A) 5000 K
B) \[{{5000}^{o}}C\]
C) 500 K
D) \[{{500}^{o}}C\]
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 absolute temperature (T) of the body. Therefore \[E=\sigma \,{{T}^{4}}\]where a is Stefans constant. \[\Rightarrow \] \[\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\] \[\Rightarrow \] \[{{T}_{2}}={{\left( \frac{{{E}_{2}}}{{{E}_{1}}} \right)}^{1/4}}{{T}_{1}}\] Given, \[{{T}_{1}}={{227}^{o}}C=273+227=500\,K\] \[{{E}_{1}}=1\times {{10}^{5}}J/s{{m}^{2}},{{E}_{2}}=1\times {{10}^{9}}J/s{{m}^{2}}\] \[\therefore \] \[{{T}_{2}}=(500)\,{{\left( \frac{1\times {{10}^{9}}}{1\times {{10}^{5}}} \right)}^{1/4}}=500\,K\].
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