Environmental Process Analysis, 1: Residence Time and First Order Processes

Journal of Geoscience Education, Sep 2004 by Torgersen, T, Branco, B, Bean, J, Sytsma, R

ABSTRACT

The environment is a system of coupled physical, chemical and biological processes that yield either a change in the state of the system or a dynamic steady-state. The conservation of mass equation is used to quantify such dynamic systems and is presented here with the acronym 'IPOLA'. The time scale for a change in state of a system can be understood with the concept of residence time. We describe a simple salt flushing laboratory activity that allows detailed investigation of rates, processes and principles of dynamic systems for both the algebra-skilled student and the minimal-calculus prepared (high school and university) student. The activity focuses on the calculation and use of the residence time as a fundamental principle defining rates-of-change in systems ("How long will it take to...?"). The 'rules-of-thumb' (time to change by 50%, time to change by 95%) and simple estimates that can be made from real data (concentration vs. time) generated by this activity provide a useful starting point for the evaluation of the environment as a dynamic process with inherent timescales for change. Students are also introduced to conversion factors, instrument correction factors, analysis of real data and a problem solving approach based on 'IPOLA'.

INTRODUCTION

The interdisciplinary nature of environmental science offers opportunities to teach scientific approaches to natural problems. Science education requires methods that are consistent with the nature of scientific inquiry (AAAS, 1990) and research in science teaching (Abrams, 1998; Jones, 2000) suggests that guided, hands-on activities have significant value. With chemistry and physics, the fundamental principles of the discipline are often best illustrated through very controlled experiments and then elaborated upon with examples (but often not demonstrations) from the real world. In the environmental sciences, the ability to exert control is often severely limited and direct observation of (significant) environmental changes are typically beyond the time- or space-scale of the classroom. Nevertheless, the underlying principles of environmental analysis can be illustrated in the classroom. Such activities need to demonstrate not only environmental change, but also how fast change occurs in the system and how the rate of change can be quantified. This paper describes a laboratory activity for students to explore the fundamental environmental question(s) of "How fast... ?"

The conservation of mass equation (equation 1) leads directly to investigation of the pertinent environmental questions. Will the amount ('stuff', concentration, etc.) increase (A>0), decrease (A

We describe here a laboratory activity that has been designed to physically, mentally and linguistically engage secondary and post-secondary students in scientific inquiry. A decade or informal evaluations and feedback from students in an undergraduate environmental science course, indicates that this activity has successfully illustrated the fundamental observations and mathematical analysis necessary to quantify rates of change and residence times. This simple activity can be accomplished in 1.5 hours with multiple (5 or more) students participating. The mathematical analysis (assigned as homework) is described below. The activity generates multiple data sets that provide experience with scientific reasoning and quantification through the use of real data, instrumental artifacts, natural variability and precision. The activity is flexible enough to suit varying educational needs. There is a conceptual level that can be taught for students who have algebra and word problem experience (including high school students) and a more detailed analysis suitable for students with minimal calculus experience. Because of the pedagogic value inherent in the scientific discussions about the limitations and nuances of this activity, we strongly suggest that the instructor conduct the activity before conducting the activity with students.

BACKGROUND

The activity described below is designed to answer the following questions for a first order process:

1. How does change occur in the system?

2. How can the rate of change be quantified?

3. How long does it take to change the system?

4. What controls the time necessary to change the system?

5. How can we predict the time necessary to change the system?

For students with a background in algebra and units (word problems) only, the activity shown in figure 2 allows them to discover the fundamental principles and apply them in a simple algebraic context. Students with a minimal understanding of calculus and natural logarithms can proceed with a more sophisticated analysis that allows them to recognize first order processes, evaluate the appropriate rate constant and ascribe physical meaning to the rate quantified.

The goal of this activity is to make observations over time within a system to quantify λ and τ. These principles can then be applied where they cannot be explicitly observed in naturally occurring environmental systems. The quantification of λ or τ, specific to the system, thus generates knowledge that may be applicable at other times (same system) and other places similar system). Questions which help students prepare for the activity include: