The temperature of the filament of a 100 watt electric lamp is 2727 °

1.	The temperature of the filament of a 100 watt electric lamp is 2727 °C. Calculate its emissivity if the length of the filament is 8 cm and its radius is 0.5 mm.
Answer» Data : T = 2727 + 273 = 3000 K, \(\frac{dQ}{dt}\) = 100 W, I = 8 cm = 8 x 10^-2 m, r = 0.5 mm = 0.5 x 10^-3 m, σ = 5.67 x 10^-8 W/m². K⁴ \(\frac{dQ}{dt}\) = σAeT⁴= σ 2\(\pi\)rleT⁴ \(\therefore\) Emissivity, e = \(\frac{\frac{dQ}{dt}}{σ2\pi rlT^4}\) = \(\frac{100}{(5.67\times10^{-8})(2\times3.142\times0.5\times10^{-3}\times8\times10^{-2})(3000)^4}\) = 0.08662

The temperature of the filament of a 100 watt electric lamp is 2727 °C. Calculate its emissivity if the length of the filament is 8 cm and its radius is 0.5 mm.

Answer»

Data : T = 2727 + 273 = 3000 K, \(\frac{dQ}{dt}\) = 100 W,

I = 8 cm = 8 x 10^-2 m, r = 0.5 mm = 0.5 x 10^-3 m,

σ = 5.67 x 10^-8 W/m². K⁴

\(\frac{dQ}{dt}\) = σAeT⁴= σ 2\(\pi\)rleT⁴

\(\therefore\) Emissivity, e = \(\frac{\frac{dQ}{dt}}{σ2\pi rlT^4}\)

= \(\frac{100}{(5.67\times10^{-8})(2\times3.142\times0.5\times10^{-3}\times8\times10^{-2})(3000)^4}\)

= 0.08662