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 \[{{\lambda }_{1}}=8000\overset{{}^\circ }{\mathop{A}}\,\] and \[{{\lambda }_{2}}=4000\overset{{}^\circ }{\mathop{A}}\,.\] |
| \[\therefore \] From Wien's displacement law \[\lambda \,T=\text{constant}\] |
| \[\Rightarrow \] \[{{\lambda }_{1}}{{T}_{1}}={{\lambda }_{2}}{{T}_{2}}\] |
| or \[8000\times {{T}_{1}}=4000\,{{T}_{2}}\] |
| or \[\frac{{{T}_{1}}}{{{T}_{2}}}\,=\frac{1}{2}\] |
| \[\text{Emissive}\,\,\text{power}=e\,\sigma \,A{{T}^{4}}\] |
| \[\therefore \] 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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