A blackbody radiator has a temperature of 3000K, and a surface area of 10 m^2. W

Question

A blackbody radiator has a temperature of 3000K, and a surface area of 10 m^2. What is the power output in Watts? In the wavelength representation, what is the wavelength (nanometers) where this spectrum has its peak? In the frequency representation, find the frequency of the peak of the blackbody spectrum of this object Convert that frequency to wavelength and compare to your first answer. Are they the same? Use the website referenced in the text to find the median emission wavelength. Using the data given for the sun, show that the blackbody temperature of the surface of the sun is about 5700K.

Explanation / Answer

T = 3000 K ; A = 10 m^2

Power output according to Stefan Boltzmann law is given by:

P = e sigma T^4

where, e is the emissivity of the object ; sigma is the Stefan Boltzmann constant and T is the surface temp/

since e is not given, assuming, e = 1

P = 1 x 5.67 x 10^-8 W/m^2 K^4 x 3000^4 = 0.459 x 10^8 W

Hence, P = 4.59 x 10^7 W

Wavelength can be calculated using Wien's displacement law

lambda(peak) T = 2.898 x 10^-3 mK

lambda(peak) = 2.898 x 10^-3/T = 2.898 x 10^-3/3000 = 966 x 10^-9 m = 966 nm

Hence, wavelength = 966 nm

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