JEE Main & Advanced Physics Transmission of Heat Distribution of Energy in the Spectrum of Black Body

A perfectly black body emits radiation of all possible wavelength.

Langley and later on Lummer and Pringsheim investigated the distribution of energy amongst the different wavelengths in the thermal spectrum of a black body radiation. The results obtained are shown in figure. From these curves it is clear that

(1) At a given temperature energy is not uniformly distributed among different wavelengths.

(2) At a given temperature intensity of heat radiation increases with wavelength, reaches a maximum at a particular wavelength and with further increase in wavelength it decreases.

(3) For all wavelengths an increase in temperature causes an increase in intensity.

(4) The area under the curve will represent the total intensity of radiation at a particular temperature i.e. Area \[=E=\int{{{E}_{\lambda }}d\lambda }\]

From Stefan's law \[E=\sigma {{T}^{4}}\Rightarrow \] Area under \[{{E}_{\lambda }}-\lambda \] curve (A) \[\propto {{T}^{4}}\]

(5) The energy \[({{E}_{\max }})\] emitted corresponding to the wavelength of maximum emission \[({{\lambda }_{m}})\] increases with fifth power of the absolute temperature of the black body i.e.,  \[{{E}_{\max }}\propto {{T}^{5}}\]