From literature, we know that making the connections between mathematics and physics is not trivial for most students, even at the advanced level. In the specific context of partial derivatives in thermodynamics, research suggests that making explicit connections between the mathematics and the physics is necessary to foster student understanding.…

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…

Two bodies initially at different temperatures gathered into an isolated container exchange heat and reach an equilibrium state with a common final temperature. During the process, the system is out of equilibrium and its intermediate temperature is not well defined. By conceiving a quasi-static process with infinitesimal steps from the initial to…

One way to develop a cross-curricular lesson is to select the most common mathematical formulas used in science and carefully develop and implement tasks that allow students to make connections between the mathematical representations and theoretical/physical science concepts. The slope-intercept formula, which is used to study relationships…

Spontaneity criteria for processes with useful (especially electrical) work have been discussed based on total differentials of thermodynamic functions. Reaction Gibbs energy ([Delta][subscript r]G) and electrochemical reaction Gibbs energy ([Delta][subscript r]G~) have been juxtaposed. Three-dimensional graphs showing the dependencies of…

Chemical equilibrium is one of the most important concepts in chemistry. The changes in properties of the chemical system at equilibrium induced by variations in pressure, volume, temperature, and concentration are always included in classroom teaching and discussions. This work introduces a novel, geometrical approach to understanding the…

The double-wall paper cup is an everyday object that can be used in the laboratory to study heat transfer. The experiment described here has been done by physics students aged 12-13 years; it can also be used in a different context to prompt debate about environmental issues.

Science students need exposure to activities that will help them to become familiar with phenomena exhibiting exponential decay. This paper describes an experiment that allows students to determine the rate of thermal energy loss by a hot object to its surroundings. It requires limited equipment, is safe, and gives reasonable results. Students…

It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process…

The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…

This is a companion to our previous paper in which we give a published example, based primarily on Perry's work, of a graph of ln "y" versus "t" when "y" is an exponential function of "t". This work led us to the idea that Lord Kelvin's (William Thomson's) estimate of the Earth's age was…

G, G°, [delta][subscript r]G, [delta][subscript r]G°, [delta]G, and [delta]G° are essential quantities to master the chemical equilibrium. Although the number of publications devoted to explaining these items is extremely high, it seems that they do not produce the desired effect because some articles and textbooks are still being written with…

This paper presents a comparative study of the thermal efficiencies of mechanical heat engines by using a graphical approach based on the pressure-volume ("P-V") diagram. Three types of idealized thermodynamic cycles--the Otto, the Diesel and the Brayton--are compared in pairs. Given the same temperature range within which the engines…

During the years 1873-1879, J. Willard Gibbs published his now-famous set of articles that form the basis of the current perspective on chemical thermodynamics. The second article of this series, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces," published in 1873, is particularly notable…

Entropy analyses as a function of the extent of reaction are presented for a number of physicochemical processes, including vaporization of a liquid, dimerization of nitrogen dioxide, and the autoionization of water. Graphs of the total entropy change versus the extent of reaction give a visual representation of chemical equilibrium and the second…