Question

Total radiation power emitted by a black body is $P$ and it radiates maximum spectral intensity around wavelength $\lambda$. If the temperature of black body is changed so that now it emits maximum spectral intensity around wavelength $\frac{3}{4}\lambda$. Find the new power radiated by the body.

• A. $\frac{196}{81}P$
• B. $\frac{256}{81}P$
• C. $\frac{16}{81}P$
• D. $\frac{729}{81}P$

Answer 1

Answer: (B)

$\frac{256}{81}P$

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

$\Rightarrow \propto T^4$

For maximum spectral intensity relation

$\lambda T=constant<WeinsLaw$

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

given that

${\lambda }_1=\lambda$

${\lambda }_2=\frac{3\lambda }{4}$

$\frac{T_2}{T_1}=\frac{{\lambda }_1}{{\lambda }_1}=\frac{4}{3}$

Power $\frac{P_1}{P_2}={\frac{T_1}{T_2}}^4\Rightarrow P_2=P_1(\frac{T_2}{T_1}{)}^4=P(\frac{4}{3}{)}^4$

$P_2=P\times \frac{256}{81}$