GATE ME 2022 Set 2 — Question 35
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Heat Transfer → Radiation → Stefan-Boltzmann & Wien's Laws
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Question
Wien’s law is stated as follows: , where is and is the wavelength at which the emissive power of a black body is maximum for a given temperature . The spectral hemispherical emissivity () of a surface is shown in the figure below (). The temperature at which the total hemispherical emissivity will be highest is __________ K (round off to the nearest integer).
Correct answer
4825 to 4835
Solution
Total hemispherical emissivity is defined as the ratio of the total emissive power of a surface to that of a blackbody at the same temperature:To maximize the total hemispherical emissivity, the peak of the blackbody spectral emissive power distribution () should coincide with the peak of the spectral emissivity curve ().From the provided graph, the spectral emissivity reaches its maximum value at a wavelength of:According to Wien's displacement law:Given the constant , we can calculate the temperature :Rounding to the nearest integer, the temperature is .
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