Project ForgeWien's law is stated as follows: λmT=C, where C is 2898 μm·K and λm is the wavelength at which the emissive power of a black body is maximum for a given temperature T. The spectral hemispherical emissivity (ελ) of a surface peaks at λ=6000 Å (1Å=10⁻¹⁰m). The temperature at which the total hemispherical emissivity will be highest is _________ K (round off to the nearest integer).
Explanation
The total hemispherical emissivity (a weighted average of ελ over the blackbody spectral distribution) is highest when the blackbody's peak spectral emissive power (per Wien's law) coincides with the wavelength where the surface's own emissivity ελ peaks, maximizing the overlap. λm=6000Å=0.6μm. T=C/λm=2898/0.6=4830 K.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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