I have a doubt in this question from iit jee 2000.
Here, the plot is of spectral intensity vs. Wavelength graph of 3 blackbodies.
And the answer is: T1>T2>T3 and the justification is given by Wien's displacement law. I do understand that solution.
But here's my question:
The area under the curve 2 greater than 3 which in turn is greater than 1. And the area under the spectral intensity vs. wavelength graph gives us the “Emissive power”(power radiated by the blackbody per unit area) and Emissive power is proportional to the fourth power of the temperature of the blackbody (According to Stefan's law).
So according to Stefan's law, the temperature T2>T3>T1. But that is not the right answer.
What exactly am I missing here?
Best Answer
The Stefan–Boltzmann law gives you the radiative power per area at a given temperature. The problem doesn't give you the radiative area of the three objects. If the object with T$_1$ is smaller, it can have a lower total intensity than a cooler object.
I am more bothered by the description of the objects as "black bodies", but the shape of the spectrum deviates significantly from a blackbody curve.