A) \[160\text{ }kcal/{{m}^{2}}\min \]
B) \[40\text{ }kcal/{{m}^{2}}\min \]
C) \[320\text{ }kcal/{{m}^{2}}\min \]
D) \[80\text{ }kcal/{{m}^{2}}\min \]
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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