A) 1 : 2
B) 1 : 4
C) \[\frac{{{(473)}^{4}}-{{(300)}^{4}}}{{{(673)}^{3}}-{{(300)}^{4}}}\]
D) \[\frac{{{(200)}^{4}}-{{(27)}^{4}}}{{{(400)}^{3}}-{{(27)}^{4}}}\]
Correct Answer: C
Solution :
From Stefans-Boltzmanns law the net rate of loss of heat by a black body is \[E=\sigma ({{T}^{4}}-T_{0}^{4})\] T and \[{{T}_{0}}\] being temperatures of body and surrounding, Given, \[{{T}_{1}}=200+273=473\,K,\] \[{{T}_{0}}=27+273=300\,K,\] \[{{T}_{2}}=400+273=673\,K,\] \[\therefore \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}-T_{0}^{4}}{T_{2}^{4}-T_{0}^{4}}\] Hence, \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{(473)}^{4}}{{(300)}^{4}}}{{{(673)}^{4}}-{{(300)}^{4}}}\]
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