Approximately 95 % of the energy developed by the filament...

Approximately $95 \%$ of the energy developed by the filament in a spherical $1.0 \cdot 10^{2} \mathrm{~W}$ light bulb is dissipated through the glass bulb. If the thickness of the bulb is $0.50 \mathrm{~mm}$ and its radius is $3.0 \mathrm{~cm},$ calculate the temperature difference between the inner and outer surfaces of the bulb.

Key Concepts

Energy Dissipation in Electrical Devices

This concept involves understanding how energy produced in electrical devices is converted into thermal energy and then dissipated. Recognizing the proportion of energy that escapes as heat (for instance, 95% in some bulbs) is crucial in setting up the problem and applying heat transfer equations to determine quantities like the temperature difference across a component.

Fourier's Law of Heat Conduction

This law states that the rate at which heat is transferred through a material is proportional to the negative gradient of temperature and the area through which the heat flows, while being inversely proportional to the thickness over which the temperature change occurs. It provides a foundational mathematical description that links the energy dissipation with the temperature difference across the material.

Thermal Conductivity

Thermal conductivity is an intrinsic property of a material that quantifies its ability to conduct heat. It directly influences the amount of heat that can be transferred through a substance and is essential in determining the temperature gradient required to sustain a given rate of energy dissipation.

Spherical Geometry in Heat Transfer

In problems involving spherical objects, such as a light bulb, the surface area available for heat transfer is calculated using the formula for the surface area of a sphere (4?r²). This geometric concept is critical when applying conduction principles, as the effective area for heat escape directly affects the computed temperature difference across the material.

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