J. Chem. Eng.

Data 2009, 54, 2269–2272 2269

Thermophysical Properties of Lemon Juice as Affected by Temperature and

Water Content

Luis A. Minim,*,† Vânia R. N. Telis,‡ Valéria P. R. Minim,† Lizzy A. P. Alcantara,† and Javier Telis-Romero‡
Department of Food Technology, Universidade Federal de Viçosa, 36570-000 Viçosa, MG, Brazil, and Department of
Engineering and Technology of Food, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil

To design equipment for food processing and estimate process times for refrigerating, freezing, heating, or
drying of foods, the thermophysical properties must be known. Since the thermophysical properties of foods
are strongly dependent upon chemical composition and temperature, composition and temperature based
models provide a means of estimating these properties. In this work, the thermophysical properties of lemon
juice were determined at a water mass fraction of (0.381 to 0.900) and a temperature of (273.45 to 353.75)
K. Density and thermal conductivity varied from (962.3 to 1282.8) kg · m-3 and (0.344 to 0.624) W · m-2 · K-1,
respectively. Heat capacity and thermal diffusivity varied from (2446.5 to 4060.1) J · kg-1 · K-1 and
(0.1160 · 10-6 to 0.1785 · 10-6) m2 · s-1, respectively. Simple polynomial functions were fitted to the
experimental data, and good agreements were obtained. In the tested range, water content showed greater
influence on the thermophysical properties.

Introduction and Rippen,3 Mohsenin,4 and Singh.5 Measurements of CP are

often made by means of an adiabatic calorimeter,6,7 which is a
Lemon (Citrus limon L.) is one of the citrus fruits that has
simple technique although it requires a careful calibration. The
been increasing its consumption worldwide. It is cultivated in
differential scanning calorimeter is the best technique for
countries with proper temperature and dry climate such as the
experimental determination of CP of foods but has the disad-
United States, Argentina, Spain, Italy, and Japan. The production
vantage of being very expensive.8,9 A simple method can be
is destined for fresh fruit markets or processing juice units,
used to determine k, according to Bellet et al.10 The great
pectin, and essential oil. Lemon juice, fresh, concentrated and
advantage of this technique is that it is possible to determine
frozen, or dehydrated and powdered, is primarily used for
CP employing the same device and modeling the unsteady state
lemonade, carbohydrate beverages, or other drinks. It is also
heat transfer in the system.
used for confectionary and pharmaceutical products. The lemon
Thermal diffusivity can be determined according to its
cv. Tahiti (Citrus latifolia) is produced mainly in tropical
definition, given by the following equation
countries such as Brazil and Mexico. The state of São Paulo is
the largest Brazilian producer with approximately 81.3 % of k
the total lemon production.1 Rcal ) (1)
FCP
The design and control of equipment for processing such
juices are difficult due to the lack of information on the behavior where Rcal is the calculated thermal diffusivity.
of the thermophysical properties with composition and temper- This method has the inconvenience of adding up the
ature. Simulation fails since the models derived from the experimental errors involved in each one of the primary physical
concepts of material conservation need such information. quantities. Alternatively, thermal diffusivity can be measured
Equipment size is usually overestimated to compensate for this directly using a transient heating technique developed by
lack of information, leading to a nonideal design with cost Dickerson.11 Singh5 discusses this and some other approaches
implications as well as inferior quality of the product. used in determining thermal diffusivity of foods as well as the
In general, modeling, optimization, and control of food main sources of errors involved.
processes is difficult due to the complexity of the raw materials Thermophysical properties of lemon juice are very scarce in
and products involved, which affect thermophysical properties the literature, and an extensive work of the dependence of such
such as density F, specific heat CP, thermal conductivity k, and properties on temperature and the water content has not yet been
thermal diffusivity R. Besides, these thermophysical properties published. In an attempt to fill this gap, the objective of this
exhibit substantial changes with temperature and water content work was to measure the thermophysical properties (F, k, CP,
during processing. These are the major properties required for and R) of lemon juice as a function of temperature T and water
designing heat transfer processes, such as refrigeration, freezing, mass fraction w and to develop simple empirical correlations
heating, or drying,2 and for purposes of optimization and control. for predicting these properties.
An extensive review of existing methods for measurement
of thermophysical properties of foods has been done by Reidy Experimental Section
Materials. Lemon juice was extracted from Lemons cv. Tahiti
* Corresponding author. Tel.: +55 31 3899 1617. Fax: +55 31 3899 2208. with the following chemical composition (mass fraction): water,
E-mail: lminim@ufv.br.
†
Universidade Federal de Viçosa. 88.0 %; total soluble solids (organic acids and sugars), 9.8 %;
‡
Universidade Estadual Paulista. protein, 1.0 %; dietary fiber, less than 0.1 %; and ash, 0.4 %;
10.1021/je900155c CCC: $40.75  2009 American Chemical Society
Published on Web 05/11/2009
2270 Journal of Chemical & Engineering Data, Vol. 54, No. 8, 2009

solution of the differential equation with the proper boundary

conditions is presented in detail by Bellet et al.10
(c) Density (G). Gravimetric determination of lemon juice
density at different temperatures and concentrations was con-
ducted using an analytical balance with a given uncertainty of
( 0.0001 g and a standard volumetric pycnometer.8 The
pycnometer was previously calibrated with distilled water, at
each temperature.
(d) Thermal DiffusiWity (r). Thermal diffusivity was deter-
mined using the method proposed by Dickerson.11 The experi-
Figure 1. Cross section of the cell used for thermal conductivity and specific mental apparatus consisted of a cylindrical cell (24.75 · 10-3 m
heat measurements.
internal radius and 248.5 · 10-3 m length) made of chromium-
plated brass with two nylon covers with thermal diffusivity of
total titratable acidity (expressed as citric acid), 0.69 %; density 1.09 · 10-7 m2 · s-1, which is similar to most liquid food products.
of 1064.4 kg · m-3; and pH of 2.98. All the experimental Two thermocouples type T were fixed at the center and on the
measurements were made using samples from the same batch external surface of the cell. The cell was immersed in a well-
of concentrated lemon juice (37.4 % water mass fraction). The agitated thermostatic bath (MK70, MLW, Dresden, Germany)
concentration process was performed using a rotoevaporator, heated at a constant rate, and the evolution of temperatures at
under vacuum. In the industrial practices, it is usual to the wall and at the center of the cell was monitored. Temper-
characterize fruit juices mainly according to their water and atures were monitored employing the same data acquisition
soluble solids contents. To obtain different concentrations, system previously specified.
concentrated juice was diluted with distilled water, and an
analytical balance (Shimadzu AUX220, Japan) was used with Results and Discussion
an uncertainty of ( 0.0001 g. The standard uncertainty of the Specific heat, thermal conductivity, thermal diffusivity, and
concentration measurements was ( 0.52 %. A complete factorial density of lemon juice with w of (0.381, 0. 443, 0.522, 0.594,
design was conducted with eight levels of T [(273.45 to 353.75) 0.650, 0.712, 0.794, and 0.90) were determined in triplicate at
K] and eight levels of w (0.381 to 0.90). The thermophysical (273.45, 282.25, 295.35, 304.25, 314.95, 327.05, 339.65, and
properties were measured in triplicate for each value of T and 353.75) K, adding up to 192 experimental values of each thermal
w adding up 192 experiments. All statistical analysis was property.
performed using the GLM (General Linear Model) procedure, Tables 1 include experimental values and respective standard
while fitted functions were obtained by using the REG (RE- deviations between triplicate measurements for F, k, CP, and R
Gression) procedure from the SAS statistical package.12 The of the system studied as related to T and w.
suitability of the fitted functions was evaluated by the level of Polynomial models for the thermophysical properties as a
significance (p), the coefficient of determination (R2), and function of T and w were fitted to the experimental data.
residual analysis. According to Fikiin and Fikiin,13 the influence of the different
Apparatus and Methods. (a) Thermal ConductiWity. Thermal solid components of foods on thermophysical properties is
conductivity at various T and w was measured using the method usually negligible, and the food material can be seen as a system
described by Bellet et al.,10 based on a cylindrical cell, where formed by only two components, water and solids. The quadratic
the liquid whose properties are being determined fills the annular complete model was first analyzed, and the nonsignificant
space between two concentric cylinders. The equipment, shown parameters were eliminated based on the t (student) test and p
in Figure 1, presented the following physical characteristics: > 0.05. The final models are presented by a polynomial like eq
two coaxial copper cylinders (A and B), 180 mm length, 2. Table 2 shows the coefficients of eq 2 for F, CP, k, and R.
separated by a 2 mm annular space, which was filled with the
sample; 50 mm thick covers (C) made of a low thermal Ψ )
0 -
1(T/K) -
2w +
3w2 +
4(T/K)·w
conductivity material (0.225 W · m-1 · K-1) to prevent axial heat (2)
transfer; an inner cylinder (A) containing a heater (D) made
with a constantan wire (resistance 15 Ω), electrically insulated where Ψ is the thermophysical property.
by a varnish and coiled around a copper stick; two thermo- The agreement between experimental and calculated values
couples type T (E) to measure temperature differences between for the thermophysical properties was very good. Figures 2 to
the two cylinders, located at half-length of the cell. The wires 5 show the relative deviations between observed and predicted
were placed inside 0.5 mm gaps, parallel to the cell axis. values of F, CP, k, and R. In all cases, despite its simplicity, eq
To keep the external temperature constant, the cell was 2 with the associated parameters in Table 2 was found to
immersed in a constant temperature water bath (MK70, represent accurately the physical properties of lemon juice in
MLW, Dresden, Germany) controlled within ( 0.05 K. The the studied range of T and w, with the determination coefficient
power input to the heater resistance was made by means of (R2) superior to 0.98. The present properties all lie within ( 4
a microprocessed, stabilized source (ETB-252, Entelbra, Sao % of the correlations and agree well with most of the observed
Paulo, Brazil), which permitted us to adjust the current with data.
a stability of 0.05 %. An HP data logger model 75.000-B, The properties studied here varied from (962.3 to 1282.8)
an interface HP-IB, and an HP PC running a data acquisition kg · m-3 for density, (0.344 to 0.624) W · m-1 · K-1 for thermal
program written in IBASIC monitored temperatures with a conductivity, (2446.5 to 4060.1) J · kg-1 · K-1 for heat capacity,
standard uncertainty of ( 0.6 K. and (0.116 · 10-6 to 0.178 · 10-6) m2 · s-1 for thermal diffusivity.
(b) Specific Heat (CP). The apparatus described above was The reported values are of the same order of magnitude as the
also used to measure specific heat. Considering unsteady heat values reported by Telis-Romero et al.14 for orange juice.
conduction through an isotropic, homogeneous medium, the It was observed that F decreased with both T and w. The
equation of energy conservation was written for the system. The variables k and CP increased linearly with T and w, and R
 Journal of Chemical & Engineering Data, Vol. 54, No. 8, 2009 2271

Table 1. Density G, Thermal Conductivity k, Heat Capacity CP, and Diffusivity r of Lemon Juice and Associated Standard Deviation of
Triplicate Measurements for Different Temperatures and Water Contents
T F k CP 106R
-3 -1 -1 -1
K w (kg · m ) (W · m · K )
2
(J · kg · K ) (m2 · s-1)
273.45 0.900 1000.6 ( 1.3 0.527 ( 0.003 3843.6 ( 11.0 0.139 ( 0.002
282.25 0.900 1004.2 ( 2.3 0.542 ( 0.005 3828.1 ( 27.4 0.142 ( 0.004
295.35 0.900 993.4 ( 2.7 0.564 ( 0.006 3938.1 ( 33.3 0.156 ( 0.005
304.25 0.900 982.5 ( 1.7 0.569 ( 0.003 3923.3 ( 11.3 0.155 ( 0.003
314.95 0.900 979.0 ( 1.8 0.582 ( 0.003 3951.0 ( 11.3 0.159 ( 0.003
327.05 0.900 974.1 ( 3.2 0.591 ( 0.007 3929.5 ( 34.6 0.162 ( 0.006
339.65 0.900 963.4 ( 2.0 0.604 ( 0.006 4027.9 ( 27.3 0.174 ( 0.004
353.75 0.900 967.7 ( 1.2 0.621 ( 0.003 4051.4 ( 11.6 0.171 ( 0.002
273.45 0.794 1053.0 ( 2.4 0.498 ( 0.005 3524.1 ( 25.2 0.132 ( 0.003
282.25 0.794 1043.2 ( 2.8 0.511 ( 0.005 3582.1 ( 21.7 0.143 ( 0.004
295.35 0.794 1031.8 ( 1.9 0.525 ( 0.003 3616.0 ( 10.4 0.144 ( 0.003
304.25 0.794 1038.5 ( 1.3 0.542 ( 0.003 3639.0 ( 10.5 0.148 ( 0.002
314.95 0.794 1023.8 ( 3.1 0.546 ( 0.005 3630.4 ( 26.0 0.150 ( 0.005
327.05 0.794 1038.6 ( 3.7 0.574 ( 0.006 3722.0 ( 28.3 0.162 ( 0.006
339.65 0.794 1003.6 ( 3.0 0.566 ( 0.003 3730.6 ( 10.8 0.159 ( 0.005
353.75 0.794 1018.4 ( 1.3 0.589 ( 0.003 3767.1 ( 10.8 0.162 ( 0.002
273.45 0.712 1084.1 ( 2.9 0.468 ( 0.005 3295.1 ( 29.1 0.128 ( 0.004
282.25 0.712 1072.3 ( 2.3 0.488 ( 0.005 3478.8 ( 55.6 0.139 ( 0.003
295.35 0.712 1080.9 ( 1.4 0.503 ( 0.003 3384.9 ( 11.0 0.139 ( 0.002
304.25 0.712 1062.1 ( 2.7 0.506 ( 0.003 3407.9 ( 11.2 0.143 ( 0.004
314.95 0.712 1084.0 ( 2.8 0.528 ( 0.006 3389.5 ( 32.9 0.144 ( 0.004
327.05 0.712 1048.9 ( 2.3 0.529 ( 0.005 3489.4 ( 23.7 0.155 ( 0.004
339.65 0.712 1072.5 ( 1.9 0.553 ( 0.003 3499.2 ( 11.4 0.153 ( 0.003
353.75 0.712 1038.2 ( 2.5 0.548 ( 0.003 3535.5 ( 11.6 0.155 ( 0.004
273.45 0.650 1106.7 ( 2.0 0.446 ( 0.002 3162.7 ( 10.3 0.127 ( 0.003
282.25 0.650 1127.3 ( 2.9 0.467 ( 0.005 3164.2 ( 25.3 0.129 ( 0.004
295.35 0.650 1113.2 ( 3.0 0.484 ( 0.004 3250.7 ( 24.7 0.140 ( 0.004
304.25 0.650 1105.2 ( 3.3 0.487 ( 0.006 3198.7 ( 31.0 0.137 ( 0.005
314.95 0.650 1091.2 ( 2.2 0.499 ( 0.004 3291.1 ( 22.3 0.147 ( 0.003
327.05 0.650 1106.0 ( 1.5 0.517 ( 0.002 3300.9 ( 10.8 0.145 ( 0.002
339.65 0.650 1094.0 ( 1.3 0.525 ( 0.003 3333.4 ( 10.9 0.148 ( 0.002
353.75 0.650 1073.5 ( 2.1 0.527 ( 0.003 3369.8 ( 11.0 0.150 ( 0.003
273.45 0.594 1147.5 ( 3.1 0.428 ( 0.005 2972.7 ( 28.8 0.123 ( 0.004
282.25 0.594 1119.2 ( 2.9 0.434 ( 0.003 3045.7 ( 18.4 0.132 ( 0.004
295.35 0.594 1154.0 ( 1.9 0.465 ( 0.002 3069.5 ( 10.0 0.132 ( 0.002
304.25 0.594 1119.9 ( 4.5 0.460 ( 0.005 3061.5 ( 24.5 0.133 ( 0.006
314.95 0.594 1132.5 ( 0.8 0.481 ( 0.001 3120.0 ( 5.1 0.139 ( 0.001
327.05 0.594 1126.8 ( 0.8 0.490 ( 0.001 3130.3 ( 10.5 0.142 ( 0.001
339.65 0.594 1129.3 ( 2.1 0.507 ( 0.004 3214.9 ( 13.9 0.142 ( 0.003
353.75 0.594 1109.7 ( 3.4 0.504 ( 0.006 3177.0 ( 19.3 0.152 ( 0.005
273.45 0.522 1190.0 ( 0.8 0.407 ( 0.001 2839.0 ( 5.6 0.122 ( 0.001
282.25 0.522 1199.4 ( 1.9 0.421 ( 0.001 2843.2 ( 4.6 0.125 ( 0.002
295.35 0.522 1186.5 ( 0.8 0.434 ( 0.001 2877.0 ( 4.6 0.129 ( 0.001
304.25 0.522 1173.4 ( 3.0 0.439 ( 0.003 2900.0 ( 14.4 0.129 ( 0.004
314.95 0.522 1169.3 ( 3.2 0.451 ( 0.005 2946.7 ( 24.3 0.138 ( 0.005
327.05 0.522 1163.4 ( 2.9 0.460 ( 0.004 2958.8 ( 14.7 0.134 ( 0.004
339.65 0.522 1150.7 ( 3.1 0.466 ( 0.005 2991.3 ( 20.7 0.143 ( 0.004
353.75 0.522 1155.8 ( 0.8 0.476 ( 0.002 2987.1 ( 16.3 0.140 ( 0.001
273.45 0.443 1251.1 ( 1.9 0.379 ( 0.001 2626.5 ( 5.2 0.118 ( 0.002
282.25 0.443 1239.4 ( 0.9 0.386 ( 0.001 2632.0 ( 4.3 0.120 ( 0.001
295.35 0.443 1225.8 ( 3.1 0.397 ( 0.003 2665.8 ( 13.2 0.122 ( 0.003
304.25 0.443 1223.1 ( 3.4 0.406 ( 0.004 2688.8 ( 18.6 0.130 ( 0.004
314.95 0.443 1234.9 ( 1.3 0.420 ( 0.001 2698.3 ( 9.0 0.128 ( 0.001
327.05 0.443 1233.9 ( 2.2 0.434 ( 0.003 2774.5 ( 10.4 0.129 ( 0.002
339.65 0.443 1215.4 ( 1.0 0.436 ( 0.001 2780.1 ( 2.2 0.133 ( 0.001
353.75 0.443 1194.2 ( 1.4 0.436 ( 0.001 2778.8 ( 15.2 0.134 ( 0.002
273.45 0.381 1271.8 ( 1.5 0.346 ( 0.002 2459.6 ( 11.4 0.117 ( 0.002
282.25 0.381 1282.0 ( 1.1 0.359 ( 0.001 2466.3 ( 2.0 0.118 ( 0.001
295.35 0.381 1268.0 ( 0.7 0.369 ( 0.000 2500.1 ( 2.0 0.121 ( 0.001
304.25 0.381 1265.1 ( 1.8 0.377 ( 0.002 2523.0 ( 6.2 0.121 ( 0.002
314.95 0.381 1260.7 ( 0.9 0.385 ( 0.001 2533.7 ( 5.0 0.125 ( 0.001
327.05 0.381 1248.7 ( 1.4 0.395 ( 0.001 2607.1 ( 9.7 0.127 ( 0.001
339.65 0.381 1257.2 ( 0.8 0.403 ( 0.001 2579.4 ( 14.1 0.127 ( 0.001
353.75 0.381 1257.0 ( 2.5 0.415 ( 0.001 2650.7 ( 2.1 0.130 ( 0.003

Table 2. Coefficients of Equation 2

0
1
2
3
4 R2
F/(kg · m-3) 1582.28203 ( 10.15165 -0.4419 ( 0.0257 -891.38227 ( 33.14545 272.44025 ( 25.86346 0.0 0.990
k/(W · m2 · K-1) 0.20923 ( 0.00248 0.000966 ( 0.000023 0.37379 ( 0.0036 0.0 0.0 0.985
CP/(J · kg-1 · K-1) 1415.65004 ( 9.32724 2.45612 ( 0.08533 2695.9344 ( 13.5325 0.0 0.0 0.995
106R/(m2 · s-1) 0.09809 ( 0.00109 0.0 0.04787 ( 0.00179 0.0 0.00046155 ( 0.0000164 0.924

decreased linearly with w and increased with T. In all cases, w Thermal diffusivities were also calculated according to the
presented a larger impact on the thermal properties of lemon definition given by eq 1 and with the fitted polynomial function
juice than T. This fact was also reported in other works.2,14,15 given by eq 2. The relative average error between the calculated
2272 Journal of Chemical & Engineering Data, Vol. 54, No. 8, 2009

Figure 2. Fractional deviations ∆F ) (Fobs - Fpred) of the observed Figure 5. Fractional deviations ∆R ) (Robs - Rpred) of the observed densities
densities Fobs of lemon juice as a function of Fobs. · · · , uncertainty of Robs of lemon juice as a function of Robs. · · · , uncertainty of eq 2.
eq 2.

polynomial functions were successfully fitted to the experimental

data, thus thermophysical properties estimation for lemon juice
using the models developed in this work is recommended,
considering the range of T and w investigated. k and CP
increased with increasing T and w. On the other hand, F of lemon
juice decreased with increasing w and T, and R decreased with
w. The water mass fraction showed a higher influence on the
thermophysical properties than T.

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Theodoro, V. C. A. Chemical composition and Tahiti lime industrial
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V. R. N.; Telis-Romero, J. Density, heat capacity and thermal
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(11) Dickerson, R. W. An apparatus for measurement of thermal diffusivity
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(12) SAS Institute Inc. SASUser’s guide: Statistics, Version 9 edition; Cary,
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(13) Fikiin, K. A.; Fikiin, A. G. Predictive equations for thermophysical
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Figure 4. Fractional deviations ∆CP ) (CP,obs - CP,pred) of the observed (14) Telis-Romero, J.; Telis, V. R. N.; Gabas, A. L.; Yamashita, F.
densities CP,obs of lemon juice as a function of CP,obs. · · · , uncertainty of Thermophysical properties of brazilian orange juice as affected by
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Received for review February 9, 2009. Accepted April 17, 2009. The
Conclusions authors wish to thank FAPESP - SP and FAPEMIG - MG for the
financial support.
In this paper, the effect of T and w on the thermophysical
properties (F, CP, k, and R) of lemon juice were studied. Simple JE900155C