Question

Thomas Alva Edison (T. Olsen’s childhood hero) tried many
things to be the filament of a reliable electric light bulb. After
he was able to confidently say of over one thousand trial
materials that they did not work, he succeeded with carbonized
thread.
Perhaps, on one particular day he had been able to measure the
brightest color as having a wavelength of 1449nm and the light
bulb emitted a total power output of 32.9W. The thread was
cylindrical in shape, with a diameter of 2.00mm. The length
of the radiating region of the thread was 0.750cm.
What is the emissivity of carbonized thread?

Answer 1

Given,

Wavelength of the brightest colour, i.e.,

Total power output,

The carbonized thread is a cylinder of length, and diameter

Radius of the thread

Area of the radiating region,

The wavelength of the brightest colour of a black body is related to its temperature by Wein's displacement law as:

From Stefan's Boltzmann law,

where

= emissivity of the carbonized thread

Thus, the emissivity of the carbonized thread = 0.77.

Regards