Wien's law is stated as \( \lambda_m T = C \), where
\( C = 2898\ \mu\text{mK} \) and \( \lambda_m \) is the wavelength at which the emissive power of a black body is maximum for a given temperature T.
The spectral hemispherical emissivity curve shows a maximum at \( \lambda_m \approx 6000\ \text{\AA} \).
The temperature at which the total hemispherical emissivity is highest is ________________ K (nearest integer).
Show Hint
Always convert wavelength units correctly before applying Wien's law—micrometers are required when using the constant \(2898\ \mu\text{m·K}\).
From the figure, the peak hemispherical emissivity occurs at: \[ \lambda_m = 6000\ \text{\AA} \] Convert the wavelength into micrometers: Since \(1\ \text{\AA} = 10^{-10}\ \text{m}\), \[ 6000\ \text{\AA} = 6000 \times 10^{-10}\ \text{m} = 6 \times 10^{-7}\ \text{m} = 0.6\ \mu\text{m} \] Using Wien's law: \[ \lambda_m T = 2898\ \mu\text{mK} \] \[ T = \frac{2898}{0.6} = 4830\ \text{K} \] Thus, rounding to the nearest integer, \[ T \approx 4830\ \text{K} \] So, the temperature at which total hemispherical emissivity is highest is \(4830\) K.
