Question

Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength ${\lambda }_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{{\lambda }_1}{2}$. The power radiated at $T_2$ is:

• A. $2P$
• B. $4P$
• C. $8P$
• D. $16P$

Answer 1

The correct option is D $16P$

We know, by Wein's displacement law,

$T{\lambda }_{max}=b$

Thus, $T_1{\lambda }_1=T_2{\lambda }_2=T_2\frac{{\lambda }_1}{2}$

$T_2=2T_1$

Also, from Stephan-Boltzmann law, radiative power:

$P=\sigma A{T}^4$

So, $\frac{P_2}{P_1}=\frac{{T_2}^4}{{T_1}^4}=16$

Hence, $P_2=16P$