Two identical plates P and Q , radiating as perfect black bodies,...

Initially : $\mathrm{W}_0=\sigma$\left(\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_{\mathrm{Q}}^4\right)$<img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/gukJjWT8BR1VAuvNQmQ44Pfz8ATGhjTwjTkWpx8s9GI.original.fullsize.png"><br>Finally :<br>Putting heat currents equal in steady state : <img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/ZhcSG5RXdEWK44ZEGtOtHHEGidzL4RmTN4wgNVgd0vw.original.fullsize.png"><br>$$\begin{aligned} & \sigma\left(\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_1^4\right)=\sigma\left(\mathrm{T}_1^4-\mathrm{T}_2^4\right) \\ & \sigma\left(\mathrm{T}_1^4-\mathrm{T}_2^4\right)=\sigma\left(\mathrm{T}_2^4-\mathrm{T}_{\mathrm{Q}}^4\right)\end{aligned}$$Adding :$\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_1^4=\mathrm{T}_2^4-\mathrm{T}_{\mathrm{Q}}^4\Rightarrow \mathrm{T}_1^4+\mathrm{T}_2^4=\mathrm{T}_{\mathrm{P}}^4+\mathrm{T}_{\mathrm{Q}}^4$and$\quad \Rightarrow \mathrm{T}_1^4-\mathrm{T}_2^4=\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_1^4$Adding :$\mathrm{T}_1^4=\frac{2 \mathrm{~T}_{\mathrm{P}}^4+\mathrm{T}_{\mathrm{Q}}^4}{3}$So$\mathrm{W}_{\mathrm{S}}=\sigma\left(\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_1^4\right)$=\sigma$\left(\mathrm{T}_{\mathrm{P}}^4-\left(\frac{2 \mathrm{~T}_{\mathrm{P}}^4+\mathrm{T}_{\mathrm{Q}}^4}{3}\right)\right)=\sigma\left(\frac{\mathrm{T}_{\mathrm{P}}^4-\mathrm{T}_{\mathrm{Q}}^4}{3}\right)$hence$\frac{\mathrm{W}_{\mathrm{S}}}{\mathrm{W}_0}=3