Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures TP and TQ, respectively, with TQ<TP, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is W0. 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 WS, then the ratio W0WS is [figure]
Answer
3
Solution
Between two black plates: W= (T14-T24). Fig. 1: W0= (TP4-TQ4).
Fig. 2 (steady state): the same WS crosses each of the three gaps: WS= (TP4-T14)= (T14-T24)= (T24-TQ4)
Adding: 3WS= (TP4-TQ4)=W0
W0WS=3
Answer: 3