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

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Correct answer: A. A

Initially : W _0= ( T _ P ^4- T _ Q ^4 ) Finally : Putting heat currents equal in steady state : aligned & ( T _ P ^4- T _1^4 )= ( T _1^4- T _2^4 ) \ & ( T _1^4- T _2^4 )= ( T _2^4- T _ Q ^4 ) aligned Adding : T _ P ^4- T _1^4= T _2^4- T _ Q ^4 T _1^4+ T _2^4= T _ P ^4+ T _ Q ^4 and T _1^4- T _2^4= T _ P ^4- T _1^4 Adding : T _1^4= 2 ~T _ P ^4+ T _ Q ^4 3 So W _ S = ( T _ P ^4- T _1^4 ) = ( T _ P ^4- ( 2 ~T _ P ^4+ T _ Q ^4 3 ) )= ( T _ P ^4- T _ Q ^4 3 ) hence W _ S W _0 =3

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