Calculation of the Heat Generated During Experiment in an Isoperibolic Calorimeter

SUPPLEMENTARY DATA

Influence of superplasticizers on the course of Portland cement hydration

Pavel Šiler[(], Iva Kolářová, Josef Krátký, Jaromír Havlica, Jiří Brandštetr

Centrum for Materials Research, Faculty of Chemistry, Brno University of Technology, Purkyňova 118, 621 00 Brno, Czech Republic

Received 18 October 2012; Revised 8 February 2013; Accepted 13 March 2013

Calculation of the heat generated during experiment in an isoperibolic calorimeter

Calculation of the heat generated during the cement paste hydration provides some presumptions: the uncertain one is that the heat capacity of the system (H2O and cement) does not change during the experiment either due to the temperature change or the physico–chemical changes in the system. In Pytlík (2000), this assumption was used to calculate the temperature change of concrete, it also enables neglecting the influence of the heat capacity of the system when the temperature of the starting material and that at the end of the experiment are equal.

Quantitative determination of the generated heat is based on the Tian equation (Krátký, 2004) Eq. (1), which, for isoperibolic calorimeter, has the form:

(1)

where TC is the temperature of the calorimetric cell, TS is the temperature of the surroundings, t is time, and K is the heat flow coefficient.

For the calculation of generated heat it is necessary to determine constant K. One of the methods for its determination is based on the measurement of the response of the system to constant heat input. The heat input can be achieved by a constant voltage or current source and a thermally stable resistor. Input heat can be calculated as:

(2)

where Q is the heat input, U is voltage, I is the current, R is the resistance of the heater, and t is time.

From Eq. (2), the heat flow (qINPUT) can be calculated (R, U, and I are constant):

(3)

To calculate constant K it is necessary to perform a series of experiments with changing voltage or current and plot the dependence of the temperature of the system near to the equilibrium on the respective parameter. The temperature response (Tc) to the constant heat input can be described by Eq. (4):

(4)

where A represents the maximum reachable temperature in t®¥, k is the velocity constant, and t is time.

Temperature difference according to Eq. (1) is adequate to the heat flow:

(5)

where the K constant can be calculated as the direction of temperature near the equilibrium dependence on the input heat flow.

Havlica (1986) pointed out that for practical reasons, the process in an isoperibolic calorimeter cannot take place in equilibrium (except for the specific states TC – TS = 0 or dT/dt = 0). This leads to a shift of the temperature response to the heat generated in the system. This is primarily the case of fast (tens of minutes) reaction peaks. For the measurements in tens of hours, this effect is almost negligible. To calculate the heat generated in the system, the fact of the unequilibrium state of system does not contribute to the calculated integral value significantly - the inaccuracy on the ascendant side of the curve is compensated by an inaccuracy on the descendant side.

The heat flow generated in the system can be calculated from Eq. (1), the heat difference can thus be calculated from:

(6)

The total heat can be calculated by numeric integration using the following equation (rectangle method):

(7)

The application of equations and considerations mentioned above is presented in the experimental part.

Heat input was achieved by putting a resistor into 300 g of cement paste made from 300 g of CEM I 42,5 Mokrá and 100 g of deionised H2O and supplying DC current from a stabilized voltage power source. The stabilized 2 × 40 V DC power source was used. For voltage and current monitoring, a digital multimeter was used. It was found that in the temperature range considered, the changes in the resistance, and thus also the changes in the heat input, were insignificant. The constant heat input was maintained for 12 h to ensure a state near the equilibrium between the heat income and the heat flow. The temperature range depends on the type of the resistor, on the power source used and on the quality of the thermal insulation envelope in question.

References

Havlica, J. (1986). Reaktivita a vlastnosti subsystémov sústavy CaO-MgO-SiO2-R2O3-H2O ako základu netradičných cementov. Bratislava, Slovakia: Slovenská Akedémia Vied. (in Slovak)

Krátký, J. (2004). Vliv přísad na vlastnosti anorganicko organických kompozitů. Ph.D. thesis, Vysoké Učení Technické, Brno, Czech Republic. (in Czech)

Pytlík, P. (2000). Technologie betonu. Brno, Czech Republic: Vysoké Učení Technické. (in Czech)

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