Spreadsheet to illustrate the application of relaxation methods for multicomponent distillation separations

Rigorous calculation methods to simulate multicomponent distillation processes involve large number of variables and equations that are difficult to solve by hand and require the use of specific software. With this purpose, commercial process simulators have been included for years as learning tools in the syllabus of Chemical Engineering degrees. Nevertheless, there is thus a possibility of using these packages as a black box and strategies to mitigate that risk have been developed, as the use of spreadsheets where students can follow and check the calculation algorithms and the details of such calculations. One alternative to solve multicomponent distillation problems is the use of relaxation methods, that find the steady-state solution of a continuous distillation column by solving unsteady-state equations from a specified initial condition, thus providing an analogy with the column startup. In this work, a novel spreadsheet to apply a relaxation method is proposed. Calculation begins with the simulation of a distillation column at total reflux, which is a common way to start up these processes. In order to facilitate the development of unsteady-state equations and operation, a batch distillation column is also simulated. Finally, the evolution of a continuous distillation column from a specified starting condition to steady-state is simulated

Secondary school preservice teachers’ references to the promotion of creativity in their master’s degree final projects

International audienceWhat do preservice teachers think about creativity and the ways to promote it in their classes? In this study, we analyze the references to creativity that appear in the master’s degree final projects of a group of secondary school preservice teachers of mathematics. The projects hold the preservice teachers’ reflections on their own practice, but it is important to note that the master’s degree does not include any specific training in creativity. In our analysis, we first searched for explicit references to creativity in the projects and registered them. Then, we classified the comments depending on the elements of the teaching and learning process that are related to creativity in each case. We observe a good variety of comments and more than half of the preservice teachers mention creativity, although some of them just do it superficially

Strategies proposed by preservice teachers to foster their students’ creativity

In this study, we aim to analyse the preservice teachers’ perspectives on creativity, in particular, if they consider that creativity can be developed, and their strategies to foster students’ creativity. The participants are 43 preservice teachers who were taking a master’s degree to become teachers of secondary school. The master’s program did not include a specific training in creativity. They answered a questionnaire about creativity and then three of them were interviewed. We did a content analysis of their answers. Most of the preservice teachers think that creativity can (and should) be developed in the mathematics classroom. They suggest different strategies to foster students’ creativity that agree with literature, but solving open-ended problems stands out among the rest of strategies.This work is part of the research project PGC2018-098603-B-I00 (MCIU/AEI/FEDER, UE), with the support of the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya and the European Social Fund (2020FI_B2 00017)

Liquid–Liquid Equilibria of Water + Ethanol + 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)imide Ternary System: Measurements and Correlation at Different Temperatures

In this work authors present the experimental liquid–liquid equilibria (LLE) data of water + ethanol + 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([bmim][Tf2N]) system at different temperatures. The LLE of the system was obtained in the temperature range from 283.2 to 323.2 K. The nonrandom two liquid (NRTL) and universal quasichemical (UNIQUAC) models were used to correlate ternary systems. The equilibrium compositions were successfully correlated by the interaction parameters from both models, however UNIQUAC gave a more accurate correlation. Finally, a study about the solvent capability of ionic liquid was made in order to evaluate the possibility of separating the mixture formed by ethanol and water using that ionic liquid.Financial support from the Ministerio de Ciencia y Tecnología of Spain, through Project No. CTQ2010-18848/PPQ and the FEDER European Program are gratefully acknowledged

El papel de la creatividad de los alumnos en la reflexión didáctica de futuros profesores de matemáticas sobre su propia práctica

El objetivo general de nuestra investigación, de la cual este trabajo es una parte inicial y exploratoria, es estudiar cómo el desarrollo de la competencia en análisis e intervención didáctica (Breda, Pino-Fan y Font, en prensa) se relaciona con el desarrollo de la competencia para el desarrollo de secuencias didácticas que promuevan el pensamiento matemático creativo en los alumnos de secundaria. El objetivo específico del trabajo que se presenta es caracterizar el tipo de reflexión didáctica que lleva a un grupo de futuros profesores de matemáticas, del máster de formación del profesorado de secundaria, a tener en cuenta la creatividad en sus trabajos de fin de máster (TFM), cuando justifican, utilizando los criterios de idoneidad didáctica propuestos por el Enfoque Ontosemiótico de la cognición e instrucción matemática (Godino, Batanero y Font, 2007), una propuesta de mejora de la unidad didáctica que previamente han implementado. Se usa una metodología de investigación cualitativa que se basa en la comprensión e interpretación de los datos extraídos de los TFM de cinco generaciones de alumnos del máster. Los análisis realizados muestran, según el criterio de idoneidad didáctico que se quiere mejorar, diferentes maneras implícitas de entender y promover la creatividad

Formación de equipos de trabajo eficaces a través de la cocina

El presente trabajo se ha desarrollado conjuntamente con alumnos de la asignatura obligatoria “Gestión Integrada y Seguridad Industrial” del Máster de Ingeniería Química y la asignatura optativa de cuarto curso “Gestión Integrada en la Industria Química” del grado de Ingeniería Química. Se ha diseñado una actividad práctica con el fin de aplicar los conceptos teóricos impartidos en estas asignaturas. Con el reto de cocinar un Mug Cake o “bizcocho en taza” se ha logrado poner en práctica varios de los contenidos teóricos de las asignaturas, especialmente el capítulo 7 de la norma ISO 9001:2008, “Realización del producto”; así como otros conceptos de liderazgo y mejora continua. Los alumnos se dividieron en dos equipos formados por el mismo número de miembros y en los que se mantenía el mismo número de alumnos del grado y del máster. Previamente a la realización del taller los alumnos elaboraron una serie de procedimientos, registros y listados de verificación. La experiencia ha resultado altamente fructífera puesto que los alumnos se han enfrentado al reto de aplicar contenidos teóricos a procesos reales, ha mejorado su motivación e interés por la materia y han desarrollado técnicas de trabajo en equipo y organización personal aumentando su productividad

Effect of temperature on the phase-separation ability of KCl in aqueous two-phase systems composed of propanols: Determination of the critical temperature and extension of the results to other salts

The phase-forming ability of KCl in propanols has been investigated, aiming to assess its utility in aqueous two-phase extraction. Equilibrium data of the different equilibrium regions (SLLV, SLV, LLV, and LV) of aqueous two-phase systems (ATPSs) of water + KCl + 1-propanol and water + KCl + 2-propanol have been determined at the boiling temperatures of the mixtures and 101.3 kPa. In addition, the lowest critical solution temperature (LCST) for the water + KCl + 1-propanol system was measured to be 271.2 K, and the equilibrium behavior of the system in the vicinity of the LCST (at 268.1 and 273.1 K) was also determined. Finally, using various methods such as the effective excluded volume (EEV) theory, Setchenov-type equations, and the plait point of the liquid-liquid region, different salt and alcohol systems have been studied and classified according to their ability to produce ATPSs.We would like to thank the ‘‘Dirección General de Investigación Científica y Técnica” DGICYT, of Spain for the financial support under project CTQ2014-59496

Influence of the temperature on the equilibrium phase diagram of the ternary system water + ammonium chloride + 2-propanol at 101.3 kPa

The phase equilibrium of the water + NH4Cl + 2-propanol mixture, at a constant pressure of 101.3 kPa, has been determined isothermally at four temperatures, as well as at the boiling temperature. Transitions between the different regions of the isothermal equilibrium diagrams have been studied, and the lowest temperature at which the salt can split water + 2-propanol mixtures into two liquid phases, is found to be 310.1 K. As the temperature is increased from this critical value, the two-liquid-phase region expands until the boiling temperature is reached. Finally, the extended UNIQUAC model for electrolytes has been used to predict the equilibrium diagram of the system. Large discrepancies with the experimental results have been found, and it will, therefore, be necessary to review the parameters of the model based on the experimental data reported in this work.We would like to thank the DGICYT of Spain for the financial support of project CTQ2014-59496

What errors do prospective teachers detect in their mathematics lessons?

MINECO/FEDER, UE, Research Project PGC2018-098603-B-I00