A) 400 K
B) 4000 K
C) 80000 K
D) 40000 K
Correct Answer: C
Solution :
According to Stefans law, the total radiant energy emitted per second from unit surface area of a black body is proportional to the fourth power of its absolute temperature, that is \[E\propto {{T}^{4}}\] or \[\frac{{{E}_{2}}}{{{E}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\] ?. (i) Given, \[{{T}_{1}}=127+273=400\,K\], \[{{E}_{1}}=2.7\times {{10}^{-3}}J/s\] \[{{E}_{2}}=4.32\times {{10}^{6}}J/s\] Substituting the values in Eq. (i), we get \[\frac{4.32\times {{10}^{6}}}{2.7\times {{10}^{-3}}}={{\left( \frac{{{T}_{2}}}{400} \right)}^{4}}\] or \[{{T}_{2}}=400{{\left( \frac{4.32\times {{10}^{6}}}{2.7\times {{10}^{-3}}} \right)}^{1/4}}\] or \[{{T}_{2}}=400\,{{(16\times {{10}^{8}})}^{1/4}}\] or \[{{T}_{2}}=400\times 2\times {{10}^{2}}=80000\,\,K\]
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