A) \[\frac{R}{4}\]
B) \[\frac{R}{16}\]
C) \[\frac{R}{2}\]
D) None of the above
Correct Answer: B
Solution :
From Stefans law, the total radiant energy emitted per second per unit surface area of a black body is proportional t6 the fourth power of the absolute temperature (T) of the body. \[\therefore \] \[E=\sigma {{T}^{4}}\] where,\[\sigma \]is Stefans constant. Given, \[{{E}_{1}}=R,{{T}_{1}}=273{}^\circ C\] \[=273+273=546\text{ }K\] \[{{T}_{2}}=0{}^\circ C=273K\] \[\therefore \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{T_{2}^{4}}{T_{1}^{4}}{{E}_{1}}\] \[\Rightarrow \] \[{{E}_{2}}=\frac{{{(273)}^{4}}}{{{(546)}^{4}}}R\] \[\therefore \] \[{{E}_{2}}=\frac{R}{16}\]
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