JEE Advanced 2025 — Paper 1 — PHY-III solution

JEE Advanced2025Paper 1PHY-III

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $T_{P}$ and $T_{Q}$ , respectively, with $T_{Q} < T_{P}$ , 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 $\frac{W _{0}}{W _{S}}$ is ___

Your answer

Solution

Initially (Fig. 1): $W_{0} = σ (T_{P}^{4} - T_{Q}^{4})$ .

For Fig. 2, let the intermediate plate temperatures be $T_{1}$ and $T_{2}$ ( $T_{P} > T_{1} > T_{2} > T_{Q}$ ). In the steady state, the same flux $W_{S}$ passes between each adjacent pair:

$W_{S} = σ (T_{P}^{4} - T_{1}^{4}) = σ (T_{1}^{4} - T_{2}^{4}) = σ (T_{2}^{4} - T_{Q}^{4})$

Adding all three relations:

$3 W_{S} = σ (T_{P}^{4} - T_{Q}^{4}) = W_{0}$

$∴ \frac{W _{0}}{W _{S}} = 3.00$ .

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