JEE Main & Advanced Physics Transmission of Heat Stefan's Law

According to it the radiant energy emitted by a perfectly black body per unit area per sec (i.e. emissive power of black body) is directly proportional to the fourth power of its absolute temperature, i.e. \[E\propto {{T}^{4}}\] \[\Rightarrow \]\[E=\sigma {{T}^{4}}\]

where \[\sigma \]  is a constant called Stefan's constant having dimension \[[M{{T}^{-3}}{{\theta }^{-4}}]\] and value \[5.67\times {{10}^{-8}}W/{{m}^{2}}{{K}^{4}}\]

(i) For ordinary body : \[e=\varepsilon E=\varepsilon \sigma {{T}^{4}}\]

(ii) Radiant energy : If Q is the total energy radiated by the ordinary body then \[e=\frac{Q}{A\times t}=\varepsilon \sigma {{T}^{4}}\] \[\Rightarrow \]\[Q=A\,\varepsilon \sigma {{T}^{4}}t\]

(iii) Radiant power (P) : It is defined as energy radiated per unit area i.e. \[P=\frac{Q}{t}=A\varepsilon \sigma {{T}^{4}}\].

(iv) If an ordinary body at temperature T is surrounded by a body at temperature T0, then Stefan's law may be put as

\[e=\varepsilon \,\sigma \,({{T}^{4}}-T_{0}^{4})\]