A) 256/81
B) 64/27
C) 16/9
D) 4/3
Correct Answer: A
Solution :
According to Wein's law lmT = constant Þ \[{{\lambda }_{{{m}_{1}}}}{{T}_{1}}={{\lambda }_{{{m}_{2}}}}{{T}_{2}}\Rightarrow {{T}_{2}}=\frac{{{\lambda }_{{{m}_{1}}}}}{{{\lambda }_{{{m}_{2}}}}}{{T}_{1}}=\frac{{{\lambda }_{0}}}{3{{\lambda }_{0}}/4}\times {{T}_{1}}=\frac{4}{3}{{T}_{1}}\] Now \[P\propto {{T}^{4}}\Rightarrow \frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]Þ \[\frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{4/3\ {{T}_{1}}}{{{T}_{1}}} \right)}^{4}}=\frac{256}{81}\]You need to login to perform this action.
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