Search Results

You are looking at 1 - 10 of 32 items for

• Author or Editor: N. Liu
• Refine by Access: All Content
Clear All Modify Search

Approximations for the temperature integral

Their underlying relationship

Journal of Thermal Analysis and Calorimetry
Authors: H. Chen and N. Liu

Abstract

The temperature integral cannot be analytically integrated and many simple closed-form expressions have been proposed to use in the integral methods. This paper first reviews two types of simple approximation expressions for temperature integral in literature, i.e. the rational approximations and exponential approximations. Then the relationship of the two types of approximations is revealed by the aid of a new equation concerning the 1st derivative of the temperature integral. It is found that the exponential approximations are essentially one kind of rational approximations with the form of h(x)=[x/(Ax+k)]. That is, they share the same assumptions that the temperature integral h(x) can be approximated by x/Ax+k). It is also found that only two of the three parameters in the general formula of exponential approximations are needed to be determined and the other one is a constant in theory. Though both types of the approximations have close relationship, the integral methods derived from the exponential approximations are recommended in kinetic analysis.

Restricted access

A procedure to approximate the generalized temperature integral

Journal of Thermal Analysis and Calorimetry
Authors: H. Chen and N. Liu

Abstract

In the paper a new procedure to approximate the generalized temperature integral
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } \exp ( - E/RT)dT$$ \end{document}
, which frequently occurs in non-isothermal thermal analysis, are presented. A series of the approximations for the temperature integral with different complexity and accuracy are proposed from the procedure. For commonly used values of m in kinetic analysis, the deviation of most approximations from the numerical values of the integral is within 0.7%, except the first approximation (within 4.0%). Since they are simple in calculation and hold high accuracy, the approximations are recommended to use in the evaluation of kinetic parameters from non-isothermal kinetic analysis.
Restricted access

New approximate formulae for the generalized temperature integral

Journal of Thermal Analysis and Calorimetry
Authors: H. Chen and N. Liu

Abstract

The generalized temperature integral
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } \exp ( - E/RT)dT$$ \end{document}
frequently occurs in non-isothermal kinetic analysis. Here E is the activation energy, R the universal gas constant and T the absolute temperature. The exponent m arises from the temperature dependence of the pre-exponential factor. This paper has proposed two new approximate formulae for the generalized temperature integral, which are in the following forms:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{gathered} h_m (x) = \frac{x} {{(1.00141 + 0.00060m)x + (1.89376 + 0.95276m)}} \hfill \\ h_m (x) = \frac{{x + (0.74981 - 0.06396m)}} {{(1.00017 + 0.00013m)x + (2.73166 + 0.92246m)}} \hfill \\ \end{gathered}$$ \end{document}
where h m(x) is the equivalent form of the generalized temperature integral. For commonly used values of m in kinetic analysis, the deviations of the new approximations from the numerical values of the integral are within 0.2 and 0.03%, respectively. In contrast to other approximations, both the present approaches are simple, accurate and can be used easily in kinetic analysis.
Restricted access

Thermodynamic properties of the azeotropic mixture of acetone and methanol

Journal of Thermal Analysis and Calorimetry
Authors: Z. Nan, N. Liu, and Z.-C. Tan

Abstract

The molar heat capacities of the pure samples of acetone and methanol, and the azeotropic mixture composed of acetone and methanol were measured with an adiabatic calorimeter in the temperature range 78–320 K. The solid–solid and solid–liquid phase transitions of the pure samples and the mixture were determined based on the curve of the heat capacity with respect to temperature. The phase transitions took place at 126.160.68 and 178.961.47 K for the sample of acetone, 157.790.95 and 175.930.95 K for methanol, which were corresponding to the solid–solid and the solid–liquid phase transitions of the acetone and the methanol, respectively. And the phase transitions occurred at 126.580.24, 157.160.42, 175.500.46 and 179.740.89 K corresponding to the solid–solid and the solid–liquid phase transitions of the acetone and the methanol in the mixture, respectively. The thermodynamic functions and the excess thermodynamic functions of the mixture relative to standard temperature 298.15 K were derived based on the relationships of the thermodynamic functions and the function of the measured heat capacity with respect to temperature.

Restricted access

Kinetics of Direct Reduction of Chrome Iron Ore

Journal of Thermal Analysis and Calorimetry
Authors: Q. Lin, R. Liu, and N. Chen

Abstract

The kinetics of direct reduction of artificial chrome iron ore was studied by isothermal and non-isothermal methods. In the initial, middle and final periods, the reaction is controlled by nucleation and growth, a phase boundary reaction, and diffusion, respectively. In the main reaction region, the kinetic equation is 1–(1– )1/3=kt and the apparent activation energy is 270 kJ mol–1. The kinetic mechanisms found with the isothermal and non-isothermal methods do not differ, and the activation energy values are approximately the same. However, the non-isothermal method can demonstrate the kinetic process completely.

Restricted access

Error evaluation of integral methods by consideration on the approximation of temperature integral

Journal of Thermal Analysis and Calorimetry
Authors: N. Liu, H. Chen, L. Shu, and M. Statheropoulos
Restricted access

Wheat cultivars at different decades vary widely in grain-filling characteristics in Shaanxi Province, China

Cereal Research Communications
Authors: Y. Sun, X. Liu, S. Zhang, and N. Wang

Eight cultivars of dry-land wheat (Triticum aestivum L.) historically planted in Shaanxi Province, China, were grown in plots with irrigation and drought treatments during the growing seasons of 2011–2014, so as to characterize the differences in the rate and duration of the grain-filling stage among cultivars. The experimental results showed no obvious change among cultivars with respect to the duration of the grain-filling stage and no significant correlation between duration and grain weight. The filling rates of all three phases (lag, linear, and mature periods) showed significant differences among cultivars and had a greater effect on the grain weight than the duration of the filling stage, even though drought decreased the filling rate in the linear and mature periods. A lower filling rate led to a lighter grain weight in inferior grains than in superior grains. For the superior and inferior grains in the central spikelets, modern cultivars possess faster filling rates, especially in the lag and linear periods, whereas for the whole spike, no significant trend with cultivar replacement was observed. Faster filling rates with stable filling durations will be beneficial in obtaining additional yield increases.

Restricted access

Daily dietary intake of minor and trace elements by upper social groups in Taiwan

Journal of Radioanalytical and Nuclear Chemistry
Authors: S. Liu, C. Chung, J. Chuang, C. Wang, and N. Aras

Abstract

Sixteen minor and trace element contents of diet samples from three different social population groups in Taiwan were determined. Samples were prepared using duplicate portion technique by collecting the 15 subjects ate and drank during a 3-day period. Samples were homogenized, freeze-dried, and elemental concentration of minor and trace elements were determined by instrumental neutron activation analysis. Elemental concentrations and daily dietary intake of the elements were compared with those in the other nations, and possible origins were discussed.

Restricted access

Smoothing and differentiation of thermogravimetric data of biomass materials

Journal of Thermal Analysis and Calorimetry
Authors: H. Chen, N. Liu, L. Shu, and R. Zong

Abstract

Due to the experimental errors, the chemical effect of minor reactions, and some physical effects of heat and mass transfer, there usually exists much noise in the mass loss data resulted from thermal decomposition experiments, and thus high quality smoothing algorithm plays an important role in obtaining reliable derivative thermogravimetric (DTG) curves required for differential kinetic analysis. In this paper three smoothing methods, i.e. Moving Average smoothing, Gaussian smoothing, and Vondrak smoothing, are investigated in detail for pre-treatment of biomass decomposition data to obtain the DTG curves, and the smoothing results are compared. It is concluded that by choosing reasonable smoothing parameters based on the spectrum analysis of the data, the Gaussian smoothing and Vondrak smoothing can be reliably used to obtain DTG curves. The kinetic parameters calculated from the original TG curves and smoothed DTG curves have excellent agreement, and thus the Gaussian and Vondrak smoothing algorithms can be used directly and accurately in kinetic analysis.

Restricted access

Selenium determination in biological samples by X-ray emission spectroscopy

Journal of Radioanalytical and Nuclear Chemistry
Authors: N. Liu, S. Galassini, G. Moschini, M. Nagj, J. Injuk, and V. Valkovic

Abstract

Determination of Se in blood serum by PIXE and XRF is presented. Two different sample preparation methods combined with two modes of sample excitation are compared. Both methods are shown to be suitable for Se determination in blood serum and in standard reference materials (horse kidney IAEA H-8 and bovine liver NBS 1577a).

Restricted access