# 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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## Buoyancy and Archimedes' Principle for Solids and Gases

The discussion of Thermal Expansion and its relationship to density leads naturally into the concept of buoyancy. When an object is immersed in fluid, it either sinks, is neutral, or it floats. In the classroom, simple experiments will lead students to draw important conclusions about the relationships between density, volume and mass. Since density is defined mathematically as mass per unit volume, students can easily use numerical and proportional reasoning to predict whether or not an object will sink or float.

Since New Haven is an urban center with beaches and an active port, students are familiar with barges, boats and other types of sea-faring vessels. Discourse and investigations about the reasons why tremendously heavy ships and barges float on water while much lighter pebbles and rocks sink immediately bring the concept of buoyancy into focus for students. A ship, although it has an extremely large mass, will float since its large volume contains a large proportion of air. The ship is simply less dense than the salt water it travels upon; therefore, it floats.

A broader discussion of buoyancy, neutral buoyancy, and natural and synthetic mechanisms to control buoyancy might deepen students appreciation for the concepts covered in this unit. Buoyant force lifts an object in a fluid and essentially makes it float. Buoyant force is described in the context of the works of the Greek philosopher and scientist Archimedes. Archimedes discovered the following: "If a solid lighter than a fluid be forcibly immersed in it, the solid will be driven upwards by a force equal to the difference between its weight and the weight of the fluid displaced."
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Students can easily calculate buoyant force, since buoyant force is equal to the weight of the fluid displaced by an object. Simply put, Weight on earth equals Mass multiplied by earth's gravity. Calculating the mass of the fluid displaced by an object is simple since the object immersed in fluid displaces its own volume in fluid. Using the fluid's density and the volume of the fluid displaced, finding the Weight of the fluid displaced (which is equal to the buoyant force) is the solution to a simple linear equation. Whether or not the object will float, sink or remain in place is decided with a simple comparison between the Weight of the object and the Buoyant Force. Although the relationship between density, mass and volume is readily seen and sometimes more accessible through experiments involving matter in a liquid state, the same principles can be applied to gases, such as air, since both liquids and gases are classified as fluids.

Students might find the example of the hot air balloon both interesting and exciting when exploring the concepts related to buoyant force. The process by which a hot air balloon stays afloat relies on thermal expansion. The introduction of heat into the balloon excites the particles inside the balloon, increasing the space between them and creating

air pressure. Air is forced out of the bottom of the balloon as a result, causing the density of air inside the balloon to decrease, and the balloon flies. The discussion of the function of hot air balloons dovetails nicely with the reasons why hot air rises. Students may have noticed that wind tunnels can be created in urban environments with clusters of man-made structures. The buildings generate heat that warms the air. The hot air rises and does so consistently, causing a continuous flow of wind on city streets.