A) \[{{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}\]
B) \[{{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]
C) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}\]
D) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\]
Correct Answer: A
Solution :
For black body, \[P=A\varepsilon \sigma {{T}^{4}}\]. For same power \[A\propto \frac{1}{{{T}^{4}}}\] Þ \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]Þ \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}\]You need to login to perform this action.
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