A) \[\frac{5}{128}\]
B) 10
C) \[\frac{5}{16}\]
D) none of these
Correct Answer: A
Solution :
| Let the body have temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] respectively at wavelength \[{{\lambda }_{1}}=8000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[{{\lambda }_{2}}=4000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] |
| \[\therefore \] From Wien?s displacement law \[\lambda \,\,\Tau =\] Constant |
| \[\Rightarrow {{\lambda }_{1}}{{T}_{1}}={{\lambda }_{2}}{{T}_{2}}\,\,or\,\,8000\times {{T}_{1}}=4000{{T}_{2}}\] \[or\,\,\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{1}{2}\] Emissive power \[=e\sigma A{{T}^{4}}\] |
| \[\therefore \]Ratio of emissive powers at these temperature is |
| \[\frac{{{e}_{1}}T_{1}^{4}}{{{e}_{2}}T_{2}^{4}}=\frac{0.5}{0.8}\times {{\left( \frac{1}{2} \right)}^{4}}=\frac{5}{128}\] |
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