Question

The power radiated by a black body is $P$ and it radiates maximum energy around the wavelength ${\lambda }_0$. If the temperature of the black body is now changed so that it radiates maximum energy around wavelength $\frac{3}{4}{\lambda }_0$, the power radiated by it will increase by a factor of

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

Answer 1

The correct option is D $\frac{256}{81}$

Using Stefan-Boltzmann's law,
Power radiated by black body is
$P=\frac{dQ}{dt}=A\sigma T^4$
From Weins displacemnt law
$\lambda T=b\text{(constant)}$
$P=A\sigma {\left(\frac{b}{\lambda }\right)}^4$
Ratio of power radiated is
$\frac{P_2}{P_1}={\left(\frac{{\lambda }_1}{{\lambda }_2}\right)}^4={\left(\frac{{\lambda }_0}{\frac{3{\lambda }_0}{4}}\right)}^4=\frac{256}{81}$