A) \[{{(727)}^{2}}\]
B) \[{{(1000)}^{4}}\]
C) \[{{(1000)}^{2}}\]
D) \[{{(727)}^{4}}\]
Correct Answer: B
Solution :
Key Idea: Amount of heat energy radiated per second by unit area of a black body is directly proportional to fourth power of absolute temperature. According to Stefan's law, \[E\,\propto \,\,{{T}^{4}}\] \[orE=\sigma {{T}^{4}}\] where \[\sigma \] is constant of proportionality and called Stefan's constant. Its value is \[5.67\times {{10}^{-8}}\,W{{m}^{-2}}\,{{K}^{-4}}\] Hence, \[E\,\propto \,\,{{(727+273)}^{4}}\] \[\Rightarrow E\,\propto \,{{(1000)}^{4}}\] Note: If the body at temperature T is surrounded by a body at temperature \[{{T}_{0}}\], then Stefan?s law is \[E=\sigma ({{T}^{4}}-T_{0}^{4})\] This statement is called Stefan-Boltzmann law:
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