# Renewable Energy

## CONTENTS OF CURRICULUM UNIT 10.04.02

- Introduction
- Unit Objectives
- Global Climate Change & Sea Level Rise
- Thermal Expansion
- Buoyancy and Archimedes' Principle for Solids and Gases
- Natural Ventilation through Convection and Solar Power
- Solar Chimney Design and Operation
- Teaching Strategy
- Example Lessons
- Vocabulary List
- Appendix A
- Appendix B
- Endnotes
- Bibliography

### Unit Guide

## The Mathematics of Convection: Nature's Model for Energy Production

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## Introduction

Global warming burst into the American consciousness in the early 1990's, as the scientific community publicized that a significant correlation between temperature fluctuations and Carbon Dioxide (CO
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) levels in the atmosphere over the past 160,000 years was discovered in ice core samples. The "Greenhouse Effect" immediately took its place among the wars and diseases of the 20
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century as a potentially inevitable apocalyptic threat. Suddenly, the industrial gains of the 20
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century which built and sustained our communication, transportation, urban infrastructure and residential communities seemed to be eroding the foundation of human existence, planet earth.

The chilling explanation is simple: a delicate balance of gases form a barrier in earth's atmosphere that allows some solar radiation to be reflected away from the earth, and some radiation to be retained on the earth's surface. Our dependence upon fossil fuels and our propensity to steamroll nature has increased dramatically over the past century, producing an over-abundance of greenhouse gases such as methane, CO
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and nitrous oxide and a reduction in the amount of carbon-consuming vegetation on our planet. This process upsets the delicate balance of nature's carbon cycle and threatens to change our climate in ways that threaten human existence.

There are the technological means available to counter this threat that fall into two main categories of the energy regime: supply and demand. Supply-side measures focus on the extensive use of renewable resources; the main targets in curbing demand are buildings and transport.
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This unit is meant to equip students with analytical knowledge pertaining to availability and feasibility of specific alternative and renewable energy sources.

As the world's best and brightest scientists attempt to harness the diverse and abundant sources of renewable energy that exist on earth, humans continue to struggle with political and economic barriers to progress in developing renewable energy sources. This unit focuses on convection and its potential role in a future without fossil fuel dependence. Important relationships between convection currents and solar energy will be discussed in the unit. One model that uses solar energy to create convection currents is the solar chimney model, which is discussed in detail in this unit.

In the United States, our addiction to consumption has thrust us to the forefront of global responsibility on climate change issues. As more forest and prairie lands give way to suburban houses and strip malls, the ecological balance of our nation's exurban and rural areas becomes increasingly precarious.
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We are in desperate need of a multifaceted but focused approach to our fossil fuel problem. This unit deals with the mathematics involved in the socio-economic and political barriers that stand in the way of large-scale movements towards renewable energy sources as primary energy sources for humanity.

Furthermore, this unit brings the purpose of mathematics and science curriculum into focus for students, and creates built-in motivation for students to perform well when exploring and describing mathematical models, comparing the sizes of numbers and performing unit conversions. The unit allows students to explore the concepts of and relationships between volume, mass and density in real-world situations, providing rich opportunities for mathematical and scientific discourse.

This unit is designed to cover approximately 2 weeks of instruction for students in an intermediate to advanced Algebra 1 course. This unit could also be used as an interdisciplinary review sequence for students in a Geometry class to prepare students for standardized tests such as the Connecticut Academic Performance Test (CAPT). Specifically, the unit addresses the mathematics and science portions of the CAPT and aims to bolster students' problem solving skills. The unit could be modified to accommodate students in Algebra 2 or above, but care must be taken to develop appropriate grade-level and content-level materials and activities or to modify the ideas contained within the unit to serve the appropriate grade level.

During the unit, students will discover the answers to basic, yet scientifically critical questions such as: Why does warm air rise? Why does a 2-ton boat float while a 1-ounce rock sinks? What are the properties of water in liquid, gas or solid form? How does a hot air balloon fly? The answers to these questions will provide a foundation for students to advance their understanding of natural phenomena associated with convection. During the unit, student discourse will play a critical role in cooperative learning situations as students discuss and debate the results of experiments and calculations.

The unit takes an experimental approach and develops mathematical models to represent real-world phenomena. Valuable connections are made between scientific and mathematical concepts. Students learn about the complex relationships between buoyancy, density, temperature and volume. While exploring these relationships, students describe, compare and contrast the relationships using the properties of linear and quadratic functions. Students make predictions and draw conclusions about scientific experiments using mathematical models. Through this process, they discover critical scientific concepts and use mathematics to make conjectures and develop evidence to support their conclusions.

During the unit, students perform simple scientific experiments and collect their own data. Students formulate educated opinions and debate the viability of their findings using research, mathematical calculations and physical observations as evidence. Students discover the importance of mathematics and science and the role they play in solving the worlds' most pressing problems. It is my hope as an educator that students develop a deeper sense of the importance of science, technology and mathematics careers. This unit should provide hope to students in a variety of ways. With careful analysis and a problem-solving approach, many problems can be solved or averted. Today's high-school students will become leaders of a world in crisis. Through this unit, students will be exposed to science and mathematics principles that they can apply directly. They will obtain perspective on the availability of meaningful and rewarding careers.

As we advance into the 21
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century, it becomes more and more apparent that our civilization must discover a healthy equilibrium with our ecosystem. In the United States, our addiction to consumption has thrust us to the forefront of global responsibility on climate change issues. As more forest and prairie lands give way to suburban houses and strip malls, the ecological balance of our nation's exurban and rural areas becomes increasingly precarious.
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Students' ideas about climate change, sustainable living, renewable energy and global warming will be significantly developed following this unit. Students will be able to analyze and discuss the consequences of continued reliance on fossil fuels as an energy source. Finally, students will learn about the efficiency and energy potential of natural phenomena such as convection and its implications for research and development of new renewable energy sources. Students will develop a respect for nature's methods for maintaining equilibrium and harmony in earth's ecosystem, and they will learn that humans are looking to nature as a primary blueprint for the development of renewable energy.