A certain lightbulb has a tungsten filament with a...

A certain lightbulb has a tungsten filament with a resistance of $19.0 \Omega$ when cold and of $140 \Omega$ when hot. Assuming that Equation $27.21$ can be used over the large temperature range involved here, find the temperature of the filament when hot. (Assume an initial temperature of $20.0^{\circ} \mathrm{C}$.)

A certain lightbulb has a tungsten filament with a resistance of $19.0 \Omega$ when cold and of $140 \Omega$ when hot. Assuming that Equation $27.21$ can be used over the large
temperature range involved here, find the temperature of the filament when hot. (Assume an initial temperature of $20.0^{\circ} \mathrm{C}$.)

Key Concepts

Temperature Dependence of Resistance

This concept describes how the resistance of a material changes as its temperature changes. In metals, resistance typically increases with temperature due to the increased scattering of conduction electrons by vibrating atoms. This relationship can often be modeled by a linear or slightly nonlinear equation over a certain temperature range, allowing one to estimate the temperature from measured resistance values.

Temperature Coefficient of Resistivity

The temperature coefficient of resistivity (often denoted as ?) quantifies how much the resistivity of a material changes per degree change in temperature relative to a reference temperature. It is a material-specific constant that is essential in calculating the new resistance at elevated temperatures, especially when dealing with applications like lightbulb filaments made of tungsten.

Electrical Resistivity

Resistivity is an intrinsic property of a material that measures how strongly it resists the flow of electric current. It is used to understand and predict the behavior of materials under varying thermal conditions. Changes in resistivity with temperature are key to designing and analyzing electrical components, such as filaments, where accurate predictions of performance under different thermal loads are critical.

Properties of Tungsten

Tungsten is widely used in high-temperature applications like lightbulb filaments due to its high melting point and favorable electrical properties. Its resistance changes significantly with temperature, and understanding these properties—especially the temperature coefficient of resistivity—is crucial in calculating the operational temperature of tungsten components based on resistance measurements.

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