Physics · Heat Transfer

JEE Advanced 2025 — Paper 1 — Question 8

Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $\mathrm{T}_{\mathrm{P}}$ and $\mathrm{T}_{\mathrm{Q}}$ , respectively, with $\mathrm{T}_{\mathrm{Q}}<\mathrm{T}_{\mathrm{P}}$ , as shown in Fig. 1. The radiated power transferred per unit area from P to Q is $W_{0}$ . Subsequently, two more plates, identical to P and Q , are introduced between P and Q , as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from $P$ to $Q$ (Fig. 2) in the steady state is $W_{S}$ , then the ratio $\frac{\mathrm{W}_{0}}{\mathrm{~W}_{\mathrm{s}}}$ is $\qquad$ Fig. 1 Fig. 2

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

Initially : $\mathrm{W}_{0}=\sigma\left(\mathrm{T}_{\mathrm{P}}^{4}-\mathrm{T}_{\mathrm{Q}}^{4}\right)$

Finally : Putting heat currents equal in steady state : $\sigma\left(T_{P}^{4}-T_{1}^{4}\right)=\sigma\left(T_{1}^{4}-T_{2}^{4}\right)$

$\sigma\left(\mathrm{T}_{1}^{4}-\mathrm{T}_{2}^{4}\right)=\sigma\left(\mathrm{T}_{2}^{4}-\mathrm{T}_{\mathrm{Q}}^{4}\right)$

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

\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 $\frac{W_{S}}{W_{0}}=3$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2025
Paper: Paper 1
Subject: Physics
Chapter: Heat Transfer
Topic: Convection and Radiation