JEE Main & Advanced Physics Transmission of Heat Emissive Power, Absorptive Power and Emissivity

If temperature of a body is more than it's surrounding then body emits thermal radiation

(1) Monochromatic Emittance or Spectral emissive power \[\mathbf{(}{{\mathbf{e}}_{\mathbf{\lambda }}}\mathbf{)}\] : For a given surface it is defined as the radiant energy emitted per sec per unit area of the surface with in a unit wavelength around l i.e. lying between \[\left( \lambda -\frac{1}{2} \right)\] to \[\left( \lambda +\frac{1}{2} \right)\].

Spectral emissive power \[({{e}_{\lambda }})=\frac{\text{Energy}}{\text{Area}\times \text{time}\times \text{wavelength}}\] 

Unit :  \[\frac{Joule}{{{m}^{2}}\times \sec }\] and     Dimension : \[[M{{L}^{-1}}{{T}^{-3}}]\]

(2) Total emittance or total emissive power (e) : It is defined as the total amount of thermal energy emitted per unit time, per unit area of the body for all possible wavelengths.   

\[e=\int_{\,0}^{\,\infty }{\,\,{{e}_{\lambda }}d\lambda }\]

Unit : \[\frac{Joule}{{{m}^{2}}\times \sec }\] or \[\frac{Watt}{{{m}^{2}}}\]   and  Dimension : \[[M{{T}^{-3}}]\]

(3) Monochromatic absorptance or spectral absorptive power \[\mathbf{(}{{a}_{\mathbf{\lambda }}}\mathbf{)}\]: It is defined as the ratio of the amount of the energy absorbed in a certain time to the total heat energy incident upon it in the same time, both in the unit wavelength interval. It is dimensionless and unit less quantity. It is represented by \[{{a}_{\lambda }}\].

(4) Total absorptance or total absorpting power (a): It is defined as the total amount of thermal energy absorbed per unit time, per unit area of the body for all possible wavelengths.

\[a=\int_{\,0}^{\,\infty }{{{a}_{\lambda }}d\lambda }\]

(5) Emissivity \[\mathbf{(\varepsilon )}\] : Emissivity of a body at a given temperature is defined as the ratio of the total emissive power of the body (e) to the total emissive power of a perfect black body (E) at that temperature i.e. \[\varepsilon =\frac{e}{E}\]         (\[\varepsilon \to \]read as epsilon)

(i) For perfectly black body \[\varepsilon =1\]

(ii) For highly polished body \[\varepsilon =0\]

(iii) But for practical bodies emissivity \[(\varepsilon )\]lies between zero and one \[(0<\varepsilon