Why does integrating Planck's function give less than peak spectral radiance?

[tovisonnenberg]

Hi! I have a question about integrating Planck's function of blackbody radiation. Why is it that the area under the blackbody curve will be less than the spectral radiance of individual wavelengths? For example, integrating the Sun's curve over all wavelengths yields a smaller value than the spectral radiance of just its peak wavelength.

 

[hutchphd]

Radiance and spectral radiance have different units. The SI unit of radiance is the watt per steradian per square metre (W·sr−1·m−2), while that of spectral radiance in frequency is the watt per steradian per square metre per hertz (W·sr−1·m−2·Hz−1)

Often the spectral radiance curve for the sun is normalized to have a max value of 1 at the peak (and is called the luminosity function I think). So probably it a normalization issue...check the units.