specific heat of individual components is different) and to the

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interactions between the components of the material [14].
Similarly, for various foods and biological materials, specific
heat increases with increase in temperature [23-27]. The
specific heat capacity of most of the substances depends on
the state variable and particularly it is dependent on
temperature [28].Semmar et al., (2004) determined the
specific heat of CMC (Carboxymethyl cellulose) and CPE
(carboxy-poly-ethylene) solution as a function of temperature
and concentration [29].
The response surface methodology is a statistical and
mathematical technique used for modeling and optimization of
processes in which a response of interest is influenced by
several variables. The primary function of RSM is to postulate
a suitable approximation for the true functional relationship
between the response and the set of independent variables.
The two most important designs extensively used in Response
surface methodology are Central Composite Design (CCD)
and Box–Behnken Design (BBD) [30].
The foremost significant part to design any process involving
pseudo-plastic fluids on an industrial scale is thermo-physical
properties. In the present study, the specific heat capacities of
xanthan gum solutions were measured, in the temperature
range of 293.15 K - 333.15 K and concentration in the range
of 0.1-0.6 %w/w compared with water. A more general
relationship that takes into account, the temperature and the
concentration has been established with an average relative
error of 0.130% using RSM-CCD.
2. MATERIALS AND METHODS
2.1Materials and Solution Preparation
Xanthan gum pure (food grade) was purchased from LOBA
Chemie. Xanthan gum (1 kg) had a particle size (100-200
mesh), ash (6.5-16%), pH of 1% solution in water (6-8),
nitrogen (1.5%), pyruvic acid (2.40%) and heavy metals,
(0.001%).
A known amount of xanthan gum was weighed (CyberlabTM)
and the weighed sample was dissolved in 350 ml distilled
water to obtain different concentrations ranging from 0.1-0.6
% w/w. The mixture was stirred well for 1 hour in a magnetic
stirrer at room temperature until the solute was dissolved
completely. The xanthan gum mixture was transferred into
copper calorimeter and the measurements of specific heat
were done.
Joules calorimeter was supplied by Precision scientific &Co,
Trichy.Joules calorimeter is electrically heated calorimeter,
such as that used in the Griffiths method and it consists of a
copper vessel of 7.62 X 5.08 cm with the outer vessel as a
superior quality teak wood box of size 9.5 X 9.5 X 11.5 cm
fitted tothe Bakelite lid with a hole for the thermometer and
stirrer.
2.2 Experimental Procedure
A Joule’s calorimeter apparatus was used; which works on
adiabatic principle [22]. It was calibrated using distilled water
as a sample fluid to test the accuracy and reliability of the
process. A schematic diagram of the Joules Calorimeter is
shown in Fig. 1.
Fig -1: Schematic diagram of a Joules calorimeter
Experimentally, the amount of electrical joule heat generated
in a circuit element of resistance R is measured by
calorimetric methods. After measuring the mass of the empty
calorimeter, the inner calorimeter cup was filled with 350 ml
of xanthan gum.
The calorimeter was placed in a wooden box. The temperature
probe was suspended to ensure that it does not touch the coil
or interfere with the stirrer. The battery was connected in
series with joules calorimeter, a rheostat, ammeter and plug
key. The switch was turned on for the power supply, voltage,
current and the time taken for equal intervals of temperature
rise were measured and the specific heat was calculated by
using equation (1) where Cp, M, w, E, I, t, Tf, Ti andCpm are
Specific heat of the fluid, Mass of the fluid, weight of the
calorimeter, Voltage, Current, time, Final temperature and
Initial temperature and specific heat of the material.
Cp =
1
M
(E×I×t)
(Tf−Ti)
– (w × Cpm
) (1)
2.3 Experimental Design
To study the effect of operating variables on the specific heat
of xanthan gum, Design Expert Software (8.0.6) was used.
Independent variables, i.e. temperature and concentration were
coded at five levels between -2 and +2, wherein the
temperature (T) in the range of 293.15 K - 333.15 K and
concentration in the range of 0.1 - 0.6 %w/w (Cx),
respectively. The experimental range and independent process
variable levels of xanthan gum solution are presented in Table
1.
A total number of 13 runs were obtained with two factors
using the Design Expert Software.To evaluate the pure error,
eight experiments were carried out with five replications at the
design center in randomized order.

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3. RESULTS AND DISCUSSIONS
The specific heat of any solution is influenced by temperature,
concentration, interaction of pseudo-plastic fluid components
and others.
The following sections 3.1 and 3.2 describe the influence of
the concentration and temperature on the specific heat of
xanthan gum solution.
Table -1: Range of experimental and independent process
variable levels for xanthan gum solution
Factors Unit
Levels and range
-2 -1 0 1 2
Temp K 284.86 293.15 313.15 333.15 341.43
Conc % 0 0.1 0.35 0.6 0.7
3.1 Effects of Temperature of Specific Heat of
Xanthan Gum Solution
The temperature and concentration influence of the specific
heat of xanthan gum solution was shown in Fig.2. It can be
inferred from Fig. 2 that the specific heat of the xanthan gum
solution increases when temperature increases for 0.1 % w/w,
0.3 % w/w and 0.5 % w/w. A similar trend was observed for
0.2 %w/w, 0.4 %w/w and 0.6 %w/w.
Fig -2: Temperature and concentration influence on the
specific heat of xanthan gum solution
Specific heat depends on the structure of the xanthan gum.
During heating, xanthan gum will expand, for the expansion, a
little amount of heat also supplied to the work required; this
will increase the specific heat of xanthan gum solutionwith a
maximum value of 7.4595 KJ/kg K for 0.5 % w/w at 333.95
K. As the xanthan gum heats up, the average temperature of
the xanthan gum molecules increases, so when they collide,
they are more likely to impart enough energy to allow rotation
and vibration to occur as the energy jumps to a higher state.
Once the rotation is induced, it contributes to the internal
energy and raises the specific heat. This is typical for all
mixtures higher the temperature higher the specific heat [31].
3.2 Effects of Concentration on Specific Heat of
Xanthan Gum Solution
Fig. 2 shows that the specific heat of xanthan gum solution
increases when the concentration increases for 0.1 %w/w, 0.3
%w/w and 0.5 %w/w at 293.15 K - 333.15 K. A similar trend
was observed for 0.2 %w/w, 0.4 %w/w and 0.6 %w/w at
293.15 K - 333.15 K. It was observed from the Fig. 2 that the
specific heat increases generally with an increase inxanthan
gum concentration. When concentration increased more heat
was required to raise the temperature of the xanthan gum by
one degree Kelvin. Increase in specific heat due to the increase
in concentration of xanthan gum increased the heat
requirement of samples. Thus the sample with 0.6 %w/w
xanthan gum required more heat to raise its temperature than
the sample with 0.1 %w/w [32].
3.3 Comparison of Experimental Values of Specific
Heat of Xanthan Gum Solution tothe Specific Heat of
Water
The specific heat of xanthan gum solution (0.1 %w/w, 0.3
%w/w and 0.5 %w/w) was compared with water at different
temperatures (308.15 K, 318.15 K and 328.15 K) as depicted
in Fig. 3.
Fig -3: Specific heat of xanthan gum solution compared with
water at different temperature (308.15 K, 318.15 K and
328.15K)
The specific heat of xanthan gum solution was higher
compared to the specific heat of water at all concentrations
considered in the present study. Bellet (1975) and Raynaud
(1985) narrated that the specific heat values of solutions are
higher than the specific heat of water [33-34].
Semmaret al., (2004) concluded that even for low values of
polymeric solution mass concentration, their specific heat
4
4.5
5
5.5
6
6.5
7
7.5
8
300 320 340
Specificheat(KJ/kgK)
Temperature (K)
0.5 %w/w
0.3 %w/w
0.1%w/w
4
4.5
5
5.5
6
6.5
7
7.5
305 315 325
Specificheat(KJ/kgK)
Temperature (K)
0.5 %w/w
0.3 %w/w
0.1%w/w
Water

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cannot be regarded as equal to that of pure water [29]. Even if
water has the highest specific heat of all liquids except
ammonia, in the presence of water molecules, molecular
chains of xanthan gum possess an energy potential which
increases with temperature and concentration, thus it has a
high specific heat compared to water.
3.4 Comparison Of Experimental Values Of Specific
Heat Of Xanthan Gum Solution To The Reference
Model Equation Of Semmar et al., (2004)
The experimental data of specific heat of xanthan gum was
also tested using second order polynomial model equation
reported for CMC and CPE solution by Semmar et al., (2004)
[29].
Semmar et al., (2004) established the following model
equation where Cp, T, T0, A & B, D and X are Specific heat,
Temperature, Temperature of pure water (T0 =273.15K),
Coefficients of temperature, Coefficients of temperature,
Coefficient of concentration and concentration [29].
Cp T, X = A T − T0
2
+ B T − To + Cp T0
DX
1+DX
(2)
A = 0.015
B = 5.45
D = -0.013 for 18gl-1
Table 2 shows the comparison of experimental results and
specific heat of xanthan gum solution estimated using the
model equation proposed by Semmar et al., (2004).
Comparison between experimental and predicted specific heat
value of xanthan gum solution reveals that the model equation
predicts the specific heat of xanthan gum solution in the
database with an absolute average deviation of 14.1. Hence,
response surface methodology was used to develop an
empirical model equation for specific heat of xanthan gum
solution as a function of temperature and concentration.
3.5 Development of a model equation for Specific
heat of xanthan gum solution using RSM
The analysis was done using the Design Expert Software
(8.0.6) which is focused on how the specific heats of xanthan
gum solution are influenced by independent variables, i.e.,
temperature and concentration.
Analysis of Variance (ANOVA)
ANOVA was used to determine the significant effects of
temperature and concentration and the results are presented in
Table 3.
It shows the comparison between the predicted result and
experimental result of specific heat of xanthan gum solution. It
can be observed from Table 4that F-values in regression
analysis are found to be higher for specific heat of xanthan
gum solution.
Table -2: Comparison between the experimental result and
specific heat of xanthan gum solution estimated using the
model equation proposed by semmar et al., (2004)
The large F-value indicates that most of the variation in the
response can be explained by the regression model equation.
Three-dimensional response surfaces generated from the
predicted results Eq. 2 for specific heat of xanthan gum with
temperature and concentration was shown in Fig. 4. The
specific heat of xanthan gum solution was modelled through a
linear multiple regression as a function of temperature (K) and
concentration (XX) as follows
Cp = 98. 78575 − 0.6495T − 15. 9955XX + 0.06TXX +
0.001109T2
− 0. 5XX
2
(3)
The predicted results of specific heat of xanthan gum solution
using the quadratic equation generated by RSM were
compared with the experimental values. The predicted value
using Eq. 3 and the experimental results are shown graphically
in Fig. 5.
It can be observed that the experimental and predicted results
are in good agreement; the variation was confirmed using
absolute average deviation (AAD). The absolute average
deviation observed was 0.130 for the specific heat of xanthan
gum.
Factor 1 Factor 2 Response
A: Temp
K
B: Conc
%
Specific heat
(KJ/kg K)
Actual Predicted
Absolute
average
deviation
293.15 0.1 4 4.31745 14.1
333.15 0.1 6.3 4.48745
293.15 0.6 4.5 4.31469
333.15 0.6 8 4.48469
284.87 0.35 4.1 4.27489
341.43 0.35 7.5 4.51527
313.15 0 3.9 4.409
313.15 0.7 5.8 4.40513
313.15 0.35 5.1 4.40707
313.15 0.35 5.1 4.40707
313.15 0.35 5.1 4.40707
313.15 0.35 5.1 4.40707
313.15 0.35 5.1 4.40707

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Fig -4: Three dimensional response of temperature and
concentration influence on specific heat of xanthan gum
solution
Goodness of fit by quadratic equation was checked using the
regression coefficient R2
. The specific heat of xanthan gum
values of quadratic equation R2
and adjusted R2
value are
found to be 0.9774, 0.9614 respectively.
Fig -5:Specific heat of xanthan gum solution predicted results
using equation 2 was compared with experimental results
Using ANOVA for the response surface, the significant effects
of the operating variables were determined and the obtained
results are shown in Table 4. The fisher F-values for specific
heat of xanthan gum solution were higher representing that the
model equation signifies the variation in the response.
Table -3: Experimental runs and comparison between the
predicted result and the experimental result of specific heat of
xanthan gum solution
Run
Factor 1 Factor 2
Response
A: Temp
K
B: Conc
%
Specific heat
(KJ/kg K)
Actual Predicted
Absolute
average
deviation
1 293.15 0.1 4 3.88 0.130
2 333.15 0.1 6.3 5.93
3 293.15 0.6 4.5 4.50
4 333.15 0.6 8 7.75
5 284.87 0.35 4.1 4.11
6 341.43 0.35 7.5 7.86
7 313.15 0.00 3.9 4.17
8 313.15 0.70 5.8 5.90
9 313.15 0.35 5.1 5.1
10 313.15 0.35 5.1 5.1
11 313.15 0.35 5.1 5.1
12 313.15 0.35 5.1 5.1
13 313.15 0.35 5.1 5.1
The model is statistically significant with larger F and p-
values. The ANOVA of regression model observed for this
quadratic equation being highly significant (p<0.0001). The
behavior of response surface in Fig. 4 also confirmed this
implication.
CONCLUSIONS
The experimental results of the specific heat of xanthan gum
obtained in this study have been analyzed for the influence of
temperature and concentration of the specific heat of xanthan
gum. The specific heat of xanthan gum solution measured by
Joules calorimeter method revealed that it depends strongly on
the concentration and temperature. An increase of specific
heat of xanthan gum solution was observed, when both
temperature and concentration increase. When compared to
the specific heat of water, the specific heat of xanthan gum
solution was higher.
The model equation proposed by semmar et al., (2004) was
tested using the experimental values of specific heat capacity
of xanthan gum solution. Based on the equation proposed
bysemmar et al., (2004) using CMC and CPE solutions and
the absolute average deviation found to be 14.1. A new
empirical equation was developed to predict the specific heat
of xanthan gum solution as a function of temperature and
concentration using CCD along with RSM.

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Table -4: ANOVA for response surface of the second-order
polynomial equation for specific heat of xanthan gum solution
Source
The sum of
Squares df
Mean
Square
F-
Value
P-value
Prob>F Remarks
Model 18.84 5 3.77 60.79 < 0.0001
Significant
A-
Temp
14.07 1 14.06 226.90 < 0.0001
B-
Conc
2.99 1 2.99 48.17 0.0002
AB 0.36 1 0.36 5.81 0.0468
A2
1.37 1 1.37 22.10 0.0022
B2
0.01 1 0.01 0.11 0.7503
Residual 0.43 7 0.06
Lack of fit 0.43 3 0.14
Pure error 0.00 4 0.00
The new model equation obtained for estimating the specific
heat of xanthan gum solution using response surface
methodology was tested with the experimental data with a
regression co-efficient of 0.9774. The proposed empirical
equation could be used for the estimation of specific heat of
xanthan gum solution for any combination of concentration
and temperature.
NOMENCLATURE AND UNITS
Cp Specific heat (KJ/kg K)
T Temperature (K)
T0 Temperature of pure water at 273.15 (K)
X Concentration (%)
M Mass (g)
I Current (amp)
E Voltage (V)
D Coefficients of concentration
A & B Coefficients of temperature
t Time (sec)
W Weight (g)
Subscripts
x Xanthan gum solution
i Initial
f Final
m Copper material
ACKNOWLEDGEMENTS
The authors wish to express their appreciation to C.S.I.R for
the financial support given for carrying out this investigation.
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BIOGRAPHIES
K.Muthamizhi graduated as a
Pharmaceutical engineer in 2007 from
Bharathidasan Institute of Technology,
Bharathidasan University, Tamil Nadu,
Tiruchirappalli, India. She received the
master degree in Chemical engineering from
Coimbatore Institute of Technology in 2010, Coimbatore and
she is now pursuing her Ph.D. degree in National Institute of
Technology, Tiruchirappalli and working as a Senior Research
Fellow in CSIR project-NIT-Trichy under the supervision of
Dr. P. Kalaichlevi.
Dr. P. Kalaichlevi,is working as Associate
Professor in the Dept. of Chem. Engg.,
National Institute Of Technology, Trichy,
Tamil Nadu, India. She received CSIR-SRF
fellowship (1996-1998) for Ph.D Program
and BOYSCAST fellowship 2004-2005,
from Department of Science and Technology, India She has
undergone a research training program in National University
of Singapore, Singapore under BOYSCAST
A. Arunagiri,is working as Assistant
Professor in the Dept. of Chem. Engg.,
National Institute Of Technology, Trichy,
Tamil Nadu, India, from 2006. He also
worked as a Lecturer at A. C. College of
Technology, Anna University, Chennai, Tamil
Nadu, India. His research interests are Transfer Operations,
Environmental Engineering and Multiphase flow. Dr. A.
Arunagiri is a life member of Indian Institute of Chemical
Engineers (LM-34030) and was awarded for Teaching
Research Associate fellowship and Senior Research
Fellowship by Anna University and CSIR respectively
RudhraAnandandid hisB. .Tech in National
Institute of Technology, Trichy, Tamil Nadu,
India and belongs 2009-2013 batch. He
coordinated Placement for 2010-2014 batch
and worked as a manager for Delta-T (Heat
Exchanger Design Event) of Pragyan
(International Techno-Management festival of NIT, Trichy) in
the year of 2012.

Measurement and model validation of specific heat of xanthan gum using joules calorimeter method

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Measurement and model validation of specific heat of xanthan gum using joules calorimeter method