An incandescent light-bulb filament behaves approximately as a cylindrical blackbody…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

An incandescent light-bulb filament behaves approximately as a cylindrical blackbody of constant surface area. When connected to a power supply, the filament quickly reaches an operating temperature of

T_{\text{hot}}=3000\,\text{K}

and radiates

P_{\text{hot}}=60\,\text{W}

of thermal power. After the bulb is switched off, the filament cools to room temperature

T_{\text{cool}}=300\,\text{K}

while its surface area remains unchanged. (a) Determine the factor by which the filament’s radiated power changes as it cools from

T_{\text{hot}}

T_{\text{cool}}

. (b) Estimate the radiated power

P_{\text{cool}}

of the filament at

300\,\text{K}

. (c) Discuss why, even though the filament still radiates energy at room temperature, it is no longer perceptibly bright to the human eye.

Related theory

Heat Transfer
Radiation laws
The greenhouse effect
Black body radiation
Waves
Blackbody radiation
Thermal Properties of Matter

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