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 $\frac{{3\lambda }_0}{4}$. The power radiated by the black body will now increase by a factor of:

• A. $\frac{256}{81}$
• B. $\frac{64}{27}$
• C. $\frac{16}{9}$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$\frac{256}{81}$

From Wien's displacement law, wavelength of maximum energy is inversely proportional to absolute temperature.
Let initial temperature be $T$
Thus final temperature=$\frac{4}{3}$T
From Stefan's law, power radiated is directly proportional to fourth power of absolute temperature.
Hence, final power is $(\frac{4}{3}{)}^4=\frac{256}{81}$ times the initial power.