Physics

Physics

Problem

A tungsten filament lamp operates at 2000 K. Its surface emissivity is 0.25 and the area of the filament is 1.0×10−4 m21.0\times10^{-4}\,\text{m}^2. Because of surface changes, the emissivity falls to 0.20. If the same 60 W of radiant power is to be maintained from the same area, to what temperature must the filament be heated? a) 1900 K1900\,\text{K} b) 2110 K2110\,\text{K} c) 2240 K2240\,\text{K} d) 2500 K2500\,\text{K}
Intuitive explanation

This problem is about the Stefan–Boltzmann law and how emissivity changes affect the temperature needed to maintain constant radiant power. Since power radiated depends on both emissivity and the fourth power of absolute temperature (P=ϵσAT4P = \epsilon \sigma A T^4), a decrease in emissivity must be compensated by an increase in temperature to keep power constant. Set up a ratio of the two power equations to eliminate the constants and solve for the new temperature.

Intuitive explanation

This problem is about the Stefan–Boltzmann law and how emissivity changes affect the temperature needed to maintain constant radiant power. Since power radiated depends on both emissivity and the fourth power of absolute temperature (P=ϵσAT4P = \epsilon \sigma A T^4), a decrease in emissivity must be compensated by an increase in temperature to keep power constant. Set up a ratio of the two power equations to eliminate the constants and solve for the new temperature.

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