Transmission Of Heat Question 229
Question: The energy spectrum of a black body exhibits a maximum around a wavelength $ {\lambda _{o}}. $ The temperature of the black body is now changed such that the energy is maximum around a wavelength $ \frac{3{\lambda _{o}}}{4} $ .The power radiated by the black body will now increase by a factor of
[KCET 2002]
Options:
A) 256/81
B) 64/27
C) 16/9
D) 4/3
Show Answer
Answer:
Correct Answer: A
Solution:
According to Wein’s law lmT = constant
Therefore $ {\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}}={{( \frac{T _{2}}{T _{1}} )}^{4}} $
Therefore $ \frac{P _{2}}{P _{1}}={{( \frac{4/3\ T _{1}}{T _{1}} )}^{4}}=\frac{256}{81} $
BETA
