Question

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

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

Answer 1

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

Let $T_0=$ initial temperature of the black body

${\lambda }_0{T}_0=b$ (constant)

Power radiated $P_0=C{T}_0^4$

($C$ is a constant)

Let $T=$ new temperature of the black body

$\frac{3{\lambda }_0}{4}T=b={\lambda }_0{T}_0$

or

$T=\frac{4T_0}{3}$

Power radiated,

$T=\frac{P}{P_0}=\frac{C{T}^4}{C{T}_0^4}={\left(\frac{4}{3}\right)}^4=\left(\frac{256}{81}\right)P_0$