Physics - Modern Physics Question with Solution | TestHub

From Stefan-Boltzmann's law, $\mathrm{P}=\frac{\mathrm{dQ}}{\mathrm{dt}}={\mathrm{A}\sigma \mathrm{T}}^4$ Also, from Wien's displacement law, $\begin{array}{rl}& {\lambda }_{\max }=\frac{\mathrm{b}}{\mathrm{T}}(\mathrm{b}\to \text{ Wien’s constant })\\ & \Rightarrow \mathrm{T}=\frac{\mathrm{b}}{\lambda }\end{array}$ $\begin{array}{rl}\therefore P& =A\cdot \sigma {\left(\frac{b}{\lambda }\right)}^4\\ \Rightarrow P& \propto \frac{1}{(\lambda {)}^4}\end{array}$ $\therefore$ Ratio of power dissipated is $\frac{{\mathrm{P}}_2}{{\mathrm{P}}_1}={\left(\frac{{\lambda }_1}{{\lambda }_2}\right)}^4$ Given ${\lambda }_1=\lambda$ and ${\dot{\lambda }}_2=\frac{2\lambda }{3}$. $\therefore \frac{{\mathrm{P}}_2}{{\mathrm{P}}_1}=\frac{(\lambda {)}^4}{{\left(\frac{2\lambda }{3}\right)}^4}=\frac{81}{16}$