A) \[{{(727)}^{2}}\]
B) \[{{(1000)}^{4}}\]
C) \[{{(1000)}^{2}}\]
D) \[{{(727)}^{4}}\]
Correct Answer: C
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, |
| \[E\,\propto \,\,{{T}^{4}}\] |
| or \[E=\sigma {{T}^{4}}\] |
| 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 Stefans law is \[E=\sigma ({{T}^{4}}-T_{0}^{4})\] |
| This statement is called Stefan-Boltzmann law: |
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