A) 9 : 16
B) 27 : 64
C) 81 : 256
D) 3 : 4
Correct Answer: C
Solution :
From Stefahs 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. That is \[E=\sigma {{T}^{4}}\] where ct is Stefans constant. Given, initial temperature \[{{T}_{1}}=273+27=300K\] final temperature \[{{T}_{2}}=127+273=400K\] Hence, we have \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}=\frac{{{(300)}^{4}}}{{{(400)}^{4}}}=\frac{81}{256}\] Therefore, \[{{E}_{1}}:{{E}_{2}}=81:256\]
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