A) \[\frac{E}{4}\]
B) \[\frac{E}{2}\]
C) \[2E\]
D) \[\frac{E}{16}\]
Correct Answer: D
Solution :
From Stefan-Boltzmann's law the radiant energy E is proportional to fourth power of absolute temperature (T) of a black body. \[E=\sigma {{T}^{4}}\] (\[\sigma \] = Stefan's constant) Given, \[{{E}_{1}}=E,\,\,\,{{T}_{1}}=T,\,\,\,\,\,{{T}_{2}}=\frac{T}{2}\] \[\therefore \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{T_{2}^{4}}{T_{1}^{4}}.{{E}_{1}}\] \[\Rightarrow \]\[{{E}_{2}}=\frac{{{\left( \frac{T}{2} \right)}^{4}}}{{{T}^{4}}}.E=\frac{E}{16}\]
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