• Underlying context

    Initial setting

    Think about a light bulb.  What image comes to mind?  Does it look like the photo to the right? People have used incandescent light bulbs like this one to light their homes, schools, and other buildings.  Recently, compact fluorescent lights (CFLs) became available. CFL manufacturers and others who are familiar with this new technology claim that replacing incandescent bulbs with CFLs gives better lighting and saves money in the long run.  Mathematics helps us to understand and to support or refute this claim.[1]

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    Detailed context

    The brief introduction above likely is enough for students to know as they begin working on the tasks in this module.  Addition information about the CFL context may be useful.  Among the topics addressed here are energy use, shape of CFLs.

    Energy use and CFLs. The major technology advantage of CFL is the reduced amount of energy consumed to get the same amount of the light (illumination) brightness (in the unit of Lumens). The electric energy is first emitted from the two electrodes at the end of the tube in the form of flow of electrons. Then the energy is transferred into ultraviolet light (invisible to human eye) when the electrons bombard the mercury atoms inside the CFL tubes. Finally the energy is conveyed in the form of illuminating light when the pre-deposited phosphors (on the inner surface of the CFL tube) give off light under the exposure of the ultraviolet light. All these processes are very efficient and the undesired heat generation and energy loss is much less compared with incandescent light.

    Shape of CFL. Depending on the specific design priorities among energy efficiency, size, visual appeal, and brightness requirement, the CFLs are designed either with extended tubular shape, U shape or twisted shape.  CFLs with extended tubular shape will yield more lumens and are brighter. For extended tube shape, it could be either U-shape, extended tubular or circular shape. All of them have extended total tube length. However, an extended tubular CFL generally has larger tube diameter thus generally better efficiency. People may also choose twisted shape for its visual appearance and it is generally even more compact than the other shape with the same brightness. However, the twisted shape generally suffers diffuse problem and may only good for close lighting.

    Advantages and disadvantages.  There are several advantages of CFLs over incandescent bulbs, yet CFLs are not a perfect solution to the lighting problem.

    Advantages

    Disadvantages

    ·        The biggest benefit of CFL is the efficient energy transfer (from electricity to light) and energy saving feature.

    ·        CFLs last 8 to 10 times longer than the incandescent light bulb.

    ·        A CFL generally can be made to produce any color of light needed.

    ·        Older CFLs need extended warm-up time (1 to 2 minutes) to reach the optimal working condition and the designed brightness.

    ·        Some CFL may produce annoying audible buzz.

    ·        The working temperature of CFL is rather limited (about 50F to 120F).

    ·        CFLs have shorter lifetimes when they are switched on and off very often.

    ·        CFLs cannot be used on dimmer switches.

    ·        Incandescent bulbs project light farther and therefore may be better for some uses, such as high-hanging fixtures.

    ·        CFL bulbs have to be properly disposed due to the toxic mercury vapor used in the tube.

    A helpful source for students to quickly find the meaning of terms is the glossary of lighting terminology available at http://www.gelighting.com/na/institute/glossary.html.

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    Context Q&A

    There are two things that make the CFL context of this module both intriguing and challenging to use in the classroom.  Cost of the materials and production change and other details about this new technology continue to evolve and emerge. To reflect the changes in the context, this module will continue to evolve and this Context Q&A section will be the place to gather more information about the context as the module is used in mathematics teaching and learning.

    Q1:      Why do incandescent light bulbs lose so much energy?

    There are two major reasons for energy loss in the incandescent light bulb: (1) heat conduction to the wire and the environment; and (2) the undesired irradiation in the spectrum range outside the visible regime.



    [1] Refuting or supporting this claim is the essence of Projects 1, 2 and 3.