A) \[160\,kcal/{{m}^{2}}\,\min \]
B) \[40\,kcal/{{m}^{2}}\min \]
C) \[320\,\,kcal/{{m}^{2}}\,\min \]
D) \[80\,\,kcal/{{m}^{2}}\,\min \]
Correct Answer: C
Solution :
According to Stefan's law, the rate at which an object radiates energy is proportional to the fourth power of its absolute temperature i.e., \[E=\sigma {{T}^{4}}\,or\,E\,\propto \,{{T}^{4}}\] or \[\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\] Here, \[{{T}_{1}}=T,\,{{T}_{2}}=2T,\,{{E}_{1}}=20\,kcal/{{m}^{2}}\]min \[\therefore \frac{20}{{{E}_{2}}}={{\left( \frac{T}{2T} \right)}^{2}}\] or \[\frac{20}{{{E}_{2}}}=\frac{1}{16}\] \[\therefore {{E}_{2}}=20\times 16\] \[=320\,kcal/{{m}^{3}}\,\min \]
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