We have two concentric blackened highly conducting spherical shells of radius a and b as shown. The inner shell is maintained at the temperature of T. List-I gives the rate of heat given (in steady state) out by certain surfaces and List-II gives the numerical expressions for them. Match them.

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P = σ ⋅ A re a ⋅ T 4 = 4 π a 2 σ T 4 (P) → (2) ( 4 π a 2 σ T 4 − 4 π a 2 σ T s 4 ​ ) = 4 π b 2 σ T s 4 ​ a 2 T 4 = ( a 2 + b 2 ) T s 4 ​ ⟹ σ T s 4 ​ = a 2 + b 2 a 2 σ T 4 ​ Q = A re a b ​ ⋅ σ T s 4 ​ ⋅ F ba ​ = ( 4 π b 2 ) ( a 2 + b 2 a 2 σ T 4 ​ ) ( b 2 a 2 ​ ) = a 2 + b 2 4 π a 4 σ T 4 ​ (Q) → (1) R = 4 π b 2 σ T s 4 ​ = 4 π b 2 ( a 2 + b 2 a 2 σ T 4 ​ ) = a 2 + b 2 4 π a 2 b 2 σ T 4 ​ (R) → (5) S = ( 4 π b 2 σ T s 4 ​ ) − Q = 4 π ( b 2 − a 2 ) σ T s 4 ​ = a 2 + b 2 4 π a 2 ( b 2 − a 2 ) σ T 4 ​ (S) → (3)

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