A) 419 W
B) 405 W
C) 210 W
D) 80 W
Correct Answer: B
Solution :
Key Idea: As temperature of a surface rises, more and more radiant energy is emitted by it which is given by Stefan's law. According to Stefan's 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 of the body. i.e., \[E=\sigma {{T}^{4}}\] where\[\sigma \] is Stefan's constant and T is absolute temperature Given, \[{{E}_{1}}=5W,\,{{T}_{1}}=400\,K\] \[{{E}_{2}}=?,\,{{T}_{2}}=1200\,K\] Putting these values in above expression, we have \[\frac{5}{{{E}_{2}}}={{\left( \frac{400}{1200} \right)}^{4}}={{\left( \frac{1}{3} \right)}^{3}}=\frac{1}{81}\] \[\Rightarrow \] \[{{E}_{2}}=5\times 81=405\,W\]
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