Question

The power radiated by a black body is $O$ and it radiates maximum energy around the wavelength ${\lambda }_0$. Now the temperature of the black body is changes so that oit radius maximum energy around wavelength ${\lambda }_0/2$. The power radiated by it will now increase by a factor of.

• A. $8$
• B. $2$
• C. $64$
• D. $16$

Answer 1

The correct option is B $2$

power $=\frac{E}{t}=eA\sigma T^4$

$\Rightarrow$ power $\propto T^4$

if $\lambda$ be wavelength for maximum energy in radiation

then $\lambda T$ = constant (constant)

$\Rightarrow {\lambda }_1{T}_1={\lambda }_2{T}_2$

$\Rightarrow T_2=\frac{{\lambda }_1{T}_1}{{\lambda }_2}=\frac{\lambda 0}{\lambda 0/2}{T}_1=2T_1$

$\frac{P_2}{P_1}=2^4=16\Leftarrow \frac{P_2}{P_1}=(\frac{T_2}{T_1}{)}^4\Leftarrow \frac{T_2}{T_1}=2$