Autores
Saraiva, W.S. (IFTO CAMPUS PARAÍSO DO TOCANTINS) ; Viroli, S.L.M. (IFTO CAMPUS PARAÍSO DO TOCANTINS) ; Ramos, M.L. (IFTO CAMPUS PARAÍSO DO TOCANTINS) ; Macedo, M.F.S. (IFTO CAMPUS PARAÍSO DO TOCANTINS)
Resumo
The volumetric expansion coefficient (β) is an important thermophysical property
for designing and dimensioning equipment that involves heat transfer. The
objective of this work was to determine the coefficient of volumetric expansion
of
pineapple, guava and mango pulps according to the specific masses and the
variation of temperatures from 10 to 60 °C, in concentrations of 15.00 °Brix,
8.50
°Brix and 12.05 °Brix respectively. The specific mass of the pulps was
determined
with the aid of pycnometers. The volumetric expansion coefficients were
performed
using the ratio In ρ0/ρ=β.(T-T0). The values of the specific gravity of the
pulps
decreased with the increase of the temperature and presented coefficients of
determination superior to 0.90, presenting a good fit.
Palavras chaves
pineapple; mango; guava
Introdução
The thermal expansion coefficient (β), specific mass, heat capacity and thermal
conductivity are thermal properties, as they are related to the reaction of
materials due to the application of heat (CALLISTER, 2008). The expansion
coefficient provides a measure of the density variation in response to a change
in temperature, under a condition of constant pressure (INCROPERA; DEWITT,
2008). The volumetric expansion coefficient (β) is an important thermophysical
property for designing, dimensioning equipment and processes that involve heat
transfer (MATTOS; MEDEROS, 2008). The knowledge of (β) allows to study the
variation in density in response to a change in temperature under constant
pressure, the expansion behavior, to evaluate the impacts on the volumetric
measurement system due to the temperature variation and to design equipment and
accessories, considering possible expansions resulting from strong temperature
changes (CANCIAM, 2014). Thus, based on the density data as a function of
temperature, it is possible to determine the coefficient of thermal expansion
(SANTOS; VIEIRA, 2010). In fruit processing, the adequate sizing of the
equipment represents excessive profit in terms of savings and energy. The
production, transport and storage of fruit pulps involve important
thermophysical properties for the correct dimensioning of the equipment intended
for these operations. In fruit processing, the adequate sizing of the equipment
represents excessive profit in terms of savings and energy. The production,
transport and storage of fruit pulps involve important thermophysical properties
for the correct dimensioning of the equipment intended for these operations.
(LIMA, 2003). It is essential to know the behavior of the specific mass of the
pulps in the processing conditions because it is changed during the transfer of
heat and mass during the processing of the food (BOLZAN; SOUZA, 2007). During
the pulp processing processes of heating, pasteurization, concentration and the
use of low temperatures are used to preserve the quality of these products.
(LIMA, 2003). The processing of fruit pulps is an economic activity that adds
value to the fruit, prevents waste and reduces losses during the sale of fresh
fruit (NASCIMENTO et al., 2013). The mathematical models for predicting
thermophysical properties represent an adequacy to increase the efficiency of
heat treatments in food processing and an alternative to replace the
experimental determination of these parameters, which can be very costly for the
industry (EGEA et al., 2015). The objective of this work was to verify the
existence of a linear correlation between the thermal expansion coefficient (β)
and the total solids content (º Brix) of the pineapple, guava and mango pulps
from the linear regression analysis of experimental data from specific gravity
as a function of temperature.
Material e métodos
This work was carried out at the General Chemistry Laboratory of the Federal
Institute of Tocantins - IFTO Paraíso do Tocantins campus, between the months of
May and December 2019. Pineapple, guava and frozen mango pulps were purchased at
local shops in the city of Paraíso do Tocantins –TO. The specific mass of the
guava and mango pulp were determined at temperatures of 10°C, 20°C, 30°C, 40°C,
50°C and 60°C, at a concentration of 15ºBrix for pineapple pulp, 8,60°Brix for
guava pulp and 12,05 °Brix for mango pulp. All experiments were carried out in
triplicate and for the calculation the average of the values obtained in the
experiments was used. The pycnometers were previously calibrated with distilled
water at each temperature of the experiment and the temperatures were controlled
through the thermostat bath and by means of the thermometers present in the
pycnometers themselves. The specific mass was calculated using Equation 1, which
establishes a relationship between mass and volume. ρ = m/v (1) in which, ρ -
Specific gravity of the product (kg.m-3); v - Volume of the
pycnometer (m3); m - Mass of the product (kg). To determine the
thermal expansion coefficient, equation 2 was used, following the same
methodology as Canciam (2012): In ρ0/ρ = β.(T-T0) (2) Where ρo and ρ correspond,
respectively, to the specific mass of the pulp at the initial temperature T0 and
the specific gravity of the pulp at the final temperature T. From these data it
is possible to obtain the volumetric expansion coefficient determined by the
line of the graph of In (ρ0/ρ) versus (T-T0) (CANCIAM, 2010).
Resultado e discussão
Tables 01, 02 and 03 and graphs 01, 02 and 03 show the experimental values of
the specific masses, volumetric expansion coefficients and the density
correlation coefficients as a function of the temperature of the pineapple,
guava and mango pulps.Canciam (2012 a) studying the correlation between the
coefficient of volumetric expansion and the total solids content for pineapple
juice of the Smooth Cayenne variety, between 17,4 and 85,8ºC, with a total
solids content of 11ºBrix, found the value 3,3930 x 10-4
ºC-1 for the volumetric expansion coefficient. Alves et al. (2017)
obtained specific masses equal to 1060,31Kg.m-3 to 1044,48
Kg.m-3 for guava pulp with 9,8°Brix and temperatures from 10°C to
50°C. Dantas Júnior et al. (2007), carrying out studies to predict the specific
mass of the mango at a temperature of 10°C to 50°C, found a variation from
1055,73 Kg.m-3 to 1009,38 Kg.m-3. Since (β) of pineapple
pulp is equal to 5,81x10-4, it means that the increase of 1ºC results
in an increase in volume of approximately 0,0581% (NETZ; ORTEGA, 2008). Thus,
following the same line of reasoning, the increase in the volume of the guava
and mango pulp ranged from approximately 0,0602% to 0,0760%. These values may
seem small, but in comparison with water, the increase in the volume of
pineapple, guava and mango pulp corresponds to 2,81%, 2,91% and 3,67%,
respectively, times greater than the increase in volume of water, considering
that (β) of water equals 2,07x10-4 ºC-1 (CABRAL; LAGO,
2002). According to Santos and Vieira (2010), from the knowledge of the thermal
expansion coefficient, it is possible to evaluate the impacts on the volumetric
measurement system. Thus, considering a volume of 1000 liters of water with a
temperature variation of 10ºC, the volume of water increases by around 2,1
liters. With this same reasoning, the volume of 1000 liters of pineapple juice
with 11ºBrix, with a temperature variation of 10ºC, the volume of this juice
increases by around 3,4 liters. Mercali et al. (2011) found that the specific
mass values decreased with increasing temperature, probably due to the
volumetric expansion of the fluid caused by the reduction of the intermolecular
force connection. Toledo and Ovalle (1985) comment that the correlation
coefficient module measures the degree of linear relationship between the paired
values of the dependent and independent variables in a sample, thus evaluating
the “quality” of the fit. That is, the closer it is to the unit, the better the
“quality” of the function's fit to the points of the scatter diagram. Lira
(2004) states that a linear correlation is classified as very strong when the
modules of the correlation coefficient values are between 0,90 and 1,0. Thus,
according to the author's classification, pineapple, guava and mango pulps
showed a very strong correlation.
Table 01 and graph 01 pineapple Table 02 and graph 02guava Table 03 and graph 03 mango
Conclusões
The values of the specific mass of the analyzed pulps decreased with increasing
temperature, ranging from 1051, 337 Kg.m-3 to 1078, 655
Kg.m-3 for pineapple pulp, 1035, 35 Kg.m-3 to 1062, 52
Kg.m-3 and 1037, 75 kg.m-3 at 1070, 31 kg.m-3
for
mango pulp being consistent with the behavior reported for fruit pulp in the
literature. The pineapple, guava and mango pulps showed volumetric expansion
coefficients equal to 5, 81 x 10-4 ºC-1, 6,02 x
10-3 ºC-1 and 7,60 X 10-4 ºC-1
respectively. The values found for the determination coefficients showed a
significant and very strong linear correlation.
Agradecimentos
To God, to the IFTO Paraíso do Tocantins campus
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