A) \[\frac{E}{16}\]
B) \[2E\]
C) \[\frac{E}{4}\]
D) \[\frac{E}{8}\]
Correct Answer: A
Solution :
From Stefans law, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature (T) of the body. \[E=\sigma {{T}^{4}}\] where \[\sigma \] is Stefans constant. Given, \[{{T}_{1}}=T\] kelvin, \[{{E}_{1}}=E\] watt/\[{{m}^{2}}\], \[{{T}_{2}}=\frac{T}{2}\]kelvin \[\therefore \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{T_{2}^{4}}{T_{1}^{4}}{{E}_{1}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{{{(T/2)}^{4}}\times E}{{{T}^{4}}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{E}{16}\]
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