A tungsten filament in an electric lamp may be treated as a grey body of emissivity 0.35

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

Problem

A tungsten filament in an electric lamp may be treated as a grey body of emissivity 0.35. The filament has a total surface area of 1.2×10−4 m21.2 \times 10^{-4}\,\text{m}^2 and is surrounded by glass at 300 K. (i) Derive an expression for the net power PnetP_{\text{net}} radiated by the filament in terms of its emissivity ϵ\epsilon, surface area AA, absolute temperature TT, and the ambient temperature T0T_0. (ii) Using the expression obtained in part (i), compute the net power radiated when the filament temperature is 2400 K. Take σ=5.67×10−8 W m−2 K−4\sigma = 5.67 \times 10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4}. (iii) The electrical resistance of the filament at 2400 K is 10 Ω10\,\Omega. Assuming that the electrical power input just balances the net radiated power, calculate the current that must flow through the filament to maintain it at 2400 K.

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