Transmission Of Heat Question 336
Question: The energy spectrum of a black body exhibits a maximum around a wavelength $ {\lambda _{0}} $ . The temperature of the black body is now changed such that the energy is maximum around a wavelength $ 3{\lambda _{0}}/4 $ . The power radiated by the black body will now increase by a factor of
Options:
A) 256/81
B) 64/27
C) 16/9
D) 4/3
Show Answer
Answer:
Correct Answer: A
Solution:
[a] According to Wien’s law, wavelength corresponding to maximum energy decreases. When the temperature of black body increases, i.e., $ {\lambda _{m}}T $ constant,
$ \Rightarrow $ $ \frac{T _{2}}{T _{1}}=\frac{{\lambda _{1}}}{{\lambda _{2}}}=\frac{{\lambda _{0}}}{3{\lambda _{0}}/4}=\frac{4}{3} $ . Now according to Stefan’s law, $ \frac{E _{2}}{E _{1}},={{( \frac{T _{2}}{T _{1}} )}^{4}}={{( \frac{4}{3} )}^{4}}=\frac{256}{81} $
BETA
